@@ -1,4 +1,4 @@
-use ark_ec::{bls12::Bls12Parameters, ModelParameters};
+use ark_ec::{bls12::Bls12Parameters, CurveConfig};
 use ark_r1cs_std::{
     fields::fp::FpVar,
     groups::{bls12, curves::twisted_edwards::AffineVar as TEAffineVar},
@@ -14,7 +14,7 @@
 /// An element of G1 (in TE Affine form) in the BLS12-377 bilinear group.
 pub type G1TEAffineVar = TEAffineVar<
     <Parameters as Bls12Parameters>::G1Parameters,
-    FpVar<<<Parameters as Bls12Parameters>::G1Parameters as ModelParameters>::BaseField>,
+    FpVar<<<Parameters as Bls12Parameters>::G1Parameters as CurveConfig>::BaseField>,
 >;
 
 /// Represents the cached precomputation that can be performed on a G1 element

@@ -1,21 +1,19 @@
 use ark_ec::models::{
-    twisted_edwards_extended::{
-        GroupAffine as TEGroupAffine, GroupProjective as TEGroupProjective,
+    short_weierstrass::{Affine as SWAffine, SWCurveConfig},
+    twisted_edwards::{
+        Affine as TEAffine, MontCurveConfig, Projective as TEProjective, TECurveConfig,
     },
-    ModelParameters, MontgomeryModelParameters, SWModelParameters, TEModelParameters,
+    CurveConfig,
 };
-use ark_ff::{MontFp, Zero};
+use ark_ff::{Field, MontFp, Zero};
 use core::ops::Neg;
 
-use crate::{
-    fields::{FQ_ONE, FQ_ZERO},
-    Fq, Fr,
-};
+use crate::{Fq, Fr};
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -24,22 +22,18 @@ const COFACTOR: &'static [u64] = &[0x0, 0x170b5d4430000000];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// = 5285428838741532253824584287042945485047145357130994810877
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "5285428838741532253824584287042945485047145357130994810877"
-    );
+    const COFACTOR_INV: Fr = MontFp!("5285428838741532253824584287042945485047145357130994810877");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 0
-    const COEFF_A: Fq = FQ_ZERO;
+    const COEFF_A: Fq = Fq::ZERO;
 
     /// COEFF_B = 1
-    const COEFF_B: Fq = FQ_ONE;
+    const COEFF_B: Fq = Fq::ONE;
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1SWAffine = G1SWAffine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -47,8 +41,9 @@ Self::BaseField::zero()
     }
 }
 
-pub type G1TEAffine = TEGroupAffine<Parameters>;
-pub type G1TEProjective = TEGroupProjective<Parameters>;
+pub type G1SWAffine = SWAffine<Parameters>;
+pub type G1TEAffine = TEAffine<Parameters>;
+pub type G1TEProjective = TEProjective<Parameters>;
 
 /// Bls12_377::G1 also has a twisted Edwards form.
 /// It can be obtained via the following script, implementing
@@ -97,18 +92,17 @@ /// TE2a = Fp(-1)
 /// # b = -TE1d/TE1a
 /// TE2d = Fp(122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179)
 /// ```
-impl TEModelParameters for Parameters {
+impl TECurveConfig for Parameters {
     /// COEFF_A = -1
-    const COEFF_A: Fq = MontFp!(Fq, "-1");
+    const COEFF_A: Fq = MontFp!("-1");
 
     /// COEFF_D = 122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179 mod q
-    const COEFF_D: Fq = MontFp!(Fq, "122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179");
+    const COEFF_D: Fq = MontFp!("122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179");
 
     /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (TE_GENERATOR_X, TE_GENERATOR_Y);
+    const GENERATOR: G1TEAffine = G1TEAffine::new_unchecked(TE_GENERATOR_X, TE_GENERATOR_Y);
 
-    type MontgomeryModelParameters = Parameters;
+    type MontCurveConfig = Parameters;
 
     /// Multiplication by `a` is multiply by `-1`.
     #[inline(always)]
@@ -146,23 +140,23 @@ // MA=Fp(228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384)
 // # MB = s
 // MB=Fp(10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931)
 // ```
-impl MontgomeryModelParameters for Parameters {
+impl MontCurveConfig for Parameters {
     /// COEFF_A = 228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384
-    const COEFF_A: Fq = MontFp!(Fq, "228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384");
+    const COEFF_A: Fq = MontFp!("228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384");
 
     /// COEFF_B = 10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931
-    const COEFF_B: Fq = MontFp!(Fq, "10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931");
+    const COEFF_B: Fq = MontFp!("10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931");
 
-    type TEModelParameters = Parameters;
+    type TECurveConfig = Parameters;
 }
 
 /// G1_GENERATOR_X =
 /// 81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695");
+pub const G1_GENERATOR_X: Fq = MontFp!("81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695");
 
 /// G1_GENERATOR_Y =
 /// 241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030");
+pub const G1_GENERATOR_Y: Fq = MontFp!("241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030");
 
 // The generator for twisted Edward form is the same SW generator converted into
 // the normalized TE form (TE2).
@@ -210,8 +204,8 @@ // assert( TE2a * TE2x^2 + TE2y^2 == 1 + TE2d * TE2x^2 * TE2y^2 )
 // ```
 /// TE_GENERATOR_X =
 /// 71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393
-pub const TE_GENERATOR_X: Fq = MontFp!(Fq, "71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393");
+pub const TE_GENERATOR_X: Fq = MontFp!("71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393");
 
 /// TE_GENERATOR_Y =
 /// 6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235
-pub const TE_GENERATOR_Y: Fq = MontFp!(Fq, "6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235");
+pub const TE_GENERATOR_Y: Fq = MontFp!("6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235");

@@ -1,12 +1,16 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{MontFp, QuadExt, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};
 
-use crate::{fields::FQ_ZERO, g1, Fq, Fq2, Fr};
+use crate::{g1, Fq, Fq2, Fr};
 
+pub type G2Affine = Affine<Parameters>;
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq2;
     type ScalarField = Fr;
 
@@ -26,15 +30,13 @@ ];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// = 6764900296503390671038341982857278410319949526107311149686707033187604810669
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "6764900296503390671038341982857278410319949526107311149686707033187604810669"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("6764900296503390671038341982857278410319949526107311149686707033187604810669");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = [0, 0]
-    const COEFF_A: Fq2 = QuadExt!(g1::Parameters::COEFF_A, g1::Parameters::COEFF_A,);
+    const COEFF_A: Fq2 = Fq2::new(g1::Parameters::COEFF_A, g1::Parameters::COEFF_A);
 
     // As per https://eprint.iacr.org/2012/072.pdf,
     // this curve has b' = b/i, where b is the COEFF_B of G1, and x^6 -i is
@@ -42,14 +44,13 @@ // the irreducible poly used to extend from Fp2 to Fp12.
     // In our case, i = u (App A.3, T_6).
     /// COEFF_B = [0,
     /// 155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906]
-    const COEFF_B: Fq2 = QuadExt!(
-        FQ_ZERO,
-        MontFp!(Fq, "155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906"),
+    const COEFF_B: Fq2 = Fq2::new(
+        Fq::ZERO,
+        MontFp!("155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906"),
     );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -57,21 +58,21 @@ Self::BaseField::zero()
     }
 }
 
-pub const G2_GENERATOR_X: Fq2 = QuadExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-pub const G2_GENERATOR_Y: Fq2 = QuadExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 /// G2_GENERATOR_X_C0 =
 /// 233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294
-pub const G2_GENERATOR_X_C0: Fq = MontFp!(Fq, "233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294");
 
 /// G2_GENERATOR_X_C1 =
 /// 140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118
-pub const G2_GENERATOR_X_C1: Fq = MontFp!(Fq, "140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118");
 
 /// G2_GENERATOR_Y_C0 =
 /// 63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423
-pub const G2_GENERATOR_Y_C0: Fq = MontFp!(Fq, "63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423");
 
 /// G2_GENERATOR_Y_C1 =
 /// 149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491
-pub const G2_GENERATOR_Y_C1: Fq = MontFp!(Fq, "149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491");

@@ -1,22 +1,19 @@
 use ark_algebra_test_templates::{
     curves::{curve_tests, edwards_tests, sw_tests},
     generate_bilinearity_test, generate_g1_generator_raw_test, generate_g1_test, generate_g2_test,
-    groups::group_test,
     msm::test_var_base_msm,
 };
-use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine};
+use ark_ec::{models::short_weierstrass::SWCurveConfig, AffineCurve, PairingEngine};
 use ark_ff::{
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     One, Zero,
 };
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign};
 
-use crate::{
-    g1, g2, Bls12_377, Fq, Fq12, Fr, G1Affine, G1Projective, G1TEProjective, G2Affine, G2Projective,
-};
+use crate::{g1, g2, Bls12_377, Fq, Fq12, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
 
-generate_g1_test!(bls12_377; curve_tests; sw_tests; edwards_tests; te_group_tests;);
+generate_g1_test!(bls12_377; curve_tests; sw_tests; edwards_tests;);
 generate_g2_test!(bls12_377; curve_tests; sw_tests;);
 generate_bilinearity_test!(Bls12_377, Fq12);
 generate_g1_generator_raw_test!(bls12_377, 1);

@@ -1,10 +1,7 @@
-use ark_ff::fields::{Fp384, MontBackend, MontConfig, MontFp};
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
 
 #[derive(MontConfig)]
 #[modulus = "258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177"]
 #[generator = "15"]
 pub struct FqConfig;
 pub type Fq = Fp384<MontBackend<FqConfig, 6>>;
-
-pub const FQ_ONE: Fq = Fq::new(FqConfig::R);
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, CubicExt, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -10,65 +10,65 @@
 impl Fp12Config for Fq12Config {
     type Fp6Config = Fq6Config;
 
-    const NONRESIDUE: Fq6 = CubicExt!(FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);
 
     const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        QuadExt!(FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "92949345220277864758624960506473182677953048909283248980960104381795901929519566951595905490535835115111760994353"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("92949345220277864758624960506473182677953048909283248980960104381795901929519566951595905490535835115111760994353"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "216465761340224619389371505802605247630151569547285782856803747159100223055385581585702401816380679166954762214499"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("216465761340224619389371505802605247630151569547285782856803747159100223055385581585702401816380679166954762214499"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "123516416119946754630746545296132064952198520638002533875843642777304321125866014634106496325844844051843001220146"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("123516416119946754630746545296132064952198520638002533875843642777304321125866014634106496325844844051843001220146"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "-1"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "165715080792691229252027773188420350858440463845631411558924158284924566418821255823372982649037525009328560463824"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("165715080792691229252027773188420350858440463845631411558924158284924566418821255823372982649037525009328560463824"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "42198664672744474621281227892288285906241943207628877683080515507620245292955241189266486323192680957485559243678"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("42198664672744474621281227892288285906241943207628877683080515507620245292955241189266486323192680957485559243678"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "135148009893022339379906188398761468584194992116912126664040619889416147222474808140862391813728516072597320238031"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("135148009893022339379906188398761468584194992116912126664040619889416147222474808140862391813728516072597320238031"),
+            Fq::ZERO,
         ),
     ];
 }

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -10,14 +10,14 @@ impl Fp2Config for Fq2Config {
     type Fp = Fq;
 
     /// NONRESIDUE = -5
-    const NONRESIDUE: Fq = MontFp!(Fq, "-5");
+    const NONRESIDUE: Fq = MontFp!("-5");
 
     /// Coefficients for the Frobenius automorphism.
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // NONRESIDUE**(((q^0) - 1) / 2)
-        FQ_ONE,
+        Fq::ONE,
         // NONRESIDUE**(((q^1) - 1) / 2)
-        MontFp!(Fq, "-1"),
+        MontFp!("-1"),
     ];
 
     #[inline(always)]
@@ -28,6 +28,3 @@ fe.double_in_place();
         fe - original
     }
 }
-
-pub const FQ2_ZERO: Fq2 = QuadExt!(FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = QuadExt!(FQ_ONE, FQ_ZERO);

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -11,59 +11,59 @@ impl Fp6Config for Fq6Config {
     type Fp2Config = Fq2Config;
 
     /// NONRESIDUE = U
-    const NONRESIDUE: Fq2 = QuadExt!(FQ_ZERO, FQ_ONE);
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ZERO, Fq::ONE);
 
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        QuadExt!(FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        QuadExt!(MontFp!(Fq, "-1"), FQ_ZERO),
+        Fq2::new(MontFp!("-1"), Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
+            Fq::ZERO,
         ),
     ];
 
     const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
-        QuadExt!(FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO
         ),
         // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
-        QuadExt!(FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
     ];
 
@@ -72,6 +72,6 @@ fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
         // Karatsuba multiplication with constant other = u.
         let c0 = Fq2Config::mul_fp_by_nonresidue(&fe.c1);
         let c1 = fe.c0;
-        QuadExt!(c0, c1)
+        Fq2::new(c0, c1)
     }
 }

@@ -3,7 +3,7 @@ fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
     biginteger::{BigInt, BigInteger, BigInteger384},
-    fields::{FftField, Field, Fp6Config, PrimeField, SquareRootField},
+    fields::{FftField, Field, Fp6Config, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};

@@ -1,11 +1,11 @@
 use ark_ec::{
     bls12,
     bls12::Bls12Parameters,
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::GroupAffine,
+    models::CurveConfig,
+    short_weierstrass::{Affine, SWCurveConfig},
     AffineCurve, ProjectiveCurve,
 };
-use ark_ff::{biginteger::BigInteger256, MontFp, Zero};
+use ark_ff::{biginteger::BigInteger256, Field, MontFp, Zero};
 use ark_std::ops::Neg;
 
 use crate::*;
@@ -16,7 +16,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -25,22 +25,19 @@ const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "52435875175126190458656871551744051925719901746859129887267498875565241663483"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("52435875175126190458656871551744051925719901746859129887267498875565241663483");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 0
-    const COEFF_A: Fq = MontFp!(Fq, "0");
+    const COEFF_A: Fq = Fq::ZERO;
 
     /// COEFF_B = 4
-    const COEFF_B: Fq = MontFp!(Fq, "4");
+    const COEFF_B: Fq = MontFp!("4");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -71,16 +68,16 @@ }
 
 /// G1_GENERATOR_X =
 /// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");
+pub const G1_GENERATOR_X: Fq = MontFp!("3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");
 
 /// G1_GENERATOR_Y =
 /// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");
+pub const G1_GENERATOR_Y: Fq = MontFp!("1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");
 
 /// BETA is a non-trivial cubic root of unity in Fq.
-pub const BETA: Fq = MontFp!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");
+pub const BETA: Fq = MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");
 
-pub fn endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
+pub fn endomorphism(p: &Affine<Parameters>) -> Affine<Parameters> {
     // Endomorphism of the points on the curve.
     // endomorphism_p(x,y) = (BETA * x, y)
     // where BETA is a non-trivial cubic root of unity in Fq.

@@ -1,11 +1,11 @@
 use ark_ec::{
     bls12,
     bls12::Bls12Parameters,
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::GroupAffine,
+    models::CurveConfig,
+    short_weierstrass::{Affine, SWCurveConfig},
     AffineCurve,
 };
-use ark_ff::{BigInt, Field, MontFp, QuadExt, Zero};
+use ark_ff::{BigInt, Field, MontFp, Zero};
 
 use crate::*;
 
@@ -15,7 +15,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq2;
     type ScalarField = Fr;
 
@@ -36,22 +36,19 @@ ];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// 26652489039290660355457965112010883481355318854675681319708643586776743290055
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "26652489039290660355457965112010883481355318854675681319708643586776743290055"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("26652489039290660355457965112010883481355318854675681319708643586776743290055");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = [0, 0]
-    const COEFF_A: Fq2 = QuadExt!(g1::Parameters::COEFF_A, g1::Parameters::COEFF_A,);
+    const COEFF_A: Fq2 = Fq2::new(g1::Parameters::COEFF_A, g1::Parameters::COEFF_A);
 
     /// COEFF_B = [4, 4]
-    const COEFF_B: Fq2 = QuadExt!(g1::Parameters::COEFF_B, g1::Parameters::COEFF_B,);
+    const COEFF_B: Fq2 = Fq2::new(g1::Parameters::COEFF_B, g1::Parameters::COEFF_B);
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -74,48 +71,45 @@ x_times_point.eq(&p_times_point)
     }
 }
 
-pub const G2_GENERATOR_X: Fq2 = QuadExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-pub const G2_GENERATOR_Y: Fq2 = QuadExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 /// G2_GENERATOR_X_C0 =
 /// 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160
-pub const G2_GENERATOR_X_C0: Fq = MontFp!(Fq, "352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160");
 
 /// G2_GENERATOR_X_C1 =
 /// 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758
-pub const G2_GENERATOR_X_C1: Fq = MontFp!(Fq, "3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758");
 
 /// G2_GENERATOR_Y_C0 =
 /// 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905
-pub const G2_GENERATOR_Y_C0: Fq = MontFp!(Fq, "1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905");
 
 /// G2_GENERATOR_Y_C1 =
 /// 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582
-pub const G2_GENERATOR_Y_C1: Fq = MontFp!(Fq, "927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582");
 
 // psi(x,y) = (x**p * PSI_X, y**p * PSI_Y) is the Frobenius composed
 // with the quadratic twist and its inverse
 
 // PSI_X = 1/(u+1)^((p-1)/3)
-pub const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = QuadExt!(
-    FQ_ZERO,
+pub const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = Fq2::new(
+    Fq::ZERO,
     MontFp!(
-        Fq,
-        "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"
+                "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"
     )
 );
 
 // PSI_Y = 1/(u+1)^((p-1)/2)
-pub const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = QuadExt!(
+pub const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = Fq2::new(
     MontFp!(
-        Fq,
-        "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
+                "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
     MontFp!(
-        Fq,
-        "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257")
+                "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257")
 );
 
-pub fn p_power_endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
+pub fn p_power_endomorphism(p: &Affine<Parameters>) -> Affine<Parameters> {
     // The p-power endomorphism for G2 is defined as follows:
     // 1. Note that G2 is defined on curve E': y^2 = x^3 + 4(u+1).
     //    To map a point (x, y) in E' to (s, t) in E,

@@ -1,10 +1,12 @@
 use ark_algebra_test_templates::{
     curves::*, generate_bilinearity_test, generate_g1_generator_raw_test, generate_g1_test,
-    generate_g2_test, groups::*, msm::*,
+    generate_g2_test, msm::*,
 };
-use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
+use ark_ec::{
+    models::short_weierstrass::SWCurveConfig, AffineCurve, PairingEngine, ProjectiveCurve,
+};
 use ark_ff::{
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_std::{rand::Rng, test_rng};

@@ -1,10 +1,7 @@
-use ark_ff::fields::{Fp384, MontBackend, MontConfig, MontFp};
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
 
 #[derive(MontConfig)]
 #[modulus = "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787"]
 #[generator = "2"]
 pub struct FqConfig;
 pub type Fq = Fp384<MontBackend<FqConfig, 6>>;
-
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, CubicExt, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -10,68 +10,68 @@
 impl Fp12Config for Fq12Config {
     type Fp6Config = Fq6Config;
 
-    const NONRESIDUE: Fq6 = CubicExt!(FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);
 
     const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "1"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
-            MontFp!(Fq, "151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
+        Fq2::new(
+            MontFp!("3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
+            MontFp!("151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
-            MontFp!(Fq, "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
+        Fq2::new(
+            MontFp!("2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
+            MontFp!("1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
-            MontFp!(Fq, "877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
+        Fq2::new(
+            MontFp!("3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
+            MontFp!("877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
         ),
         // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "-1"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
-            MontFp!(Fq, "3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
+        Fq2::new(
+            MontFp!("151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
+            MontFp!("3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
         ),
         // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
-            MontFp!(Fq, "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
+        Fq2::new(
+            MontFp!("1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
+            MontFp!("2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
         ),
         // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        QuadExt!(
-            MontFp!(Fq, "877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
-            MontFp!(Fq, "3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
+        Fq2::new(
+            MontFp!("877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
+            MontFp!("3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
         ),
     ];
 }

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -10,14 +10,14 @@ impl Fp2Config for Fq2Config {
     type Fp = Fq;
 
     /// NONRESIDUE = -1
-    const NONRESIDUE: Fq = MontFp!(Fq, "-1");
+    const NONRESIDUE: Fq = MontFp!("-1");
 
     /// Coefficients for the Frobenius automorphism.
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // Fq(-1)**(((q^0) - 1) / 2)
-        MontFp!(Fq, "1"),
+        Fq::ONE,
         // Fq(-1)**(((q^1) - 1) / 2)
-        MontFp!(Fq, "-1"),
+        MontFp!("-1"),
     ];
 
     #[inline(always)]
@@ -25,6 +25,3 @@ fn mul_fp_by_nonresidue(fp: &Self::Fp) -> Self::Fp {
         -(*fp)
     }
 }
-
-pub const FQ2_ZERO: Fq2 = QuadExt!(FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = QuadExt!(FQ_ONE, FQ_ZERO);

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -11,72 +11,72 @@ impl Fp6Config for Fq6Config {
     type Fp2Config = Fq2Config;
 
     /// NONRESIDUE = (U + 1)
-    const NONRESIDUE: Fq2 = QuadExt!(FQ_ONE, FQ_ONE);
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ONE, Fq::ONE);
 
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "1"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "0"),
-            MontFp!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+        Fq2::new(
+            Fq::ZERO,
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "0"),
-            MontFp!(Fq, "1"),
+        Fq2::new(
+            Fq::ZERO,
+            Fq::ONE,
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        QuadExt!(
-            MontFp!(Fq, "0"),
-            MontFp!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+        Fq2::new(
+            Fq::ZERO,
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
         ),
 ];
 
     #[rustfmt::skip]
     const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
         // Fq2(u + 1)**(((2q^0) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "1"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^1) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^2) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^3) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "-1"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^4) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^5) - 2) / 3)
-        QuadExt!(
-            MontFp!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
+            Fq::ZERO,
         ),
     ];
 

@@ -3,7 +3,7 @@ fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
     biginteger::{BigInt, BigInteger, BigInteger384},
-    fields::{FftField, Field, Fp12Config, Fp2Config, Fp6Config, PrimeField, SquareRootField},
+    fields::{FftField, Field, Fp12Config, Fp2Config, Fp6Config, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -21,7 +21,7 @@ generate_field_serialization_test!(bls12_381; fq2; fq6; fq12;);
 
 #[test]
 fn test_negative_one() {
-    let neg_one = Fq::new(BigInt::new([
+    let neg_one = Fq::new_unchecked(BigInt::new([
         0x43f5fffffffcaaae,
         0x32b7fff2ed47fffd,
         0x7e83a49a2e99d69,
@@ -737,23 +737,6 @@ 0x536d5b15b514373f,
             0x22d582b,
         ])
     );
-}
-
-#[test]
-fn test_neg_one() {
-    let o = -Fq::one();
-
-    let thing: [u64; 6] = [
-        0x43f5fffffffcaaae,
-        0x32b7fff2ed47fffd,
-        0x7e83a49a2e99d69,
-        0xeca8f3318332bb7a,
-        0xef148d1ea0f4c069,
-        0x40ab3263eff0206,
-    ];
-    let negative_one = Fq::new(BigInt::new(thing));
-
-    assert_eq!(negative_one, o);
 }
 
 #[test]

@@ -1,12 +1,17 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{MontFp, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};
 
 use crate::{Fq, Fr};
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+pub type G1Affine = Affine<Parameters>;
+
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -14,19 +19,18 @@ /// COFACTOR = 1
     const COFACTOR: &'static [u64] = &[0x1];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
-    const COFACTOR_INV: Fr = MontFp!(Fr, "1");
+    const COFACTOR_INV: Fr = Fr::ONE;
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 0
-    const COEFF_A: Fq = MontFp!(Fq, "0");
+    const COEFF_A: Fq = Fq::ZERO;
 
     /// COEFF_B = 3
-    const COEFF_B: Fq = MontFp!(Fq, "3");
+    const COEFF_B: Fq = MontFp!("3");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -35,7 +39,7 @@ }
 }
 
 /// G1_GENERATOR_X = 1
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "1");
+pub const G1_GENERATOR_X: Fq = Fq::ONE;
 
 /// G1_GENERATOR_Y = 2
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "2");
+pub const G1_GENERATOR_Y: Fq = MontFp!("2");

@@ -1,12 +1,17 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{MontFp, QuadExt, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};
 
 use crate::{Fq, Fq2, Fr};
 
+pub type G2Affine = Affine<Parameters>;
+
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq2;
     type ScalarField = Fr;
 
@@ -21,32 +26,23 @@ 0x30644e72e131a029,
     ];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "10944121435919637613327163357776759465618812564592884533313067514031822496649"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("10944121435919637613327163357776759465618812564592884533313067514031822496649");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = [0, 0]
-    const COEFF_A: Fq2 = QuadExt!(MontFp!(Fq, "0"), MontFp!(Fq, "0"));
+    const COEFF_A: Fq2 = Fq2::ZERO;
 
     /// COEFF_B = 3/(u+9)
     /// (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
-    const COEFF_B: Fq2 = QuadExt!(
-        MontFp!(
-            Fq,
-            "19485874751759354771024239261021720505790618469301721065564631296452457478373"
-        ),
-        MontFp!(
-            Fq,
-            "266929791119991161246907387137283842545076965332900288569378510910307636690"
-        ),
+    const COEFF_B: Fq2 = Fq2::new(
+        MontFp!("19485874751759354771024239261021720505790618469301721065564631296452457478373"),
+        MontFp!("266929791119991161246907387137283842545076965332900288569378510910307636690"),
     );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -54,33 +50,25 @@ Self::BaseField::zero()
     }
 }
 
-pub const G2_GENERATOR_X: Fq2 = QuadExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-pub const G2_GENERATOR_Y: Fq2 = QuadExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 /// G2_GENERATOR_X_C0 =
 /// 10857046999023057135944570762232829481370756359578518086990519993285655852781
-pub const G2_GENERATOR_X_C0: Fq = MontFp!(
-    Fq,
-    "10857046999023057135944570762232829481370756359578518086990519993285655852781"
-);
+pub const G2_GENERATOR_X_C0: Fq =
+    MontFp!("10857046999023057135944570762232829481370756359578518086990519993285655852781");
 
 /// G2_GENERATOR_X_C1 =
 /// 11559732032986387107991004021392285783925812861821192530917403151452391805634
-pub const G2_GENERATOR_X_C1: Fq = MontFp!(
-    Fq,
-    "11559732032986387107991004021392285783925812861821192530917403151452391805634"
-);
+pub const G2_GENERATOR_X_C1: Fq =
+    MontFp!("11559732032986387107991004021392285783925812861821192530917403151452391805634");
 
 /// G2_GENERATOR_Y_C0 =
 /// 8495653923123431417604973247489272438418190587263600148770280649306958101930
-pub const G2_GENERATOR_Y_C0: Fq = MontFp!(
-    Fq,
-    "8495653923123431417604973247489272438418190587263600148770280649306958101930"
-);
+pub const G2_GENERATOR_Y_C0: Fq =
+    MontFp!("8495653923123431417604973247489272438418190587263600148770280649306958101930");
 
 /// G2_GENERATOR_Y_C1 =
 /// 4082367875863433681332203403145435568316851327593401208105741076214120093531
-pub const G2_GENERATOR_Y_C1: Fq = MontFp!(
-    Fq,
-    "4082367875863433681332203403145435568316851327593401208105741076214120093531"
-);
+pub const G2_GENERATOR_Y_C1: Fq =
+    MontFp!("4082367875863433681332203403145435568316851327593401208105741076214120093531");

@@ -2,7 +2,7 @@ use ark_ec::{
     bn,
     bn::{Bn, BnParameters, TwistType},
 };
-use ark_ff::{MontFp, QuadExt};
+use ark_ff::MontFp;
 
 use crate::*;
 
@@ -24,25 +24,13 @@ 0, 1, 1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 1, 1, 0,
         -1, 0, 0, 1, 0, 1, 1,
     ];
 
-    const TWIST_MUL_BY_Q_X: Fq2 = QuadExt!(
-        MontFp!(
-            Fq,
-            "21575463638280843010398324269430826099269044274347216827212613867836435027261"
-        ),
-        MontFp!(
-            Fq,
-            "10307601595873709700152284273816112264069230130616436755625194854815875713954"
-        ),
+    const TWIST_MUL_BY_Q_X: Fq2 = Fq2::new(
+        MontFp!("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
+        MontFp!("10307601595873709700152284273816112264069230130616436755625194854815875713954"),
     );
-    const TWIST_MUL_BY_Q_Y: Fq2 = QuadExt!(
-        MontFp!(
-            Fq,
-            "2821565182194536844548159561693502659359617185244120367078079554186484126554"
-        ),
-        MontFp!(
-            Fq,
-            "3505843767911556378687030309984248845540243509899259641013678093033130930403"
-        ),
+    const TWIST_MUL_BY_Q_Y: Fq2 = Fq2::new(
+        MontFp!("2821565182194536844548159561693502659359617185244120367078079554186484126554"),
+        MontFp!("3505843767911556378687030309984248845540243509899259641013678093033130930403"),
     );
     const TWIST_TYPE: TwistType = TwistType::D;
     type Fp = Fq;

@@ -1,5 +1,5 @@
 use ark_algebra_test_templates::{
-    curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test, groups::*, msm::*,
+    curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test, msm::*,
 };
 use ark_ec::{AffineCurve, PairingEngine};
 use ark_ff::{

@@ -1,10 +1,7 @@
-use ark_ff::fields::{Fp256, MontBackend, MontConfig, MontFp};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
 
 #[derive(MontConfig)]
 #[modulus = "21888242871839275222246405745257275088696311157297823662689037894645226208583"]
 #[generator = "3"]
 pub struct FqConfig;
 pub type Fq = Fp256<MontBackend<FqConfig, 4>>;
-
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, CubicExt, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -10,108 +10,78 @@
 impl Fp12Config for Fq12Config {
     type Fp6Config = Fq6Config;
 
-    const NONRESIDUE: Fq6 = CubicExt!(FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);
 
     const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        QuadExt!(MontFp!(Fq, "1"), MontFp!(Fq, "0"),),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        QuadExt!(
-            MontFp!(
-                Fq,
-                "8376118865763821496583973867626364092589906065868298776909617916018768340080"
-            ),
+        Fq2::new(
+            MontFp!("8376118865763821496583973867626364092589906065868298776909617916018768340080"),
             MontFp!(
-                Fq,
                 "16469823323077808223889137241176536799009286646108169935659301613961712198316"
             ),
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "21888242871839275220042445260109153167277707414472061641714758635765020556617"
             ),
-            MontFp!(Fq, "0"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "11697423496358154304825782922584725312912383441159505038794027105778954184319"
             ),
-            MontFp!(
-                Fq,
-                "303847389135065887422783454877609941456349188919719272345083954437860409601"
-            ),
+            MontFp!("303847389135065887422783454877609941456349188919719272345083954437860409601"),
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "21888242871839275220042445260109153167277707414472061641714758635765020556616"
             ),
-            MontFp!(Fq, "0"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        QuadExt!(
-            MontFp!(
-                Fq,
-                "3321304630594332808241809054958361220322477375291206261884409189760185844239"
-            ),
-            MontFp!(
-                Fq,
-                "5722266937896532885780051958958348231143373700109372999374820235121374419868"
-            ),
+        Fq2::new(
+            MontFp!("3321304630594332808241809054958361220322477375291206261884409189760185844239"),
+            MontFp!("5722266937896532885780051958958348231143373700109372999374820235121374419868"),
         ),
         // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        QuadExt!(MontFp!(Fq, "-1"), MontFp!(Fq, "0"),),
+        Fq2::new(MontFp!("-1"), Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "13512124006075453725662431877630910996106405091429524885779419978626457868503"
             ),
-            MontFp!(
-                Fq,
-                "5418419548761466998357268504080738289687024511189653727029736280683514010267"
-            ),
+            MontFp!("5418419548761466998357268504080738289687024511189653727029736280683514010267"),
         ),
         // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        QuadExt!(
-            MontFp!(
-                Fq,
-                "2203960485148121921418603742825762020974279258880205651966"
-            ),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "10190819375481120917420622822672549775783927716138318623895010788866272024264"
             ),
             MontFp!(
-                Fq,
                 "21584395482704209334823622290379665147239961968378104390343953940207365798982"
             ),
         ),
         // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        QuadExt!(
-            MontFp!(
-                Fq,
-                "2203960485148121921418603742825762020974279258880205651967"
-            ),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651967"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "18566938241244942414004596690298913868373833782006617400804628704885040364344"
             ),
             MontFp!(
-                Fq,
                 "16165975933942742336466353786298926857552937457188450663314217659523851788715"
             ),
         ),

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -10,14 +10,14 @@ impl Fp2Config for Fq2Config {
     type Fp = Fq;
 
     /// NONRESIDUE = -1
-    const NONRESIDUE: Fq = MontFp!(Fq, "-1");
+    const NONRESIDUE: Fq = MontFp!("-1");
 
     /// Coefficients for the Frobenius automorphism.
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // NONRESIDUE**(((q^0) - 1) / 2)
-        MontFp!(Fq, "1"),
+        Fq::ONE,
         // NONRESIDUE**(((q^1) - 1) / 2)
-        MontFp!(Fq, "-1"),
+        MontFp!("-1"),
     ];
 
     #[inline(always)]
@@ -25,6 +25,3 @@ fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
         -(*fe)
     }
 }
-
-pub const FQ2_ZERO: Fq2 = QuadExt!(FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = QuadExt!(FQ_ONE, FQ_ZERO);

@@ -1,4 +1,4 @@
-use ark_ff::{fields::*, MontFp, QuadExt};
+use ark_ff::{fields::*, MontFp};
 
 use crate::*;
 
@@ -11,113 +11,81 @@ impl Fp6Config for Fq6Config {
     type Fp2Config = Fq2Config;
 
     /// NONRESIDUE = U+9
-    const NONRESIDUE: Fq2 = QuadExt!(MontFp!(Fq, "9"), MontFp!(Fq, "1"));
+    const NONRESIDUE: Fq2 = Fq2::new(MontFp!("9"), Fq::ONE);
 
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        QuadExt!(MontFp!(Fq, "1"), MontFp!(Fq, "0"),),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "21575463638280843010398324269430826099269044274347216827212613867836435027261"
             ),
             MontFp!(
-                Fq,
                 "10307601595873709700152284273816112264069230130616436755625194854815875713954"
             ),
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "21888242871839275220042445260109153167277707414472061641714758635765020556616"
             ),
-            MontFp!(Fq, "0"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        QuadExt!(
-            MontFp!(
-                Fq,
-                "3772000881919853776433695186713858239009073593817195771773381919316419345261"
-            ),
-            MontFp!(
-                Fq,
-                "2236595495967245188281701248203181795121068902605861227855261137820944008926"
-            ),
+        Fq2::new(
+            MontFp!("3772000881919853776433695186713858239009073593817195771773381919316419345261"),
+            MontFp!("2236595495967245188281701248203181795121068902605861227855261137820944008926"),
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        QuadExt!(
-            MontFp!(
-                Fq,
-                "2203960485148121921418603742825762020974279258880205651966"
-            ),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "18429021223477853657660792034369865839114504446431234726392080002137598044644"
             ),
-            MontFp!(
-                Fq,
-                "9344045779998320333812420223237981029506012124075525679208581902008406485703"
-            ),
+            MontFp!("9344045779998320333812420223237981029506012124075525679208581902008406485703"),
         ),
     ];
 
     const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
-        QuadExt!(MontFp!(Fq, "1"), MontFp!(Fq, "0"),),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
-        QuadExt!(
+        Fq2::new(
+            MontFp!("2581911344467009335267311115468803099551665605076196740867805258568234346338"),
             MontFp!(
-                Fq,
-                "2581911344467009335267311115468803099551665605076196740867805258568234346338"
-            ),
-            MontFp!(
-                Fq,
                 "19937756971775647987995932169929341994314640652964949448313374472400716661030"
             ),
         ),
         // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
-        QuadExt!(
-            MontFp!(
-                Fq,
-                "2203960485148121921418603742825762020974279258880205651966"
-            ),
-            MontFp!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
-        QuadExt!(
+        Fq2::new(
+            MontFp!("5324479202449903542726783395506214481928257762400643279780343368557297135718"),
             MontFp!(
-                Fq,
-                "5324479202449903542726783395506214481928257762400643279780343368557297135718"
-            ),
-            MontFp!(
-                Fq,
                 "16208900380737693084919495127334387981393726419856888799917914180988844123039"
             ),
         ),
         // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "21888242871839275220042445260109153167277707414472061641714758635765020556616"
             ),
-            MontFp!(Fq, "0"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
-        QuadExt!(
+        Fq2::new(
             MontFp!(
-                Fq,
                 "13981852324922362344252311234282257507216387789820983642040889267519694726527"
             ),
-            MontFp!(
-                Fq,
-                "7629828391165209371577384193250820201684255241773809077146787135900891633097"
-            ),
+            MontFp!("7629828391165209371577384193250820201684255241773809077146787135900891633097"),
         ),
     ];
 
@@ -128,6 +96,6 @@ let mut f = *fe;
         f.double_in_place().double_in_place().double_in_place();
         let c0 = f.c0 + fe.c0 + Fq2Config::mul_fp_by_nonresidue(&fe.c1);
         let c1 = f.c1 + fe.c1 + fe.c0;
-        QuadExt!(c0, c1)
+        Fq2::new(c0, c1)
     }
 }

@@ -3,7 +3,7 @@ fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
     biginteger::{BigInt, BigInteger, BigInteger256},
-    fields::{FftField, Field, Fp6Config, PrimeField, SquareRootField},
+    fields::{FftField, Field, Fp6Config, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};

@@ -1,18 +1,18 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
 };
-use ark_ff::MontFp;
+use ark_ff::{Field, MontFp};
 
 use crate::{Fq, Fr};
 
-pub type G1Affine = GroupAffine<Parameters>;
-pub type G1Projective = GroupProjective<Parameters>;
+pub type G1Affine = Affine<Parameters>;
+pub type G1Projective = Projective<Parameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -30,19 +30,18 @@ ];
 
     /// COFACTOR^(-1) mod r =
     /// 91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804
-    const COFACTOR_INV: Fr = MontFp!(Fr, "91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804");
+    const COFACTOR_INV: Fr = MontFp!("91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 0
-    const COEFF_A: Fq = MontFp!(Fq, "0");
+    const COEFF_A: Fq = Fq::ZERO;
 
     /// COEFF_B = -1
-    const COEFF_B: Fq = MontFp!(Fq, "-1");
+    const COEFF_B: Fq = MontFp!("-1");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
     #[inline(always)]
     fn mul_by_a(_elem: &Self::BaseField) -> Self::BaseField {
         use ark_ff::Zero;
@@ -52,8 +51,8 @@ }
 
 /// G1_GENERATOR_X =
 /// 6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237");
+pub const G1_GENERATOR_X: Fq = MontFp!("6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237");
 
 /// G1_GENERATOR_Y =
 /// 2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099");
+pub const G1_GENERATOR_Y: Fq = MontFp!("2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099");

@@ -1,18 +1,18 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
 };
-use ark_ff::MontFp;
+use ark_ff::{Field, MontFp};
 
 use crate::{Fq, Fr};
 
-pub type G2Affine = GroupAffine<Parameters>;
-pub type G2Projective = GroupProjective<Parameters>;
+pub type G2Affine = Affine<Parameters>;
+pub type G2Projective = Projective<Parameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -30,19 +30,18 @@ ];
 
     /// COFACTOR^(-1) mod r =
     /// 214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124
-    const COFACTOR_INV: Fr = MontFp!(Fr, "214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124");
+    const COFACTOR_INV: Fr = MontFp!("214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 0
-    const COEFF_A: Fq = MontFp!(Fq, "0");
+    const COEFF_A: Fq = Fq::ZERO;
 
     /// COEFF_B = 4
-    const COEFF_B: Fq = MontFp!(Fq, "4");
+    const COEFF_B: Fq = MontFp!("4");
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_elem: &Self::BaseField) -> Self::BaseField {
@@ -53,8 +52,8 @@ }
 
 /// G2_GENERATOR_X =
 ///  6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428
-pub const G2_GENERATOR_X: Fq = MontFp!(Fq, "6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428");
+pub const G2_GENERATOR_X: Fq = MontFp!("6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428");
 
 /// G2_GENERATOR_Y =
 /// 562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041
-pub const G2_GENERATOR_Y: Fq = MontFp!(Fq, "562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041");
+pub const G2_GENERATOR_Y: Fq = MontFp!("562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041");

@@ -1,5 +1,5 @@
 use ark_algebra_test_templates::{
-    curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test, groups::*, msm::*,
+    curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test, msm::*,
 };
 use ark_ec::{AffineCurve, PairingEngine};
 use ark_ff::{Field, One, PrimeField};

@@ -1,10 +1,7 @@
-use ark_ff::fields::{Fp768, MontBackend, MontConfig, MontFp};
+use ark_ff::fields::{Fp768, MontBackend, MontConfig};
 
 #[derive(MontConfig)]
 #[modulus = "6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299"]
 #[generator = "2"]
 pub struct FqConfig;
 pub type Fq = Fp768<MontBackend<FqConfig, 12>>;
-
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");

@@ -1,12 +1,9 @@
 use ark_ff::{
     fields::fp3::{Fp3, Fp3Config},
-    CubicExt, MontFp,
+    Field, MontFp,
 };
 
-use crate::{
-    fields::{FQ_ONE, FQ_ZERO},
-    Fq,
-};
+use crate::Fq;
 
 pub type Fq3 = Fp3<Fq3Config>;
 
@@ -17,7 +14,7 @@ type Fp = Fq;
 
     /// NONRESIDUE = -4
     // Fq3 = Fq\[u\]/u^3+4
-    const NONRESIDUE: Fq = MontFp!(Fq, "-4");
+    const NONRESIDUE: Fq = MontFp!("-4");
 
     // (MODULUS^3 - 1) % 2^TWO_ADICITY == 0
     const TWO_ADICITY: u32 = 1;
@@ -64,24 +61,24 @@ 0x5de9825a0e,
     ];
 
     // NONRESIDUE^T % q
-    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = CubicExt!(
-        MontFp!(Fq, "6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068298"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068298"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
     const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        FQ_ONE,
-        MontFp!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
-        MontFp!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        Fq::ONE,
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
     ];
 
     // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
     const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
-        FQ_ONE,
-        MontFp!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
-        MontFp!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        Fq::ONE,
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
     ];
 
     #[inline(always)]

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp6_2over3::{Fp6, Fp6Config},
-    CubicExt, MontFp,
+    Field, MontFp,
 };
 
-use crate::{Fq, Fq3, Fq3Config, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq3, Fq3Config};
 
 pub type Fq6 = Fp6<Fq6Config>;
 
@@ -13,14 +13,14 @@ impl Fp6Config for Fq6Config {
     type Fp3Config = Fq3Config;
 
     /// NONRESIDUE = (0, 1, 0)
-    const NONRESIDUE: Fq3 = CubicExt!(FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        MontFp!(Fq, "1"),
-        MontFp!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775649"),
-        MontFp!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
-        MontFp!(Fq, "-1"),
-        MontFp!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
-        MontFp!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292651"),
+        Fq::ONE,
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775649"),
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        MontFp!("-1"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292651"),
     ];
 }

@@ -1,12 +1,12 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};
 
 use crate::*;
 
-generate_field_test!(bw6_761; fq3; fq6; mont(12, 6); );
+generate_field_test!(bw6_761; fq3; fq6_2_on_3; false; mont(12, 6); );
 generate_field_serialization_test!(bw6_761;);

@@ -1,18 +1,18 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
 };
 use ark_ff::MontFp;
 
 use crate::{Fq, Fr};
 
-pub type G1Affine = GroupAffine<Parameters>;
-pub type G1Projective = GroupProjective<Parameters>;
+pub type G1Affine = Affine<Parameters>;
+pub type G1Projective = Projective<Parameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -31,25 +31,24 @@ ];
 
     /// COFACTOR^(-1) mod r =
     /// 163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788
-    const COFACTOR_INV: Fr = MontFp!(Fr, "163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788");
+    const COFACTOR_INV: Fr = MontFp!("163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 5
-    const COEFF_A: Fq = MontFp!(Fq, "5");
+    const COEFF_A: Fq = MontFp!("5");
 
     /// COEFF_B = 17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414
-    const COEFF_B: Fq = MontFp!(Fq, "17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414");
+    const COEFF_B: Fq = MontFp!("17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 }
 
 /// G1_GENERATOR_X =
 /// 5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646");
+pub const G1_GENERATOR_X: Fq = MontFp!("5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646");
 
 /// G1_GENERATOR_Y =
 /// 7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443");
+pub const G1_GENERATOR_Y: Fq = MontFp!("7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443");

@@ -1,18 +1,18 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
 };
-use ark_ff::{CubicExt, MontFp};
+use ark_ff::{Field, MontFp};
 
-use crate::{Fq, Fq3, Fr, FQ_ZERO};
+use crate::{Fq, Fq3, Fr};
 
-pub type G2Affine = GroupAffine<Parameters>;
-pub type G2Projective = GroupProjective<Parameters>;
+pub type G2Affine = Affine<Parameters>;
+pub type G2Projective = Projective<Parameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq3;
     type ScalarField = Fr;
 
@@ -55,50 +55,49 @@ ];
 
     /// COFACTOR^(-1) mod r =
     /// 45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598
-    const COFACTOR_INV: Fr = MontFp!(Fr, "45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598");
+    const COFACTOR_INV: Fr = MontFp!("45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598");
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = (0, 0, COEFF_A * TWIST^2) = (0, 0, 5)
-    const COEFF_A: Fq3 = CubicExt!(FQ_ZERO, FQ_ZERO, MontFp!(Fq, "5"),);
+    const COEFF_A: Fq3 = Fq3::new(Fq::ZERO, Fq::ZERO, MontFp!("5"));
 
     /// COEFF_B = (G1::COEFF_B * TWIST^3, 0, 0) =
     /// (7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612,
     /// 0, 0)
-    const COEFF_B: Fq3 = CubicExt!(
-        MontFp!(Fq, "7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const COEFF_B: Fq3 = Fq3::new(
+        MontFp!("7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 }
 
-const G2_GENERATOR_X: Fq3 = CubicExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
-const G2_GENERATOR_Y: Fq3 = CubicExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
+const G2_GENERATOR_X: Fq3 = Fq3::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
+const G2_GENERATOR_Y: Fq3 = Fq3::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
 
 /// G2_GENERATOR_X_C0 =
 /// 13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338
-pub const G2_GENERATOR_X_C0: Fq = MontFp!(Fq, "13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338");
 
 /// G2_GENERATOR_X_C1 =
 /// 20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610
-pub const G2_GENERATOR_X_C1: Fq = MontFp!(Fq, "20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610");
 
 /// G2_GENERATOR_X_C2 =
 /// 3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980
-pub const G2_GENERATOR_X_C2: Fq = MontFp!(Fq, "3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980");
+pub const G2_GENERATOR_X_C2: Fq = MontFp!("3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980");
 
 /// G2_GENERATOR_Y_C0 =
 /// 8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243
-pub const G2_GENERATOR_Y_C0: Fq = MontFp!(Fq, "8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243");
 
 /// G2_GENERATOR_Y_C1 =
 /// 3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752
-pub const G2_GENERATOR_Y_C1: Fq = MontFp!(Fq, "3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752");
 
 /// G2_GENERATOR_Y_C2 =
 /// 10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721
-pub const G2_GENERATOR_Y_C2: Fq = MontFp!(Fq, "10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721");
+pub const G2_GENERATOR_Y_C2: Fq = MontFp!("10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721");

@@ -1,11 +1,11 @@
-use ark_ec::{models::SWModelParameters, PairingEngine};
+use ark_ec::{models::short_weierstrass::SWCurveConfig, PairingEngine};
 use ark_ff::{
     biginteger::BigInteger832,
     fields::{BitIteratorBE, Field},
-    BigInt, CubicExt, One,
+    BigInt, One,
 };
 
-use crate::{Fq, Fq3, Fq6, Fr, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq3, Fq6, Fr};
 
 pub mod g1;
 pub use self::g1::{G1Affine, G1Projective};
@@ -87,7 +87,7 @@ gamma_twist_px.mul_assign_by_fp(&px);
 
             let x = py_twist_squared;
             let y = gamma_old_rx - &old_ry - &gamma_twist_px;
-            let ell_rr_at_p = Fq6::new(x, y);
+            let ell_rr_at_p: Fq6 = Fq6::new(x, y);
 
             rx = gamma.square() - &old_rx.double();
             ry = gamma * &(old_rx - &rx) - &old_ry;
@@ -105,7 +105,7 @@ gamma_twist_px.mul_assign_by_fp(&px);
 
                 let x = py_twist_squared;
                 let y = gamma_qx - &qy - &gamma_twist_px;
-                let ell_rq_at_p = Fq6::new(x, y);
+                let ell_rq_at_p: Fq6 = Fq6::new(x, y);
 
                 rx = gamma.square() - &old_rx - &qx;
                 ry = gamma * &(old_rx - &rx) - &old_ry;
@@ -153,7 +153,7 @@ }
 }
 
 /// TWIST = (0, 1, 0)
-pub const TWIST: Fq3 = CubicExt!(FQ_ZERO, FQ_ONE, FQ_ZERO);
+pub const TWIST: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
 /// ATE_IS_LOOP_COUNT_NEG = false
 pub const ATE_IS_LOOP_COUNT_NEG: bool = false;

@@ -1,5 +1,5 @@
 use ark_algebra_test_templates::{
-    curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test, groups::*, msm::*,
+    curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test, msm::*,
 };
 use ark_ec::{AffineCurve, PairingEngine};
 use ark_ff::{Field, One, PrimeField};

@@ -1,10 +1,7 @@
-use ark_ff::fields::{Fp832, MontBackend, MontConfig, MontFp};
+use ark_ff::fields::{Fp832, MontBackend, MontConfig};
 
 #[derive(MontConfig)]
 #[modulus = "22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577"]
 #[generator = "13"]
 pub struct FqConfig;
 pub type Fq = Fp832<MontBackend<FqConfig, 13>>;
-
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp3::{Fp3, Fp3Config},
-    CubicExt, Field, MontFp,
+    Field, MontFp,
 };
 
-use crate::{fields::FQ_ZERO, Fq};
+use crate::Fq;
 
 pub type Fq3 = Fp3<Fq3Config>;
 
@@ -13,7 +13,7 @@ impl Fp3Config for Fq3Config {
     type Fp = Fq;
 
     /// NONRESIDUE = 13
-    const NONRESIDUE: Fq = MontFp!(Fq, "13");
+    const NONRESIDUE: Fq = MontFp!("13");
 
     const TWO_ADICITY: u32 = 3;
 
@@ -58,22 +58,22 @@ 0x34c96a73372daf9a,
         0x2b87fda171,
     ];
 
-    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = CubicExt!(
-        MontFp!(Fq, "5759691735434357221228070840130186543101559976323700017469395641639510585333061695996665166662748527158637897523704071820491869715512532675375604262649010727161924084052120196921150869218319839231115277876207074651754402338718419191428"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("5759691735434357221228070840130186543101559976323700017469395641639510585333061695996665166662748527158637897523704071820491869715512532675375604262649010727161924084052120196921150869218319839231115277876207074651754402338718419191428"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        MontFp!(Fq, "1"),
-        MontFp!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
-        MontFp!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        Fq::ONE,
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
     ];
 
     const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
-        MontFp!(Fq, "1"),
-        MontFp!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
-        MontFp!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        Fq::ONE,
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
     ];
 
     #[inline(always)]

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp6_2over3::{Fp6, Fp6Config},
-    CubicExt, MontFp,
+    Field, MontFp,
 };
 
-use crate::{Fq, Fq3, Fq3Config, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq3, Fq3Config};
 
 pub type Fq6 = Fp6<Fq6Config>;
 
@@ -13,14 +13,14 @@ impl Fp6Config for Fq6Config {
     type Fp3Config = Fq3Config;
 
     /// NONRESIDUE = (0, 1, 0).
-    const NONRESIDUE: Fq3 = CubicExt!(FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        MontFp!(Fq, "1"),
-        MontFp!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756862"),
-        MontFp!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
-        MontFp!(Fq, "22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825576"),
-        MontFp!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
-        MontFp!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068716"),
+        Fq::ONE,
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756862"),
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        MontFp!("22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825576"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068716"),
     ];
 }

@@ -1,12 +1,12 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};
 
 use crate::*;
 
-generate_field_test!(cp6_782; fq3; fq6; mont(13, 6); );
+generate_field_test!(cp6_782; fq3; fq6_2_on_3; mont(13, 6); );
 generate_field_serialization_test!(cp6_782;);

@@ -8,7 +8,7 @@ };
 use ark_ec::{PairingEngine, ProjectiveCurve};
 use ark_ff::{
     biginteger::{BigInteger256 as FrRepr, BigInteger384 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
+    BigInteger, Field, PrimeField, UniformRand,
 };
 
 mod g1 {

@@ -8,7 +8,7 @@ };
 use ark_ec::{PairingEngine, ProjectiveCurve};
 use ark_ff::{
     biginteger::{BigInteger256 as FrRepr, BigInteger384 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
+    BigInteger, Field, PrimeField, UniformRand,
 };
 
 mod g1 {

@@ -6,9 +6,7 @@ fq::Fq, fq2::Fq2, fr::Fr, Bn254, Fq12, G1Affine, G1Projective as G1, G2Affine,
     G2Projective as G2,
 };
 use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
+use ark_ff::{biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, UniformRand};
 
 mod g1 {
     use super::*;

@@ -8,7 +8,7 @@ };
 use ark_ec::{PairingEngine, ProjectiveCurve};
 use ark_ff::{
     biginteger::{BigInteger384 as FrRepr, BigInteger768 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
+    BigInteger, Field, PrimeField, UniformRand,
 };
 
 mod g1 {

@@ -8,7 +8,7 @@ };
 use ark_ec::{PairingEngine, ProjectiveCurve};
 use ark_ff::{
     biginteger::{BigInteger384 as FrRepr, BigInteger832 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
+    BigInteger, Field, PrimeField, UniformRand,
 };
 
 mod g1 {

@@ -3,9 +3,7 @@ use ark_std::ops::{AddAssign, MulAssign, SubAssign};
 
 use ark_ec::ProjectiveCurve;
 use ark_ed_on_bls12_381::{fq::Fq, fr::Fr, EdwardsAffine as GAffine, EdwardsProjective as G};
-use ark_ff::{
-    biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
+use ark_ff::{biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, UniformRand};
 
 mod g {
     use super::*;

@@ -2,10 +2,7 @@ use ark_curve_benches::*;
 use ark_std::ops::{AddAssign, MulAssign, SubAssign};
 
 use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::BigInteger320 as FqRepr, BigInteger, Field, PrimeField, SquareRootField,
-    UniformRand,
-};
+use ark_ff::{biginteger::BigInteger320 as FqRepr, BigInteger, Field, PrimeField, UniformRand};
 use ark_mnt4_298::{
     fq::Fq, fq2::Fq2, fr::Fr, Fq4, G1Affine, G1Projective as G1, G2Affine, G2Projective as G2,
     MNT4_298,

@@ -2,10 +2,7 @@ use ark_curve_benches::*;
 use ark_std::ops::{AddAssign, MulAssign, SubAssign};
 
 use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::BigInteger768 as FqRepr, BigInteger, Field, PrimeField, SquareRootField,
-    UniformRand,
-};
+use ark_ff::{biginteger::BigInteger768 as FqRepr, BigInteger, Field, PrimeField, UniformRand};
 use ark_mnt4_753::{
     fq::Fq, fq2::Fq2, fr::Fr, Fq4, G1Affine, G1Projective as G1, G2Affine, G2Projective as G2,
     MNT4_753,

@@ -2,10 +2,7 @@ use ark_curve_benches::*;
 use ark_std::ops::{AddAssign, MulAssign, SubAssign};
 
 use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::BigInteger320 as FqRepr, BigInteger, Field, PrimeField, SquareRootField,
-    UniformRand,
-};
+use ark_ff::{biginteger::BigInteger320 as FqRepr, BigInteger, Field, PrimeField, UniformRand};
 use ark_mnt6_298::{
     fq::Fq, fq3::Fq3, fr::Fr, Fq6, G1Affine, G1Projective as G1, G2Affine, G2Projective as G2,
     MNT6_298,

@@ -2,10 +2,7 @@ use ark_curve_benches::*;
 use ark_std::ops::{AddAssign, MulAssign, SubAssign};
 
 use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::BigInteger768 as FqRepr, BigInteger, Field, PrimeField, SquareRootField,
-    UniformRand,
-};
+use ark_ff::{biginteger::BigInteger768 as FqRepr, BigInteger, Field, PrimeField, UniformRand};
 use ark_mnt6_753::{
     fq::Fq, fq3::Fq3, fr::Fr, Fq6, G1Affine, G1Projective as G1, G2Affine, G2Projective as G2,
     MNT6_753,

@@ -2,9 +2,7 @@ use ark_curve_benches::*;
 use ark_std::ops::{AddAssign, MulAssign, SubAssign};
 
 use ark_ec::ProjectiveCurve;
-use ark_ff::{
-    biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
+use ark_ff::{biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, UniformRand};
 use ark_pallas::{fq::Fq, fr::Fr, Affine as GAffine, Projective as G};
 
 mod g {

@@ -2,9 +2,7 @@ use ark_curve_benches::*;
 use ark_std::ops::{AddAssign, MulAssign, SubAssign};
 
 use ark_ec::ProjectiveCurve;
-use ark_ff::{
-    biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
+use ark_ff::{biginteger::BigInteger256 as Repr, BigInteger, Field, PrimeField, UniformRand};
 use ark_vesta::{fq::Fq, fr::Fr, Affine as GAffine, Projective as G};
 
 mod g {

@@ -223,6 +223,7 @@ });
         }
 
         fn msm_131072(b: &mut $crate::bencher::Bencher) {
+            use ark_ec::msm::VariableBaseMSM;
             use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
             const SAMPLES: usize = 131072;
 
@@ -234,7 +235,7 @@ let scalars: Vec<_> = (0..SAMPLES)
                 .map(|_| Fr::rand(&mut rng).into_bigint())
                 .collect();
             b.bench_n(1, |b| {
-                b.iter(|| ark_ec::msm::VariableBase::msm(&v, &scalars));
+                b.iter(|| <$projective as VariableBaseMSM>::msm_bigint(&v, &scalars));
             })
         }
 

@@ -2,14 +2,14 @@ #![macro_use]
 extern crate ark_relations;
 
 pub mod fields {
-    use ark_ff::{BitIteratorLE, Field, UniformRand};
+    use ark_ff::{BigInteger, BitIteratorLE, Field, PrimeField, UniformRand};
     use ark_r1cs_std::prelude::*;
     use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
     use ark_std::{test_rng, vec::Vec};
 
     pub fn field_test<F, ConstraintF, AF>() -> Result<(), SynthesisError>
     where
-        F: Field,
+        F: PrimeField,
         ConstraintF: Field,
         AF: FieldVar<F, ConstraintF>,
         AF: TwoBitLookupGadget<ConstraintF, TableConstant = F>,
@@ -176,10 +176,10 @@ let _ = r.to_bits_le()?;
             assert!(cs.is_satisfied().unwrap());
 
             let bytes = r.to_non_unique_bytes()?;
-            assert_eq!(ark_ff::to_bytes!(r_native).unwrap(), bytes.value().unwrap());
+            assert_eq!(r_native.into_bigint().to_bytes_le(), bytes.value().unwrap());
             assert!(cs.is_satisfied().unwrap());
             let bytes = r.to_bytes()?;
-            assert_eq!(ark_ff::to_bytes!(r_native).unwrap(), bytes.value().unwrap());
+            assert_eq!(r_native.into_bigint().to_bytes_le(), bytes.value().unwrap());
             assert!(cs.is_satisfied().unwrap());
 
             let ab_false = &a + (AF::from(Boolean::Constant(false)) * b_native);
@@ -231,8 +231,8 @@ }
 
 pub mod curves {
     use ark_ec::{
-        short_weierstrass_jacobian::GroupProjective as SWProjective,
-        twisted_edwards_extended::GroupProjective as TEProjective, ProjectiveCurve,
+        short_weierstrass::Projective as SWProjective, twisted_edwards::Projective as TEProjective,
+        ProjectiveCurve,
     };
     use ark_ff::{BitIteratorLE, Field, One, PrimeField};
     use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
@@ -380,7 +380,7 @@ }
 
     pub fn sw_test<P, GG>() -> Result<(), SynthesisError>
     where
-        P: ark_ec::SWModelParameters,
+        P: ark_ec::models::short_weierstrass::SWCurveConfig,
         GG: CurveVar<SWProjective<P>, <P::BaseField as Field>::BasePrimeField>,
         for<'a> &'a GG: GroupOpsBounds<'a, SWProjective<P>, GG>,
     {
@@ -391,8 +391,6 @@ AllocationMode::Witness,
             AllocationMode::Constant,
         ];
         for &mode in &modes {
-            use ark_ec::group::Group;
-
             let mut rng = test_rng();
 
             let cs = ConstraintSystem::<<P::BaseField as Field>::BasePrimeField>::new_ref();
@@ -428,7 +426,7 @@ let gadget_a_zero = &gadget_a + &zero;
             gadget_a_zero.enforce_equal(&gadget_a)?;
 
             // Check doubling
-            let aa = Group::double(&a);
+            let aa = &a.double();
             let aa_affine = aa.into_affine();
             gadget_a.double_in_place()?;
             let aa_val = gadget_a.value()?.into_affine();
@@ -453,7 +451,7 @@ }
 
     pub fn te_test<P, GG>() -> Result<(), SynthesisError>
     where
-        P: ark_ec::TEModelParameters,
+        P: ark_ec::twisted_edwards::TECurveConfig,
         GG: CurveVar<TEProjective<P>, <P::BaseField as Field>::BasePrimeField>,
         for<'a> &'a GG: GroupOpsBounds<'a, TEProjective<P>, GG>,
     {
@@ -464,8 +462,6 @@ AllocationMode::Witness,
             AllocationMode::Constant,
         ];
         for &mode in &modes {
-            use ark_ec::group::Group;
-
             let mut rng = test_rng();
 
             let cs = ConstraintSystem::<<P::BaseField as Field>::BasePrimeField>::new_ref();
@@ -498,7 +494,7 @@ assert_eq!(ab_val, ab_affine, "Result of addition is unequal");
             assert!(cs.is_satisfied().unwrap());
 
             // Check doubling
-            let aa = Group::double(&a);
+            let aa = &a.double();
             let aa_affine = aa.into_affine();
             gadget_a.double_in_place()?;
             let aa_val = gadget_a.value()?.into_affine();

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_ed_on_bls12_377`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,6 +1,6 @@
 use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
 use ark_ff::MontFp;
 
@@ -9,13 +9,13 @@
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
+pub type EdwardsAffine = Affine<EdwardsParameters>;
+pub type EdwardsProjective = Projective<EdwardsParameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct EdwardsParameters;
 
-impl ModelParameters for EdwardsParameters {
+impl CurveConfig for EdwardsParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -24,23 +24,21 @@ const COFACTOR: &'static [u64] = &[4];
 
     /// COFACTOR_INV =
     /// 527778859339273151515551558673846658209717731602102048798421311598680340096
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "527778859339273151515551558673846658209717731602102048798421311598680340096"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("527778859339273151515551558673846658209717731602102048798421311598680340096");
 }
 
-impl TEModelParameters for EdwardsParameters {
+impl TECurveConfig for EdwardsParameters {
     /// COEFF_A = -1
-    const COEFF_A: Fq = MontFp!(Fq, "-1");
+    const COEFF_A: Fq = MontFp!("-1");
 
     /// COEFF_D = 3021
-    const COEFF_D: Fq = MontFp!(Fq, "3021");
+    const COEFF_D: Fq = MontFp!("3021");
 
     /// Generated randomly
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
 
-    type MontgomeryModelParameters = EdwardsParameters;
+    type MontCurveConfig = EdwardsParameters;
 
     /// Multiplication by `a` is just negation.
     /// Is `a` 1 or -1?
@@ -50,34 +48,26 @@ -*elem
     }
 }
 
-impl MontgomeryModelParameters for EdwardsParameters {
+impl MontCurveConfig for EdwardsParameters {
     /// COEFF_A = 0x8D26E3FADA9010A26949031ECE3971B93952AD84D4753DDEDB748DA37E8F552
     ///         = 3990301581132929505568273333084066329187552697088022219156688740916631500114
-    const COEFF_A: Fq = MontFp!(
-        Fq,
-        "3990301581132929505568273333084066329187552697088022219156688740916631500114"
-    );
+    const COEFF_A: Fq =
+        MontFp!("3990301581132929505568273333084066329187552697088022219156688740916631500114");
 
     /// COEFF_B = 0x9D8F71EEC83A44C3A1FBCEC6F5418E5C6154C2682B8AC231C5A3725C8170AAD
     ///         = 4454160168295440918680551605697480202188346638066041608778544715000777738925
-    const COEFF_B: Fq = MontFp!(
-        Fq,
-        "4454160168295440918680551605697480202188346638066041608778544715000777738925"
-    );
+    const COEFF_B: Fq =
+        MontFp!("4454160168295440918680551605697480202188346638066041608778544715000777738925");
 
-    type TEModelParameters = EdwardsParameters;
+    type TECurveConfig = EdwardsParameters;
 }
 
 /// GENERATOR_X =
 /// 4497879464030519973909970603271755437257548612157028181994697785683032656389,
-const GENERATOR_X: Fq = MontFp!(
-    Fq,
-    "4497879464030519973909970603271755437257548612157028181994697785683032656389"
-);
+const GENERATOR_X: Fq =
+    MontFp!("4497879464030519973909970603271755437257548612157028181994697785683032656389");
 
 /// GENERATOR_Y =
 /// 4357141146396347889246900916607623952598927460421559113092863576544024487809
-const GENERATOR_Y: Fq = MontFp!(
-    Fq,
-    "4357141146396347889246900916607623952598927460421559113092863576544024487809"
-);
+const GENERATOR_Y: Fq =
+    MontFp!("4357141146396347889246900916607623952598927460421559113092863576544024487809");

@@ -1,6 +1,5 @@
-use ark_algebra_test_templates::{curves::*, groups::*};
-use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_std::{rand::Rng, test_rng};
+use ark_algebra_test_templates::curves::*;
+use ark_ec::AffineCurve;
 
 use crate::*;
 
@@ -12,46 +11,10 @@ edwards_tests::<EdwardsParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
 fn test_generator() {
     let generator = EdwardsAffine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_conversion() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
 }
 
 #[test]

@@ -2,7 +2,7 @@ use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
-    fields::{Field, PrimeField, SquareRootField},
+    fields::{Field, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_ed_on_bls12_381`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,10 +1,7 @@
 use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    short_weierstrass_jacobian::{
-        GroupAffine as SWGroupAffine, GroupProjective as SWGroupProjective,
-    },
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
-    SWModelParameters,
+    models::CurveConfig,
+    short_weierstrass::{self, SWCurveConfig},
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
 use ark_ff::MontFp;
 
@@ -13,10 +10,10 @@
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<JubjubParameters>;
-pub type EdwardsProjective = GroupProjective<JubjubParameters>;
-pub type SWAffine = SWGroupAffine<JubjubParameters>;
-pub type SWProjective = SWGroupProjective<JubjubParameters>;
+pub type EdwardsAffine = Affine<JubjubParameters>;
+pub type EdwardsProjective = Projective<JubjubParameters>;
+pub type SWAffine = short_weierstrass::Affine<JubjubParameters>;
+pub type SWProjective = short_weierstrass::Projective<JubjubParameters>;
 
 /// `JubJub` is a twisted Edwards curve. These curves have equations of the
 /// form: ax² + y² = 1 - dx²y².
@@ -56,7 +53,7 @@ pub struct JubjubParameters;
 pub type EdwardsParameters = JubjubParameters;
 pub type SWParameters = JubjubParameters;
 
-impl ModelParameters for JubjubParameters {
+impl CurveConfig for JubjubParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -65,26 +62,22 @@ const COFACTOR: &'static [u64] = &[8];
 
     /// COFACTOR^(-1) mod r =
     /// 819310549611346726241370945440405716213240158234039660170669895299022906775
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "819310549611346726241370945440405716213240158234039660170669895299022906775"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("819310549611346726241370945440405716213240158234039660170669895299022906775");
 }
 
-impl TEModelParameters for JubjubParameters {
+impl TECurveConfig for JubjubParameters {
     /// COEFF_A = -1
-    const COEFF_A: Fq = MontFp!(Fq, "-1");
+    const COEFF_A: Fq = MontFp!("-1");
 
     /// COEFF_D = (10240/10241) mod q
-    const COEFF_D: Fq = MontFp!(
-        Fq,
-        "19257038036680949359750312669786877991949435402254120286184196891950884077233"
-    );
+    const COEFF_D: Fq =
+        MontFp!("19257038036680949359750312669786877991949435402254120286184196891950884077233");
 
     /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
 
-    type MontgomeryModelParameters = JubjubParameters;
+    type MontCurveConfig = JubjubParameters;
 
     /// Multiplication by `a` is simply negation here.
     #[inline(always)]
@@ -93,52 +86,39 @@ -(*elem)
     }
 }
 
-impl MontgomeryModelParameters for JubjubParameters {
+impl MontCurveConfig for JubjubParameters {
     /// COEFF_A = 40962
-    const COEFF_A: Fq = MontFp!(Fq, "40962");
+    const COEFF_A: Fq = MontFp!("40962");
 
     /// COEFF_B = -40964
-    const COEFF_B: Fq = MontFp!(Fq, "-40964");
+    const COEFF_B: Fq = MontFp!("-40964");
 
-    type TEModelParameters = JubjubParameters;
+    type TECurveConfig = JubjubParameters;
 }
 
-const GENERATOR_X: Fq = MontFp!(
-    Fq,
-    "8076246640662884909881801758704306714034609987455869804520522091855516602923"
-);
+const GENERATOR_X: Fq =
+    MontFp!("8076246640662884909881801758704306714034609987455869804520522091855516602923");
 
-const GENERATOR_Y: Fq = MontFp!(
-    Fq,
-    "13262374693698910701929044844600465831413122818447359594527400194675274060458"
-);
+const GENERATOR_Y: Fq =
+    MontFp!("13262374693698910701929044844600465831413122818447359594527400194675274060458");
 
-impl SWModelParameters for JubjubParameters {
+impl SWCurveConfig for JubjubParameters {
     /// COEFF_A = 52296097456646850916096512823759002727550416093741407922227928430486925478210
-    const COEFF_A: Self::BaseField = MontFp!(
-        Fq,
-        "52296097456646850916096512823759002727550416093741407922227928430486925478210"
-    );
+    const COEFF_A: Self::BaseField =
+        MontFp!("52296097456646850916096512823759002727550416093741407922227928430486925478210");
 
     /// COEFF_B = 48351165704696163914533707656614864561753505123260775585269522553028192119009
-    const COEFF_B: Self::BaseField = MontFp!(
-        Fq,
-        "48351165704696163914533707656614864561753505123260775585269522553028192119009"
-    );
+    const COEFF_B: Self::BaseField =
+        MontFp!("48351165704696163914533707656614864561753505123260775585269522553028192119009");
 
     /// generators
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (SW_GENERATOR_X, SW_GENERATOR_Y);
+    const GENERATOR: SWAffine = SWAffine::new_unchecked(SW_GENERATOR_X, SW_GENERATOR_Y);
 }
 
 /// x coordinate for SW curve generator
-const SW_GENERATOR_X: Fq = MontFp!(
-    Fq,
-    "33835869156188682335217394949746694649676633840125476177319971163079011318731"
-);
+const SW_GENERATOR_X: Fq =
+    MontFp!("33835869156188682335217394949746694649676633840125476177319971163079011318731");
 
 /// y coordinate for SW curve generator
-const SW_GENERATOR_Y: Fq = MontFp!(
-    Fq,
-    "43777270878440091394432848052353307184915192688165709016756678962558652055320"
-);
+const SW_GENERATOR_Y: Fq =
+    MontFp!("43777270878440091394432848052353307184915192688165709016756678962558652055320");

@@ -1,7 +1,7 @@
-use ark_algebra_test_templates::{curves::*, groups::*};
+use ark_algebra_test_templates::curves::*;
 use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_ff::{bytes::FromBytes, Zero};
-use ark_std::{rand::Rng, str::FromStr, test_rng};
+use ark_ff::Zero;
+use ark_std::str::FromStr;
 
 use crate::*;
 
@@ -15,31 +15,6 @@ sw_tests::<JubjubParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-
-    let c = rng.gen();
-    let d = rng.gen();
-
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-        group_test::<SWProjective>(c, d);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
 fn test_generator() {
     // edward curve
     let generator = EdwardsAffine::prime_subgroup_generator();
@@ -53,22 +28,6 @@ assert!(generator.is_in_correct_subgroup_assuming_on_curve());
 }
 
 #[test]
-fn test_conversion() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
-}
-
-#[test]
 fn test_scalar_multiplication() {
     let f1 = Fr::from_str(
         "4691331900926794624732159288782398864809513177368446695323460897088210774597",
@@ -96,19 +55,6 @@
     let f1g = g.mul(f1).into_affine();
     assert_eq!(g.mul(f1 * &f2).into_affine(), f1f2g);
     assert_eq!(f1g.mul(f2).into_affine(), f1f2g);
-}
-
-#[test]
-fn test_bytes() {
-    let g_from_repr = EdwardsAffine::from_str(
-        "(1158870117176967269192899343636553522971009777237254192973081388797299308391, \
-         36933624999642413792569726058244472742169727126562409632889593958355839948294)",
-    )
-    .unwrap();
-
-    let g_bytes = ark_ff::to_bytes![g_from_repr].unwrap();
-    let g = EdwardsAffine::read(g_bytes.as_slice()).unwrap();
-    assert_eq!(g_from_repr, g);
 }
 
 #[test]

@@ -3,8 +3,7 @@ fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
     biginteger::BigInteger256 as BigInteger,
-    bytes::{FromBytes, ToBytes},
-    fields::{Field, LegendreSymbol::*, PrimeField, SquareRootField},
+    fields::{Field, LegendreSymbol::*, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -299,22 +298,6 @@ assert_eq!(QuadraticNonResidue, Fq::from(e).legendre());
 }
 
 #[test]
-fn test_fq_bytes() {
-    let f1_from_repr = Fq::from(BigInteger::new([
-        0xab8a2535947d1a77,
-        0x9ba74cbfda0bbcda,
-        0xe928b59724d60baf,
-        0x1cccaaeb9bb1680a,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fq::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
-}
-
-#[test]
 fn test_fr_add() {
     let f1 = Fr::from(BigInteger::new([
         0xc81265fb4130fe0c,
@@ -358,22 +341,6 @@ 0xce83310e6ac4105d,
         0x98032e0f206320a,
     ]));
     assert_eq!(f1 * &f2, f3);
-}
-
-#[test]
-fn test_fr_bytes() {
-    let f1_from_repr = Fr::from(BigInteger::new([
-        0xc81265fb4130fe0c,
-        0xb308836c14e22279,
-        0x699e887f96bff372,
-        0x84ecc7e76c11ad,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fr::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
 }
 
 #[test]

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_bandersnatch`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,10 +1,7 @@
 use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    short_weierstrass_jacobian::{
-        GroupAffine as SWGroupAffine, GroupProjective as SWGroupProjective,
-    },
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
-    SWModelParameters,
+    models::CurveConfig,
+    short_weierstrass::{self, SWCurveConfig},
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
 use ark_ff::{Field, MontFp};
 
@@ -13,11 +10,11 @@
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<BandersnatchParameters>;
-pub type EdwardsProjective = GroupProjective<BandersnatchParameters>;
+pub type EdwardsAffine = Affine<BandersnatchParameters>;
+pub type EdwardsProjective = Projective<BandersnatchParameters>;
 
-pub type SWAffine = SWGroupAffine<BandersnatchParameters>;
-pub type SWProjective = SWGroupProjective<BandersnatchParameters>;
+pub type SWAffine = short_weierstrass::Affine<BandersnatchParameters>;
+pub type SWProjective = short_weierstrass::Projective<BandersnatchParameters>;
 
 /// `bandersnatch` is a twisted Edwards curve. These curves have equations of
 /// the form: ax² + y² = 1 - dx²y².
@@ -57,7 +54,7 @@
 pub type EdwardsParameters = BandersnatchParameters;
 pub type SWParameters = BandersnatchParameters;
 
-impl ModelParameters for BandersnatchParameters {
+impl CurveConfig for BandersnatchParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -66,28 +63,23 @@ const COFACTOR: &'static [u64] = &[4];
 
     /// COFACTOR^(-1) mod r =
     /// 9831726595336160714896451345284868594481866920080427688839802480047265754601
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "9831726595336160714896451345284868594481866920080427688839802480047265754601"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("9831726595336160714896451345284868594481866920080427688839802480047265754601");
 }
 
-impl TEModelParameters for BandersnatchParameters {
+impl TECurveConfig for BandersnatchParameters {
     /// COEFF_A = -5
-    const COEFF_A: Fq = MontFp!(Fq, "-5");
+    const COEFF_A: Fq = MontFp!("-5");
 
     /// COEFF_D = (138827208126141220649022263972958607803/
     /// 171449701953573178309673572579671231137) mod q
-    const COEFF_D: Fq = MontFp!(
-        Fq,
-        "45022363124591815672509500913686876175488063829319466900776701791074614335719"
-    );
+    const COEFF_D: Fq =
+        MontFp!("45022363124591815672509500913686876175488063829319466900776701791074614335719");
 
     /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (TE_GENERATOR_X, TE_GENERATOR_Y);
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(TE_GENERATOR_X, TE_GENERATOR_Y);
 
-    type MontgomeryModelParameters = BandersnatchParameters;
+    type MontCurveConfig = BandersnatchParameters;
 
     /// Multiplication by `a` is multiply by `-5`.
     #[inline(always)]
@@ -97,20 +89,16 @@ -(t + *elem)
     }
 }
 
-impl MontgomeryModelParameters for BandersnatchParameters {
+impl MontCurveConfig for BandersnatchParameters {
     /// COEFF_A = 29978822694968839326280996386011761570173833766074948509196803838190355340952
-    const COEFF_A: Fq = MontFp!(
-        Fq,
-        "29978822694968839326280996386011761570173833766074948509196803838190355340952"
-    );
+    const COEFF_A: Fq =
+        MontFp!("29978822694968839326280996386011761570173833766074948509196803838190355340952");
 
     /// COEFF_B = 25465760566081946422412445027709227188579564747101592991722834452325077642517
-    const COEFF_B: Fq = MontFp!(
-        Fq,
-        "25465760566081946422412445027709227188579564747101592991722834452325077642517"
-    );
+    const COEFF_B: Fq =
+        MontFp!("25465760566081946422412445027709227188579564747101592991722834452325077642517");
 
-    type TEModelParameters = BandersnatchParameters;
+    type TECurveConfig = BandersnatchParameters;
 }
 
 // The TE form generator is generated following Zcash's fashion:
@@ -123,43 +111,30 @@ // obtained from the scripts:
 //   <https://github.com/zhenfeizhang/bandersnatch/blob/main/bandersnatch/script/bandersnatch.sage>
 
 /// x coordinate for TE curve generator
-const TE_GENERATOR_X: Fq = MontFp!(
-    Fq,
-    "18886178867200960497001835917649091219057080094937609519140440539760939937304"
-);
+const TE_GENERATOR_X: Fq =
+    MontFp!("18886178867200960497001835917649091219057080094937609519140440539760939937304");
 
 /// y coordinate for TE curve generator
-const TE_GENERATOR_Y: Fq = MontFp!(
-    Fq,
-    "19188667384257783945677642223292697773471335439753913231509108946878080696678"
-);
+const TE_GENERATOR_Y: Fq =
+    MontFp!("19188667384257783945677642223292697773471335439753913231509108946878080696678");
 
 /// x coordinate for SW curve generator
-const SW_GENERATOR_X: Fq = MontFp!(
-    Fq,
-    "30900340493481298850216505686589334086208278925799850409469406976849338430199"
-);
+const SW_GENERATOR_X: Fq =
+    MontFp!("30900340493481298850216505686589334086208278925799850409469406976849338430199");
 
 /// y coordinate for SW curve generator
-const SW_GENERATOR_Y: Fq = MontFp!(
-    Fq,
-    "12663882780877899054958035777720958383845500985908634476792678820121468453298"
-);
+const SW_GENERATOR_Y: Fq =
+    MontFp!("12663882780877899054958035777720958383845500985908634476792678820121468453298");
 
-impl SWModelParameters for BandersnatchParameters {
+impl SWCurveConfig for BandersnatchParameters {
     /// COEFF_A = 10773120815616481058602537765553212789256758185246796157495669123169359657269
-    const COEFF_A: Self::BaseField = MontFp!(
-        Fq,
-        "10773120815616481058602537765553212789256758185246796157495669123169359657269"
-    );
+    const COEFF_A: Self::BaseField =
+        MontFp!("10773120815616481058602537765553212789256758185246796157495669123169359657269");
 
     /// COEFF_B = 29569587568322301171008055308580903175558631321415017492731745847794083609535
-    const COEFF_B: Self::BaseField = MontFp!(
-        Fq,
-        "29569587568322301171008055308580903175558631321415017492731745847794083609535"
-    );
+    const COEFF_B: Self::BaseField =
+        MontFp!("29569587568322301171008055308580903175558631321415017492731745847794083609535");
 
     /// generators
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (SW_GENERATOR_X, SW_GENERATOR_Y);
+    const GENERATOR: SWAffine = SWAffine::new_unchecked(SW_GENERATOR_X, SW_GENERATOR_Y);
 }

@@ -1,7 +1,7 @@
-use ark_algebra_test_templates::{curves::*, groups::*};
+use ark_algebra_test_templates::curves::*;
 use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_ff::{bytes::FromBytes, Zero};
-use ark_std::{rand::Rng, str::FromStr, test_rng};
+use ark_ff::Zero;
+use ark_std::str::FromStr;
 
 use crate::*;
 
@@ -15,31 +15,6 @@ sw_tests::<BandersnatchParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-
-    let c = rng.gen();
-    let d = rng.gen();
-
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-        group_test::<SWProjective>(c, d);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
 fn test_generator() {
     // edward curve
     let generator = EdwardsAffine::prime_subgroup_generator();
@@ -53,31 +28,6 @@ assert!(generator.is_in_correct_subgroup_assuming_on_curve());
 }
 
 #[test]
-fn test_conversion() {
-    // edward curve
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
-
-    // weierstrass curve
-    let mut rng = test_rng();
-    let a: SWProjective = rng.gen();
-    let b: SWProjective = rng.gen();
-    let a_b = { (a + &b).double().double() };
-    let a_b2 = (a + &b).double().double();
-    assert_eq!(a_b.into_affine(), a_b2.into_affine());
-}
-
-#[test]
 fn test_scalar_multiplication() {
     let f1 = Fr::from_str(
         "4257185345094557079734489188109952172285839137338142340240392707284963971010",
@@ -105,19 +55,6 @@
     let f1g = g.mul(f1).into_affine();
     assert_eq!(g.mul(f1 * &f2).into_affine(), f1f2g);
     assert_eq!(f1g.mul(f2).into_affine(), f1f2g);
-}
-
-#[test]
-fn test_bytes() {
-    let g_from_repr = EdwardsAffine::from_str(
-        "(29627151942733444043031429156003786749302466371339015363120350521834195802525, \
-         27488387519748396681411951718153463804682561779047093991696427532072116857978)",
-    )
-    .unwrap();
-
-    let g_bytes = ark_ff::to_bytes![g_from_repr].unwrap();
-    let g = EdwardsAffine::read(g_bytes.as_slice()).unwrap();
-    assert_eq!(g_from_repr, g);
 }
 
 #[test]

@@ -3,8 +3,7 @@ fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
     biginteger::BigInteger256 as BigInteger,
-    bytes::{FromBytes, ToBytes},
-    fields::{Field, LegendreSymbol::*, PrimeField, SquareRootField},
+    fields::{Field, LegendreSymbol::*, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -299,22 +298,6 @@ assert_eq!(QuadraticNonResidue, Fq::from(e).legendre());
 }
 
 #[test]
-fn test_fq_bytes() {
-    let f1_from_repr = Fq::from(BigInteger::new([
-        0xab8a2535947d1a77,
-        0x9ba74cbfda0bbcda,
-        0xe928b59724d60baf,
-        0x1cccaaeb9bb1680a,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fq::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
-}
-
-#[test]
 fn test_fr_add() {
     let f1 = Fr::from(BigInteger::new([
         0xc81265fb4130fe0c,
@@ -358,22 +341,6 @@ 0x1c234ad6dcdc70c9,
         0x15a75fba99bc8ad,
     ]));
     assert_eq!(f1 * &f2, f3);
-}
-
-#[test]
-fn test_fr_bytes() {
-    let f1_from_repr = Fr::from(BigInteger::new([
-        0xc81265fb4130fe0c,
-        0xb308836c14e22279,
-        0x699e887f96bff372,
-        0x84ecc7e76c11ad,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fr::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
 }
 
 #[test]

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_ed_on_bn254`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,16 +1,16 @@
 use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
-use ark_ff::MontFp;
+use ark_ff::{Field, MontFp};
 
 use crate::{Fq, Fr};
 
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
+pub type EdwardsAffine = Affine<EdwardsParameters>;
+pub type EdwardsProjective = Projective<EdwardsParameters>;
 
 /// `Baby-JubJub` is a twisted Edwards curve. These curves have equations of the
 /// form: ax² + y² = 1 + dx²y².
@@ -22,7 +22,7 @@ /// q = 21888242871839275222246405745257275088548364400416034343698204186575808495617
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct EdwardsParameters;
 
-impl ModelParameters for EdwardsParameters {
+impl CurveConfig for EdwardsParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -31,15 +31,13 @@ const COFACTOR: &'static [u64] = &[8];
 
     /// COFACTOR^(-1) mod r =
     /// 2394026564107420727433200628387514462817212225638746351800188703329891451411
-    const COFACTOR_INV: Fr = MontFp!(
-        Fr,
-        "2394026564107420727433200628387514462817212225638746351800188703329891451411"
-    );
+    const COFACTOR_INV: Fr =
+        MontFp!("2394026564107420727433200628387514462817212225638746351800188703329891451411");
 }
 
-impl TEModelParameters for EdwardsParameters {
+impl TECurveConfig for EdwardsParameters {
     /// COEFF_A = 1
-    const COEFF_A: Fq = MontFp!(Fq, "1");
+    const COEFF_A: Fq = Fq::ONE;
 
     #[inline(always)]
     fn mul_by_a(elem: &Self::BaseField) -> Self::BaseField {
@@ -48,32 +46,26 @@ }
 
     /// COEFF_D = 168696/168700 mod q
     ///         = 9706598848417545097372247223557719406784115219466060233080913168975159366771
-    const COEFF_D: Fq = MontFp!(
-        Fq,
-        "9706598848417545097372247223557719406784115219466060233080913168975159366771"
-    );
+    const COEFF_D: Fq =
+        MontFp!("9706598848417545097372247223557719406784115219466060233080913168975159366771");
 
     /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
 
-    type MontgomeryModelParameters = EdwardsParameters;
+    type MontCurveConfig = EdwardsParameters;
 }
 
-impl MontgomeryModelParameters for EdwardsParameters {
+impl MontCurveConfig for EdwardsParameters {
     /// COEFF_A = 168698
-    const COEFF_A: Fq = MontFp!(Fq, "168698");
+    const COEFF_A: Fq = MontFp!("168698");
     /// COEFF_B = 168700
-    const COEFF_B: Fq = MontFp!(Fq, "168700");
+    const COEFF_B: Fq = MontFp!("168700");
 
-    type TEModelParameters = EdwardsParameters;
+    type TECurveConfig = EdwardsParameters;
 }
 
-const GENERATOR_X: Fq = MontFp!(
-    Fq,
-    "19698561148652590122159747500897617769866003486955115824547446575314762165298"
-);
+const GENERATOR_X: Fq =
+    MontFp!("19698561148652590122159747500897617769866003486955115824547446575314762165298");
 
-const GENERATOR_Y: Fq = MontFp!(
-    Fq,
-    "19298250018296453272277890825869354524455968081175474282777126169995084727839"
-);
+const GENERATOR_Y: Fq =
+    MontFp!("19298250018296453272277890825869354524455968081175474282777126169995084727839");

@@ -1,7 +1,7 @@
-use ark_algebra_test_templates::{curves::*, groups::*};
+use ark_algebra_test_templates::curves::*;
 use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_ff::{bytes::FromBytes, Zero};
-use ark_std::{rand::Rng, str::FromStr, test_rng};
+use ark_ff::Zero;
+use ark_std::str::FromStr;
 
 use crate::*;
 
@@ -13,26 +13,6 @@ edwards_tests::<EdwardsParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
 fn test_generator() {
     let generator = EdwardsAffine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
@@ -40,22 +20,6 @@ assert!(generator.is_in_correct_subgroup_assuming_on_curve());
 }
 
 #[test]
-fn test_conversion() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
-}
-
-#[test]
 fn test_scalar_multiplication() {
     let f1 = Fr::from_str(
         "4691331900926794624732159288782398864809513177368446695323460897088210774597",
@@ -83,19 +47,6 @@
     let f1g = g.mul(f1).into_affine();
     assert_eq!(g.mul(f1 * &f2).into_affine(), f1f2g);
     assert_eq!(f1g.mul(f2).into_affine(), f1f2g);
-}
-
-#[test]
-fn test_bytes() {
-    let g_from_repr = EdwardsAffine::from_str(
-        "(15863623088992515880085393097393553694825975317405843389771115419751650972659, \
-         16950150798460657717958625567821834550301663161624707787222815936182638968203)",
-    )
-    .unwrap();
-
-    let g_bytes = ark_ff::to_bytes![g_from_repr].unwrap();
-    let g = EdwardsAffine::read(g_bytes.as_slice()).unwrap();
-    assert_eq!(g_from_repr, g);
 }
 
 #[test]

@@ -3,8 +3,7 @@ fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
     biginteger::BigInteger256 as BigInteger,
-    bytes::{FromBytes, ToBytes},
-    fields::{Field, LegendreSymbol::*, PrimeField, SquareRootField},
+    fields::{Field, LegendreSymbol::*, PrimeField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -294,22 +293,6 @@ assert_eq!(QuadraticNonResidue, Fq::from(e).legendre());
 }
 
 #[test]
-fn test_fq_bytes() {
-    let f1_from_repr = Fq::from(BigInteger::new([
-        0xab8a2535947d1a77,
-        0x9ba74cbfda0bbcda,
-        0xe928b59724d60baf,
-        0x1cccaaeb9bb1680a,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fq::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
-}
-
-#[test]
 fn test_fr_add() {
     let f1 = Fr::from(BigInteger::new([
         0xccfc9a195e0f5c46,
@@ -353,21 +336,6 @@ 0x835582d896b4d13f,
         0x4808736e213036e,
     ]));
     assert_eq!(f1 * &f2, f3);
-}
-#[test]
-fn test_fr_bytes() {
-    let f1_from_repr = Fr::from(BigInteger::new([
-        0xc81265fb4130fe0c,
-        0xb308836c14e22279,
-        0x699e887f96bff372,
-        0x84ecc7e76c11ad,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fr::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
 }
 
 #[test]

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_ed_on_bw6_761`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -2,7 +2,7 @@ #![allow(unreachable_pub)]
 //! This module implements the R1CS equivalent of `ark_ed_on_cp6_782`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,6 +1,6 @@
 use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
 use ark_ff::MontFp;
 
@@ -9,13 +9,13 @@
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
+pub type EdwardsAffine = Affine<EdwardsParameters>;
+pub type EdwardsProjective = Projective<EdwardsParameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct EdwardsParameters;
 
-impl ModelParameters for EdwardsParameters {
+impl CurveConfig for EdwardsParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -24,20 +24,20 @@ const COFACTOR: &'static [u64] = &[8];
 
     /// COFACTOR^(-1) mod r =
     /// 12124894969357926281749346891948134384518445910386624712788431705725441736421489799867521238554906438478484045560
-    const COFACTOR_INV: Fr = MontFp!(Fr, "12124894969357926281749346891948134384518445910386624712788431705725441736421489799867521238554906438478484045560");
+    const COFACTOR_INV: Fr = MontFp!("12124894969357926281749346891948134384518445910386624712788431705725441736421489799867521238554906438478484045560");
 }
 
-impl TEModelParameters for EdwardsParameters {
+impl TECurveConfig for EdwardsParameters {
     /// COEFF_A = -1 =
-    const COEFF_A: Fq = MontFp!(Fq, "-1");
+    const COEFF_A: Fq = MontFp!("-1");
 
     /// COEFF_D = 79743
-    const COEFF_D: Fq = MontFp!(Fq, "79743");
+    const COEFF_D: Fq = MontFp!("79743");
 
     /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
 
-    type MontgomeryModelParameters = EdwardsParameters;
+    type MontCurveConfig = EdwardsParameters;
 
     /// Multiplication by `a` is just negation.
     #[inline(always)]
@@ -46,20 +46,20 @@ -*elem
     }
 }
 
-impl MontgomeryModelParameters for EdwardsParameters {
+impl MontCurveConfig for EdwardsParameters {
     /// COEFF_A = 0x95D53EB3F6AC3F7A53C26020144439DC6073BCAE513E03FD06B6B3BAA390F25E51534B26719E33F4CD906D4DA9B535
-    const COEFF_A: Fq = MontFp!(Fq, "90083623084271891037116870487743067984710080209539149685414147055329063590616489392386084989619674926965747987765");
+    const COEFF_A: Fq = MontFp!("90083623084271891037116870487743067984710080209539149685414147055329063590616489392386084989619674926965747987765");
 
     /// COEFF_B = 0x118650763CE64AB4BE743604C8D05013DC2663652A3D58B21ECAB7BFF65B70DB8BA09F9098E61CC903B2F92B2564ACA
-    const COEFF_B: Fq = MontFp!(Fq, "168580802928697202973535863207150465551683432545375510854470115611391404757724333382582803149953685197474573470410");
+    const COEFF_B: Fq = MontFp!("168580802928697202973535863207150465551683432545375510854470115611391404757724333382582803149953685197474573470410");
 
-    type TEModelParameters = EdwardsParameters;
+    type TECurveConfig = EdwardsParameters;
 }
 
 /// GENERATOR_X =
 /// 174701772324485506941690903512423551998294352968833659960042362742684869862495746426366187462669992073196420267127
-const GENERATOR_X: Fq = MontFp!(Fq, "174701772324485506941690903512423551998294352968833659960042362742684869862495746426366187462669992073196420267127");
+const GENERATOR_X: Fq = MontFp!("174701772324485506941690903512423551998294352968833659960042362742684869862495746426366187462669992073196420267127");
 
 /// GENERATOR_Y =
 /// 208487200052258845495340374451540775445408439654930191324011635560142523886549663106522691296420655144190624954833
-const GENERATOR_Y: Fq = MontFp!(Fq, "208487200052258845495340374451540775445408439654930191324011635560142523886549663106522691296420655144190624954833");
+const GENERATOR_Y: Fq = MontFp!("208487200052258845495340374451540775445408439654930191324011635560142523886549663106522691296420655144190624954833");

@@ -1,6 +1,5 @@
-use ark_algebra_test_templates::{curves::*, groups::*};
-use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_std::{rand::Rng, test_rng};
+use ark_algebra_test_templates::curves::*;
+use ark_ec::AffineCurve;
 
 use crate::*;
 
@@ -12,46 +11,10 @@ edwards_tests::<EdwardsParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
 fn test_generator() {
     let generator = EdwardsAffine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_conversion() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
 }
 
 #[test]

@@ -1,7 +1,7 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_ed_on_mnt4_298`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,6 +1,6 @@
 use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
 use ark_ff::MontFp;
 
@@ -9,13 +9,13 @@
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
+pub type EdwardsAffine = Affine<EdwardsParameters>;
+pub type EdwardsProjective = Projective<EdwardsParameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct EdwardsParameters;
 
-impl ModelParameters for EdwardsParameters {
+impl CurveConfig for EdwardsParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -25,7 +25,6 @@
     /// COFACTOR_INV (mod r) =
     /// 29745142885578832859584328103315528221570304936126890280067991221921526670592508030983158
     const COFACTOR_INV: Fr = MontFp!(
-        Fr,
         "29745142885578832859584328103315528221570304936126890280067991221921526670592508030983158"
     );
 }
@@ -35,23 +34,23 @@ // discussed below. Some useful numbers:
 // R for Fq: 223364648326281414938801705359223029554923725549792420683051274872200260503540791531766876
 // R for Fr: 104384076783966083500464392945960916666734135485183910065100558776489954102951241798239545
 
-impl TEModelParameters for EdwardsParameters {
+impl TECurveConfig for EdwardsParameters {
     /// COEFF_A = -1
     /// Needs to be in the Montgomery residue form in Fq
     /// I.e., -1 * R for Fq
     ///     = 252557637842979910814547544293825421990201153003031094870216460866964386803867699028196261
-    const COEFF_A: Fq = MontFp!(Fq, "-1");
+    const COEFF_A: Fq = MontFp!("-1");
 
     /// COEFF_D = 4212
     /// Needs to be in the Montgomery residue form in Fq
     /// I.e., 4212 * R for Fq
     ///     = 389461279836940033614665658623660232171971995346409183754923941118154161474636585314923000
-    const COEFF_D: Fq = MontFp!(Fq, "4212");
+    const COEFF_D: Fq = MontFp!("4212");
 
     /// Generated randomly
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
 
-    type MontgomeryModelParameters = EdwardsParameters;
+    type MontCurveConfig = EdwardsParameters;
 
     /// Multiplication by `a` is just negation.
     #[inline(always)]
@@ -60,26 +59,24 @@ -*elem
     }
 }
 
-impl MontgomeryModelParameters for EdwardsParameters {
+impl MontCurveConfig for EdwardsParameters {
     /// COEFF_A = 203563247015667910991582090642011229452721346107806307863040223071914240315202967004285204
-    const COEFF_A: Fq = MontFp!(Fq, "203563247015667910991582090642011229452721346107806307863040223071914240315202967004285204");
+    const COEFF_A: Fq = MontFp!("203563247015667910991582090642011229452721346107806307863040223071914240315202967004285204");
 
     /// COEFF_B = 272359039153593414761767159011037222092403532445017207690227512667250406992205523555677931
-    const COEFF_B: Fq = MontFp!(Fq, "272359039153593414761767159011037222092403532445017207690227512667250406992205523555677931");
+    const COEFF_B: Fq = MontFp!("272359039153593414761767159011037222092403532445017207690227512667250406992205523555677931");
 
-    type TEModelParameters = EdwardsParameters;
+    type TECurveConfig = EdwardsParameters;
 }
 
 /// GENERATOR_X =
 /// 282406820114868156776872298252698015906762052916420164316497572033519876761239463633892227
 const GENERATOR_X: Fq = MontFp!(
-    Fq,
     "282406820114868156776872298252698015906762052916420164316497572033519876761239463633892227"
 );
 
 /// GENERATOR_Y =
 /// 452667754940241021433619311795265643711152068500301853535337412655162600774122192283142703
 const GENERATOR_Y: Fq = MontFp!(
-    Fq,
     "452667754940241021433619311795265643711152068500301853535337412655162600774122192283142703"
 );

@@ -1,58 +1,13 @@
-use ark_algebra_test_templates::{curves::*, groups::*};
-use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_std::{rand::Rng, test_rng};
+use ark_algebra_test_templates::curves::*;
+use ark_ec::AffineCurve;
 
 use crate::*;
 
 #[test]
-fn test_projective_curve() {
-    curve_tests::<EdwardsProjective>();
-
-    edwards_tests::<EdwardsParameters>();
-}
-
-#[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
 fn test_generator() {
     let generator = EdwardsAffine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_conversion() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
 }
 
 #[test]

@@ -1,7 +1,7 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_ed_on_mnt4_753`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,6 +1,6 @@
 use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
 use ark_ff::MontFp;
 
@@ -9,13 +9,13 @@
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
+pub type EdwardsAffine = Affine<EdwardsParameters>;
+pub type EdwardsProjective = Projective<EdwardsParameters>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct EdwardsParameters;
 
-impl ModelParameters for EdwardsParameters {
+impl CurveConfig for EdwardsParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -24,20 +24,20 @@ const COFACTOR: &'static [u64] = &[8];
 
     /// COFACTOR_INV (mod r) =
     /// 4582647449616135528381398492791944685893671397494963179726320631987147963874964803303316505414568319530101512550297775574042810022553679071007001162683923594233560231270043634777390699589793776691858866199511300853468155295505
-    const COFACTOR_INV: Fr = MontFp!(Fr, "4582647449616135528381398492791944685893671397494963179726320631987147963874964803303316505414568319530101512550297775574042810022553679071007001162683923594233560231270043634777390699589793776691858866199511300853468155295505");
+    const COFACTOR_INV: Fr = MontFp!("4582647449616135528381398492791944685893671397494963179726320631987147963874964803303316505414568319530101512550297775574042810022553679071007001162683923594233560231270043634777390699589793776691858866199511300853468155295505");
 }
 
-impl TEModelParameters for EdwardsParameters {
+impl TECurveConfig for EdwardsParameters {
     /// COEFF_A = -1
-    const COEFF_A: Fq = MontFp!(Fq, "-1");
+    const COEFF_A: Fq = MontFp!("-1");
 
     /// COEFF_D = 317690
-    const COEFF_D: Fq = MontFp!(Fq, "317690");
+    const COEFF_D: Fq = MontFp!("317690");
 
     /// Generated randomly
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
 
-    type MontgomeryModelParameters = EdwardsParameters;
+    type MontCurveConfig = EdwardsParameters;
 
     /// Multiplication by `a` is just negation.
     #[inline(always)]
@@ -46,20 +46,20 @@ -*elem
     }
 }
 
-impl MontgomeryModelParameters for EdwardsParameters {
+impl MontCurveConfig for EdwardsParameters {
     /// COEFF_A = 40212480635445336270302172549278415015971955924352275480357619589919378421241453024646804979794897776496091377551124233752850182852486874251193367187677349266115879541798515219680194853352256809837126277708211496794264654247419
-    const COEFF_A: Fq = MontFp!(Fq, "40212480635445336270302172549278415015971955924352275480357619589919378421241453024646804979794897776496091377551124233752850182852486874251193367187677349266115879541798515219680194853352256809837126277708211496794264654247419");
+    const COEFF_A: Fq = MontFp!("40212480635445336270302172549278415015971955924352275480357619589919378421241453024646804979794897776496091377551124233752850182852486874251193367187677349266115879541798515219680194853352256809837126277708211496794264654247419");
 
     /// COEFF_B = 1686010332473617132042042241962222112198753995601673591425883331105974391329653748412088783995441144921979594337334243570322874639106980818502874667119046899605536783551549221790223284494141659774809441351696667426519821912580
-    const COEFF_B: Fq = MontFp!(Fq, "1686010332473617132042042241962222112198753995601673591425883331105974391329653748412088783995441144921979594337334243570322874639106980818502874667119046899605536783551549221790223284494141659774809441351696667426519821912580");
+    const COEFF_B: Fq = MontFp!("1686010332473617132042042241962222112198753995601673591425883331105974391329653748412088783995441144921979594337334243570322874639106980818502874667119046899605536783551549221790223284494141659774809441351696667426519821912580");
 
-    type TEModelParameters = EdwardsParameters;
+    type TECurveConfig = EdwardsParameters;
 }
 
 /// GENERATOR_X =
 /// 41126137307536311801428235632419266329480236393691483739251051053325519918069469184425962602019877935619960143044210127218431046103600632347238890180171944971817510488009355627861577881883236134824745174469522277738875418206826
-const GENERATOR_X: Fq = MontFp!(Fq, "41126137307536311801428235632419266329480236393691483739251051053325519918069469184425962602019877935619960143044210127218431046103600632347238890180171944971817510488009355627861577881883236134824745174469522277738875418206826");
+const GENERATOR_X: Fq = MontFp!("41126137307536311801428235632419266329480236393691483739251051053325519918069469184425962602019877935619960143044210127218431046103600632347238890180171944971817510488009355627861577881883236134824745174469522277738875418206826");
 
 /// GENERATOR_Y =
 /// 18249602579663240810999977712212098844157230095713722119136881953011435881503578209163288529034825612841855863913294174196656077002578342108932925693640046298989762289691399012056048139253937882385653600831389370198228562812681
-const GENERATOR_Y: Fq = MontFp!(Fq, "18249602579663240810999977712212098844157230095713722119136881953011435881503578209163288529034825612841855863913294174196656077002578342108932925693640046298989762289691399012056048139253937882385653600831389370198228562812681");
+const GENERATOR_Y: Fq = MontFp!("18249602579663240810999977712212098844157230095713722119136881953011435881503578209163288529034825612841855863913294174196656077002578342108932925693640046298989762289691399012056048139253937882385653600831389370198228562812681");

@@ -1,6 +1,5 @@
-use ark_algebra_test_templates::{curves::*, groups::*};
-use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_std::{rand::Rng, test_rng};
+use ark_algebra_test_templates::curves::*;
+use ark_ec::AffineCurve;
 
 use crate::*;
 
@@ -12,47 +11,10 @@ edwards_tests::<EdwardsParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
 fn test_generator() {
     let generator = EdwardsAffine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_conversion() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
 }
 
 #[test]

@@ -1,7 +1,7 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};

@@ -1,10 +1,10 @@
 use ark_ec::{
     mnt4,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::MontFp;
+use ark_ff::{Field, MontFp};
 
-use crate::{Fq, Fr, FR_ONE};
+use crate::{Fq, Fr};
 
 pub type G1Affine = mnt4::G1Affine<crate::Parameters>;
 pub type G1Projective = mnt4::G1Projective<crate::Parameters>;
@@ -13,7 +13,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -22,21 +22,20 @@ const COFACTOR: &'static [u64] = &[1];
 
     /// COFACTOR^(-1) mod r =
     /// 1
-    const COFACTOR_INV: Fr = FR_ONE;
+    const COFACTOR_INV: Fr = Fr::ONE;
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 2
     /// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L116>
-    const COEFF_A: Fq = MontFp!(Fq, "2");
+    const COEFF_A: Fq = MontFp!("2");
 
     /// COEFF_B = 423894536526684178289416011533888240029318103673896002803341544124054745019340795360841685
     /// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L117>
-    const COEFF_B: Fq = MontFp!(Fq, "423894536526684178289416011533888240029318103673896002803341544124054745019340795360841685");
+    const COEFF_B: Fq = MontFp!("423894536526684178289416011533888240029318103673896002803341544124054745019340795360841685");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 }
 
 // Generator of G1
@@ -45,13 +44,11 @@ // Y = 363732850702582978263902770815145784459747722357071843971107674179038674942891694705904306,
 /// G1_GENERATOR_X
 /// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L137>
 pub const G1_GENERATOR_X: Fq = MontFp!(
-    Fq,
     "60760244141852568949126569781626075788424196370144486719385562369396875346601926534016838"
 );
 
 /// G1_GENERATOR_Y
 /// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L138>
 pub const G1_GENERATOR_Y: Fq = MontFp!(
-    Fq,
     "363732850702582978263902770815145784459747722357071843971107674179038674942891694705904306"
 );

@@ -1,11 +1,11 @@
 use ark_ec::{
     mnt4,
     mnt4::MNT4Parameters,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{MontFp, QuadExt};
+use ark_ff::{Field, MontFp};
 
-use crate::{Fq, Fq2, Fr, FQ_ZERO, G1_COEFF_A_NON_RESIDUE};
+use crate::{Fq, Fq2, Fr, G1_COEFF_A_NON_RESIDUE};
 
 pub type G2Affine = mnt4::G2Affine<crate::Parameters>;
 pub type G2Projective = mnt4::G2Projective<crate::Parameters>;
@@ -14,7 +14,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq2;
     type ScalarField = Fr;
 
@@ -31,7 +31,7 @@ ];
 
     /// COFACTOR^(-1) mod r =
     /// 475922286169261325753349249653048451545124878207887910632124039320641839552134835598065665
-    const COFACTOR_INV: Fr = MontFp!(Fr, "475922286169261325753349249653048451545124878207887910632124039320641839552134835598065665");
+    const COFACTOR_INV: Fr = MontFp!("475922286169261325753349249653048451545124878207887910632124039320641839552134835598065665");
 }
 
 /// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
@@ -40,7 +40,7 @@
 /// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
 pub const MUL_BY_A_C1: Fq = G1_COEFF_A_NON_RESIDUE;
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     const COEFF_A: Fq2 = crate::Parameters::TWIST_COEFF_A;
     // B coefficient of MNT4-298 G2 =
     // ```
@@ -51,23 +51,22 @@ //  = (ZERO, G1_B_COEFF * NON_RESIDUE);
     //  =
     //  (0, 67372828414711144619833451280373307321534573815811166723479321465776723059456513877937430)
     // ```
-    const COEFF_B: Fq2 = QuadExt!(
-        FQ_ZERO,
-        MontFp!(Fq, "67372828414711144619833451280373307321534573815811166723479321465776723059456513877937430"),
+    const COEFF_B: Fq2 = Fq2::new(
+        Fq::ZERO,
+        MontFp!("67372828414711144619833451280373307321534573815811166723479321465776723059456513877937430"),
     );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(elt: &Fq2) -> Fq2 {
-        QuadExt!(MUL_BY_A_C0 * &elt.c0, MUL_BY_A_C1 * &elt.c1,)
+        Fq2::new(MUL_BY_A_C0 * &elt.c0, MUL_BY_A_C1 * &elt.c1)
     }
 }
 
-const G2_GENERATOR_X: Fq2 = QuadExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-const G2_GENERATOR_Y: Fq2 = QuadExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 // Generator of G2
 // These are two Fq elements each because X and Y (and Z) are elements of Fq^2
@@ -76,21 +75,17 @@ //     37620953615500480110935514360923278605464476459712393277679280819942849043649216370485641,
 // Y = 37437409008528968268352521034936931842973546441370663118543015118291998305624025037512482,
 //     424621479598893882672393190337420680597584695892317197646113820787463109735345923009077489,
 pub const G2_GENERATOR_X_C0: Fq = MontFp!(
-    Fq,
     "438374926219350099854919100077809681842783509163790991847867546339851681564223481322252708"
 );
 
 pub const G2_GENERATOR_X_C1: Fq = MontFp!(
-    Fq,
     "37620953615500480110935514360923278605464476459712393277679280819942849043649216370485641"
 );
 
 pub const G2_GENERATOR_Y_C0: Fq = MontFp!(
-    Fq,
     "37437409008528968268352521034936931842973546441370663118543015118291998305624025037512482"
 );
 
 pub const G2_GENERATOR_Y_C1: Fq = MontFp!(
-    Fq,
     "424621479598893882672393190337420680597584695892317197646113820787463109735345923009077489"
 );

@@ -1,7 +1,7 @@
 use ark_ec::models::mnt4::{MNT4Parameters, MNT4};
-use ark_ff::{biginteger::BigInteger320, BigInt, Fp2, MontFp, QuadExt};
+use ark_ff::{biginteger::BigInteger320, BigInt, Field, MontFp};
 
-use crate::{Fq, Fq2Config, Fq4Config, Fr};
+use crate::{Fq, Fq2, Fq2Config, Fq4Config, Fr};
 
 pub mod g1;
 pub mod g2;
@@ -19,14 +19,14 @@
 pub struct Parameters;
 
 impl MNT4Parameters for Parameters {
-    const TWIST: Fp2<Self::Fp2Config> = QuadExt!(FQ_ZERO, FQ_ONE);
+    const TWIST: Fq2 = Fq2::new(Fq::ZERO, Fq::ONE);
     // A coefficient of MNT4-298 G2 =
     // ```
     // mnt4298_twist_coeff_a = mnt4298_Fq2(mnt4298_G1::coeff_a * non_residue, mnt6298_Fq::zero());
     //  = (A_COEFF * NONRESIDUE, ZERO)
     //  = (34, ZERO)
     // ```
-    const TWIST_COEFF_A: Fp2<Self::Fp2Config> = QuadExt!(G1_COEFF_A_NON_RESIDUE, FQ_ZERO);
+    const TWIST_COEFF_A: Fq2 = Fq2::new(G1_COEFF_A_NON_RESIDUE, Fq::ZERO);
 
     const ATE_LOOP_COUNT: &'static [u64] = &[993502997770534912, 5071219579242586943, 2027349];
     const ATE_IS_LOOP_COUNT_NEG: bool = false;
@@ -43,8 +43,4 @@ type G2Parameters = self::g2::Parameters;
 }
 
 // 34
-pub const G1_COEFF_A_NON_RESIDUE: Fq = MontFp!(Fq, "34");
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");
-pub const FR_ZERO: Fr = MontFp!(Fr, "0");
-pub const FR_ONE: Fr = MontFp!(Fr, "1");
+pub const G1_COEFF_A_NON_RESIDUE: Fq = MontFp!("34");

@@ -1,6 +1,6 @@
 use ark_algebra_test_templates::{
     curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test,
-    generate_product_of_pairings_test, groups::*, msm::*,
+    generate_product_of_pairings_test, msm::*,
 };
 use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
 use ark_ff::{Field, One, PrimeField, UniformRand};

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp2::{Fp2, Fp2Config},
-    MontFp,
+    Field, MontFp,
 };
 
-use crate::{Fq, FQ_ONE};
+use crate::Fq;
 
 pub type Fq2 = Fp2<Fq2Config>;
 
@@ -14,12 +14,12 @@ type Fp = Fq;
 
     /// The quadratic non-residue (17) used to construct the extension is
     /// the same as that used in [`libff`](https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L102).
-    const NONRESIDUE: Fq = MontFp!(Fq, "17");
+    const NONRESIDUE: Fq = MontFp!("17");
 
     /// Precomputed coefficients:
     /// `[1, 475922286169261325753349249653048451545124879242694725395555128576210262817955800483758080]`
     const FROBENIUS_COEFF_FP2_C1: &'static [Self::Fp] = &[
-        FQ_ONE,
-        MontFp!(Fq, "475922286169261325753349249653048451545124879242694725395555128576210262817955800483758080"),
+        Fq::ONE,
+        MontFp!("475922286169261325753349249653048451545124879242694725395555128576210262817955800483758080"),
     ];
 }

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp4::{Fp4, Fp4Config},
-    MontFp, QuadExt,
+    Field, MontFp,
 };
 
-use crate::{Fq, Fq2, Fq2Config, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq2, Fq2Config};
 
 pub type Fq4 = Fp4<Fq4Config>;
 
@@ -12,7 +12,7 @@
 impl Fp4Config for Fq4Config {
     type Fp2Config = Fq2Config;
 
-    const NONRESIDUE: Fq2 = QuadExt!(FQ_ZERO, FQ_ONE);
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ZERO, Fq::ONE);
 
     // Coefficients for the Frobenius automorphism.
     // c1[0] = 1,
@@ -23,9 +23,9 @@ //
     // These are calculated as
     // `FROBENIUS_COEFF_FP4_C1[i] = Fp2Config::NONRESIDUE^((q^i - 1) / 4)`.
     const FROBENIUS_COEFF_FP4_C1: &'static [Fq] = &[
-        FQ_ONE,
-        MontFp!(Fq, "7684163245453501615621351552473337069301082060976805004625011694147890954040864167002308"),
-        MontFp!(Fq, "475922286169261325753349249653048451545124879242694725395555128576210262817955800483758080"),
-        MontFp!(Fq, "468238122923807824137727898100575114475823797181717920390930116882062371863914936316755773"),
+        Fq::ONE,
+        MontFp!("7684163245453501615621351552473337069301082060976805004625011694147890954040864167002308"),
+        MontFp!("475922286169261325753349249653048451545124879242694725395555128576210262817955800483758080"),
+        MontFp!("468238122923807824137727898100575114475823797181717920390930116882062371863914936316755773"),
     ];
 }

@@ -1,7 +1,7 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};

@@ -1,10 +1,10 @@
 use ark_ec::{
     mnt4,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::MontFp;
+use ark_ff::{Field, MontFp};
 
-use crate::{Fq, Fr, FR_ONE};
+use crate::{Fq, Fr};
 
 pub type G1Affine = mnt4::G1Affine<crate::Parameters>;
 pub type G1Projective = mnt4::G1Projective<crate::Parameters>;
@@ -13,7 +13,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -21,19 +21,18 @@ /// COFACTOR = 1
     const COFACTOR: &'static [u64] = &[1];
 
     /// COFACTOR^(-1) mod r = 1
-    const COFACTOR_INV: Fr = FR_ONE;
+    const COFACTOR_INV: Fr = Fr::ONE;
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 2
-    const COEFF_A: Fq = MontFp!(Fq, "2");
+    const COEFF_A: Fq = MontFp!("2");
 
     /// COEFF_B = 0x01373684A8C9DCAE7A016AC5D7748D3313CD8E39051C596560835DF0C9E50A5B59B882A92C78DC537E51A16703EC9855C77FC3D8BB21C8D68BB8CFB9DB4B8C8FBA773111C36C8B1B4E8F1ECE940EF9EAAD265458E06372009C9A0491678EF4
-    const COEFF_B: Fq = MontFp!(Fq, "28798803903456388891410036793299405764940372360099938340752576406393880372126970068421383312482853541572780087363938442377933706865252053507077543420534380486492786626556269083255657125025963825610840222568694137138741554679540");
+    const COEFF_B: Fq = MontFp!("28798803903456388891410036793299405764940372360099938340752576406393880372126970068421383312482853541572780087363938442377933706865252053507077543420534380486492786626556269083255657125025963825610840222568694137138741554679540");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 }
 
 // Generator of G1
@@ -41,8 +40,8 @@ // X = 7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569,
 // Y = 6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648,
 /// G1_GENERATOR_X =
 /// 7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569");
+pub const G1_GENERATOR_X: Fq = MontFp!("7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569");
 
 /// G1_GENERATOR_Y =
 /// 6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648");
+pub const G1_GENERATOR_Y: Fq = MontFp!("6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648");

@@ -1,11 +1,11 @@
 use ark_ec::{
     mnt4,
     mnt4::MNT4Parameters,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{MontFp, QuadExt};
+use ark_ff::{Field, MontFp};
 
-use crate::{Fq, Fq2, Fr, FQ_ZERO, G1_COEFF_A_NON_RESIDUE};
+use crate::{Fq, Fq2, Fr, G1_COEFF_A_NON_RESIDUE};
 
 pub type G2Affine = mnt4::G2Affine<crate::Parameters>;
 pub type G2Projective = mnt4::G2Projective<crate::Parameters>;
@@ -14,7 +14,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq2;
     type ScalarField = Fr;
 
@@ -38,7 +38,7 @@ ];
 
     /// COFACTOR^(-1) mod r =
     /// 102345604409665481004734934052318066391634848395005988700111949231215905051467807945653833683883449458834877235200
-    const COFACTOR_INV: Fr = MontFp!(Fr, "102345604409665481004734934052318066391634848395005988700111949231215905051467807945653833683883449458834877235200");
+    const COFACTOR_INV: Fr = MontFp!("102345604409665481004734934052318066391634848395005988700111949231215905051467807945653833683883449458834877235200");
 }
 
 /// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
@@ -47,7 +47,7 @@
 /// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
 pub const MUL_BY_A_C1: Fq = G1_COEFF_A_NON_RESIDUE;
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     const COEFF_A: Fq2 = crate::Parameters::TWIST_COEFF_A;
     // B coefficient of MNT4-753 G2 =
     // ```
@@ -58,23 +58,22 @@ //  = (ZERO, G1_B_COEFF * NON_RESIDUE);
     //  =
     //  (0, 39196523001581428369576759982967177918859161321667605855515469914917622337081756705006832951954384669101573360625169461998308377011601613979275218690841934572954991361632773738259652003389826903175898479855893660378722437317212)
     // ```
-    const COEFF_B: Fq2 = QuadExt!(
-        FQ_ZERO,
-        MontFp!(Fq, "39196523001581428369576759982967177918859161321667605855515469914917622337081756705006832951954384669101573360625169461998308377011601613979275218690841934572954991361632773738259652003389826903175898479855893660378722437317212")
+    const COEFF_B: Fq2 = Fq2::new(
+        Fq::ZERO,
+        MontFp!("39196523001581428369576759982967177918859161321667605855515469914917622337081756705006832951954384669101573360625169461998308377011601613979275218690841934572954991361632773738259652003389826903175898479855893660378722437317212")
     );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(elt: &Fq2) -> Fq2 {
-        QuadExt!(MUL_BY_A_C0 * &elt.c0, MUL_BY_A_C1 * &elt.c1,)
+        Fq2::new(MUL_BY_A_C0 * &elt.c0, MUL_BY_A_C1 * &elt.c1)
     }
 }
 
-const G2_GENERATOR_X: Fq2 = QuadExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-const G2_GENERATOR_Y: Fq2 = QuadExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 // Generator of G2
 // These are two Fq elements each because X and Y (and Z) are elements of Fq^2
@@ -82,10 +81,10 @@ // X = 29483965110843144675703364744708836524643960105538608078862508397502447349913068434941060515343254862580437318493682762113105361632548148204806052114008731372757389645383891982211245013965175213456066452587869519098351487925167,
 // 19706011319630172391076079624799753948158506771222147486237995321925443331396169656568431378974558350664383559981183980668976846806019030432389169137953988990802000581078994008283967768348275973921598166274857631001635633631000,
 // Y = 39940152670760519653940320314827327941993141403708338666925204282084477074754642625849927569427860786384998614863651207257467076192649385174108085803168743803491780568503369317093191101779534035377266300185099318717465441820654,
 // 17608637424964395737041291373756657139607306440193731804102457011726690702169238966996114255971643893157857311132388792357391583164125870757541009035041469463366528798593952884745987697403056488744603829437448927398468360797245,
-pub const G2_GENERATOR_X_C0: Fq = MontFp!(Fq, "29483965110843144675703364744708836524643960105538608078862508397502447349913068434941060515343254862580437318493682762113105361632548148204806052114008731372757389645383891982211245013965175213456066452587869519098351487925167");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("29483965110843144675703364744708836524643960105538608078862508397502447349913068434941060515343254862580437318493682762113105361632548148204806052114008731372757389645383891982211245013965175213456066452587869519098351487925167");
 
-pub const G2_GENERATOR_X_C1: Fq = MontFp!(Fq, "19706011319630172391076079624799753948158506771222147486237995321925443331396169656568431378974558350664383559981183980668976846806019030432389169137953988990802000581078994008283967768348275973921598166274857631001635633631000");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("19706011319630172391076079624799753948158506771222147486237995321925443331396169656568431378974558350664383559981183980668976846806019030432389169137953988990802000581078994008283967768348275973921598166274857631001635633631000");
 
-pub const G2_GENERATOR_Y_C0: Fq = MontFp!(Fq, "39940152670760519653940320314827327941993141403708338666925204282084477074754642625849927569427860786384998614863651207257467076192649385174108085803168743803491780568503369317093191101779534035377266300185099318717465441820654");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("39940152670760519653940320314827327941993141403708338666925204282084477074754642625849927569427860786384998614863651207257467076192649385174108085803168743803491780568503369317093191101779534035377266300185099318717465441820654");
 
-pub const G2_GENERATOR_Y_C1: Fq = MontFp!(Fq, "17608637424964395737041291373756657139607306440193731804102457011726690702169238966996114255971643893157857311132388792357391583164125870757541009035041469463366528798593952884745987697403056488744603829437448927398468360797245");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("17608637424964395737041291373756657139607306440193731804102457011726690702169238966996114255971643893157857311132388792357391583164125870757541009035041469463366528798593952884745987697403056488744603829437448927398468360797245");

@@ -1,7 +1,7 @@
 use ark_ec::models::mnt4::{MNT4Parameters, MNT4};
 use ark_ff::{
     biginteger::{BigInt, BigInteger768},
-    Fp2, MontFp, QuadExt,
+    Field, Fp2, MontFp,
 };
 
 use crate::{Fq, Fq2Config, Fq4Config, Fr};
@@ -22,14 +22,14 @@
 pub struct Parameters;
 
 impl MNT4Parameters for Parameters {
-    const TWIST: Fp2<Self::Fp2Config> = QuadExt!(FQ_ZERO, FQ_ONE);
+    const TWIST: Fp2<Self::Fp2Config> = Fp2::new(Fq::ZERO, Fq::ONE);
     // A coefficient of MNT4-753 G2 =
     // ```
     // mnt4753_twist_coeff_a = mnt4753_Fq2(mnt4753_G1::coeff_a * non_residue, mnt6753_Fq::zero());
     //  = (A_COEFF * NONRESIDUE, ZERO)
     //  = (26, ZERO)
     // ```
-    const TWIST_COEFF_A: Fp2<Self::Fp2Config> = QuadExt!(G1_COEFF_A_NON_RESIDUE, FQ_ZERO,);
+    const TWIST_COEFF_A: Fp2<Self::Fp2Config> = Fp2::new(G1_COEFF_A_NON_RESIDUE, Fq::ZERO);
     // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt4753.ml
     const ATE_LOOP_COUNT: &'static [u64] = &[
         8824542903220142080,
@@ -66,9 +66,4 @@ type G2Parameters = self::g2::Parameters;
 }
 
 // 26
-pub const G1_COEFF_A_NON_RESIDUE: Fq = MontFp!(Fq, "26");
-
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");
-pub const FR_ZERO: Fr = MontFp!(Fr, "0");
-pub const FR_ONE: Fr = MontFp!(Fr, "1");
+pub const G1_COEFF_A_NON_RESIDUE: Fq = MontFp!("26");

@@ -1,6 +1,6 @@
 use ark_algebra_test_templates::{
     curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test,
-    generate_product_of_pairings_test, groups::*, msm::*,
+    generate_product_of_pairings_test, msm::*,
 };
 use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
 use ark_ff::{Field, One, PrimeField, UniformRand};

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp2::{Fp2, Fp2Config},
-    MontFp,
+    Field, MontFp,
 };
 
-use crate::{Fq, FQ_ONE};
+use crate::Fq;
 
 pub type Fq2 = Fp2<Fq2Config>;
 
@@ -13,13 +13,13 @@ impl Fp2Config for Fq2Config {
     type Fp = Fq;
 
     // non_residue = 13
-    const NONRESIDUE: Fq = MontFp!(Fq, "13");
+    const NONRESIDUE: Fq = MontFp!("13");
 
     // Coefficients:
     // [1, 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600]
     // see https://github.com/o1-labs/snarky/blob/2cf5ef3a14989e57c17518832b3c52590068fc48/src/camlsnark_c/libsnark-caml/depends/libff/libff/algebra/curves/mnt753/mnt4753/mnt4753_init.cpp
     const FROBENIUS_COEFF_FP2_C1: &'static [Self::Fp] = &[
-        FQ_ONE,
-        MontFp!(Fq, "41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600"),
+        Fq::ONE,
+        MontFp!("41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600"),
     ];
 }

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp4::{Fp4, Fp4Config},
-    MontFp, QuadExt,
+    Field, MontFp,
 };
 
-use crate::{Fq, Fq2, Fq2Config, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq2, Fq2Config};
 
 pub type Fq4 = Fp4<Fq4Config>;
 
@@ -12,7 +12,7 @@
 impl Fp4Config for Fq4Config {
     type Fp2Config = Fq2Config;
 
-    const NONRESIDUE: Fq2 = QuadExt!(FQ_ZERO, FQ_ONE);
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ZERO, Fq::ONE);
 
     // Coefficients for the Frobenius automorphism.
     // c1[0] = 1,
@@ -23,9 +23,9 @@ //
     // These are calculated as `FROBENIUS_COEFF_FP4_C1[i] =
     // Fp2Config::NONRESIDUE^((q^i - 1) / 4)`.
     const FROBENIUS_COEFF_FP4_C1: &'static [Fq] = &[
-        FQ_ONE,
-        MontFp!(Fq, "18691656569803771296244054523431852464958959799019013859007259692542121208304602539555350517075508287829753932558576476751900235650227380562700444433662761577027341858128610410779088384480737679672900770810745291515010467307990"),
-        MontFp!(Fq, "41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600"),
-        MontFp!(Fq, "23206834398115182106100160267808784663211750120934935212776243228483231604266504233503543246714830633588317039329677309362453490879357004638891161288350364891904062489821230132228897943262725174047727280881395973788104254381611"),
+        Fq::ONE,
+        MontFp!("18691656569803771296244054523431852464958959799019013859007259692542121208304602539555350517075508287829753932558576476751900235650227380562700444433662761577027341858128610410779088384480737679672900770810745291515010467307990"),
+        MontFp!("41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600"),
+        MontFp!("23206834398115182106100160267808784663211750120934935212776243228483231604266504233503543246714830633588317039329677309362453490879357004638891161288350364891904062489821230132228897943262725174047727280881395973788104254381611"),
     ];
 }

@@ -1,7 +1,7 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};

@@ -1,8 +1,8 @@
 use ark_ec::{
     mnt6,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::MontFp;
+use ark_ff::{Field, MontFp};
 
 use crate::{Fq, Fr};
 
@@ -13,7 +13,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -21,25 +21,24 @@ /// COFACTOR = 1
     const COFACTOR: &'static [u64] = &[1];
 
     /// COFACTOR^(-1) mod r = 1
-    const COFACTOR_INV: Fr = MontFp!(Fr, "1");
+    const COFACTOR_INV: Fr = Fr::ONE;
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 11
-    const COEFF_A: Fq = MontFp!(Fq, "11");
+    const COEFF_A: Fq = MontFp!("11");
 
     /// COEFF_B = 106700080510851735677967319632585352256454251201367587890185989362936000262606668469523074
-    const COEFF_B: Fq = MontFp!(Fq, "106700080510851735677967319632585352256454251201367587890185989362936000262606668469523074");
+    const COEFF_B: Fq = MontFp!("106700080510851735677967319632585352256454251201367587890185989362936000262606668469523074");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 }
 
 /// G1_GENERATOR_X =
 #[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "336685752883082228109289846353937104185698209371404178342968838739115829740084426881123453");
+pub const G1_GENERATOR_X: Fq = MontFp!("336685752883082228109289846353937104185698209371404178342968838739115829740084426881123453");
 
 /// G1_GENERATOR_Y =
 #[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "402596290139780989709332707716568920777622032073762749862342374583908837063963736098549800");
+pub const G1_GENERATOR_Y: Fq = MontFp!("402596290139780989709332707716568920777622032073762749862342374583908837063963736098549800");

@@ -1,11 +1,11 @@
 use ark_ec::{
     mnt6,
     mnt6::MNT6Parameters,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{CubicExt, MontFp};
+use ark_ff::{Field, MontFp};
 
-use crate::{g1, Fq, Fq3, Fr, FQ_ZERO};
+use crate::{g1, Fq, Fq3, Fr};
 
 pub type G2Affine = mnt6::G2Affine<crate::Parameters>;
 pub type G2Projective = mnt6::G2Projective<crate::Parameters>;
@@ -14,7 +14,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq3;
     type ScalarField = Fr;
 
@@ -37,36 +37,34 @@
     /// COFACTOR^(-1) mod r =
     /// 79320381028210220958891541608841408590854146655427655872973753568875979721417185067925504
     const COFACTOR_INV: Fr = MontFp!(
-        Fr,
         "79320381028210220958891541608841408590854146655427655872973753568875979721417185067925504"
     );
 }
 
 /// MUL_BY_A_C0 = NONRESIDUE * COEFF_A = 5 * 11
-pub const MUL_BY_A_C0: Fq = MontFp!(Fq, "55");
+pub const MUL_BY_A_C0: Fq = MontFp!("55");
 
 /// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
-pub const MUL_BY_A_C1: Fq = MontFp!(Fq, "55");
+pub const MUL_BY_A_C1: Fq = MontFp!("55");
 
 /// MUL_BY_A_C2 = COEFF_A
 pub const MUL_BY_A_C2: Fq = g1::Parameters::COEFF_A;
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     const COEFF_A: Fq3 = crate::Parameters::TWIST_COEFF_A;
-    const COEFF_B: Fq3 = CubicExt!(
+    const COEFF_B: Fq3 = Fq3::new(
         // 5 * G1::COEFF_B
-        MontFp!(Fq, "57578116384997352636487348509878309737146377454014423897662211075515354005624851787652233"),
-        FQ_ZERO,
-        FQ_ZERO,
+        MontFp!("57578116384997352636487348509878309737146377454014423897662211075515354005624851787652233"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(elt: &Fq3) -> Fq3 {
-        CubicExt!(
+        Fq3::new(
             MUL_BY_A_C0 * &elt.c1,
             MUL_BY_A_C1 * &elt.c2,
             MUL_BY_A_C2 * &elt.c0,
@@ -74,31 +72,25 @@ )
     }
 }
 
-const G2_GENERATOR_X: Fq3 = CubicExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
-const G2_GENERATOR_Y: Fq3 = CubicExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
+const G2_GENERATOR_X: Fq3 = Fq3::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
+const G2_GENERATOR_Y: Fq3 = Fq3::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
 
 pub const G2_GENERATOR_X_C0: Fq = MontFp!(
-    Fq,
     "421456435772811846256826561593908322288509115489119907560382401870203318738334702321297427"
 );
 pub const G2_GENERATOR_X_C1: Fq = MontFp!(
-    Fq,
     "103072927438548502463527009961344915021167584706439945404959058962657261178393635706405114"
 );
 pub const G2_GENERATOR_X_C2: Fq = MontFp!(
-    Fq,
     "143029172143731852627002926324735183809768363301149009204849580478324784395590388826052558"
 );
 
 pub const G2_GENERATOR_Y_C0: Fq = MontFp!(
-    Fq,
     "464673596668689463130099227575639512541218133445388869383893594087634649237515554342751377"
 );
 pub const G2_GENERATOR_Y_C1: Fq = MontFp!(
-    Fq,
     "100642907501977375184575075967118071807821117960152743335603284583254620685343989304941678"
 );
 pub const G2_GENERATOR_Y_C2: Fq = MontFp!(
-    Fq,
     "123019855502969896026940545715841181300275180157288044663051565390506010149881373807142903"
 );

@@ -1,8 +1,8 @@
 use ark_ec::{
     models::mnt6::{MNT6Parameters, MNT6},
-    SWModelParameters,
+    short_weierstrass::SWCurveConfig,
 };
-use ark_ff::{biginteger::BigInteger320, BigInt, CubicExt, Fp3, MontFp};
+use ark_ff::{biginteger::BigInteger320, BigInt, Field, Fp3};
 
 use crate::{Fq, Fq3Config, Fq6Config, Fr};
 
@@ -22,9 +22,9 @@
 pub struct Parameters;
 
 impl MNT6Parameters for Parameters {
-    const TWIST: Fp3<Self::Fp3Config> = CubicExt!(FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const TWIST: Fp3<Self::Fp3Config> = Fp3::<Self::Fp3Config>::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
     const TWIST_COEFF_A: Fp3<Self::Fp3Config> =
-        CubicExt!(FQ_ZERO, FQ_ZERO, g1::Parameters::COEFF_A,);
+        Fp3::<Self::Fp3Config>::new(Fq::ZERO, Fq::ZERO, g1::Parameters::COEFF_A);
     const ATE_LOOP_COUNT: &'static [u64] = &[0xdc9a1b671660000, 0x46609756bec2a33f, 0x1eef55];
     const ATE_IS_LOOP_COUNT_NEG: bool = true;
     const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger320 = BigInt::new([0x1, 0x0, 0x0, 0x0, 0x0]);
@@ -38,6 +38,3 @@ type Fp6Config = Fq6Config;
     type G1Parameters = self::g1::Parameters;
     type G2Parameters = self::g2::Parameters;
 }
-
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");

@@ -1,6 +1,6 @@
 use ark_algebra_test_templates::{
     curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test,
-    generate_product_of_pairings_test, groups::*, msm::*,
+    generate_product_of_pairings_test, msm::*,
 };
 use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
 use ark_ff::{Field, One, PrimeField, UniformRand};

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp3::{Fp3, Fp3Config},
-    CubicExt, MontFp,
+    Field, MontFp,
 };
 
-use crate::{fq::Fq, FQ_ZERO};
+use crate::fq::Fq;
 
 pub type Fq3 = Fp3<Fq3Config>;
 
@@ -12,7 +12,7 @@
 impl Fp3Config for Fq3Config {
     type Fp = Fq;
 
-    const NONRESIDUE: Fq = MontFp!(Fq, "5");
+    const NONRESIDUE: Fq = MontFp!("5");
 
     const TWO_ADICITY: u32 = 34;
 
@@ -34,16 +34,16 @@ 0x62e990f43dfc42d6,
         0x6878f58,
     ];
 
-    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = CubicExt!(
-        MontFp!(Fq, "154361449678783505076984156275977937654331103361174469632346230549735979552469642799720052"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("154361449678783505076984156275977937654331103361174469632346230549735979552469642799720052"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        MontFp!(Fq, "1"),
-        MontFp!(Fq, "471738898967521029133040851318449165997304108729558973770077319830005517129946578866686956"),
-        MontFp!(Fq, "4183387201740296620308398334599285547820769823264541783190415909159130177461911693276180"),
+        Fq::ONE,
+        MontFp!("471738898967521029133040851318449165997304108729558973770077319830005517129946578866686956"),
+        MontFp!("4183387201740296620308398334599285547820769823264541783190415909159130177461911693276180"),
     ];
 
     const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp6_2over3::{Fp6, Fp6Config},
-    CubicExt, MontFp,
+    Field, MontFp,
 };
 
-use crate::{Fq, Fq3, Fq3Config, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq3, Fq3Config};
 
 pub type Fq6 = Fp6<Fq6Config>;
 
@@ -12,14 +12,14 @@
 impl Fp6Config for Fq6Config {
     type Fp3Config = Fq3Config;
 
-    const NONRESIDUE: Fq3 = CubicExt!(FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        MontFp!(Fq, "1"),
-        MontFp!(Fq, "471738898967521029133040851318449165997304108729558973770077319830005517129946578866686957"),
-        MontFp!(Fq, "471738898967521029133040851318449165997304108729558973770077319830005517129946578866686956"),
-        MontFp!(Fq, "475922286169261325753349249653048451545124878552823515553267735739164647307408490559963136"),
-        MontFp!(Fq, "4183387201740296620308398334599285547820769823264541783190415909159130177461911693276180"),
-        MontFp!(Fq, "4183387201740296620308398334599285547820769823264541783190415909159130177461911693276181"),
+        Fq::ONE,
+        MontFp!("471738898967521029133040851318449165997304108729558973770077319830005517129946578866686957"),
+        MontFp!("471738898967521029133040851318449165997304108729558973770077319830005517129946578866686956"),
+        MontFp!("475922286169261325753349249653048451545124878552823515553267735739164647307408490559963136"),
+        MontFp!("4183387201740296620308398334599285547820769823264541783190415909159130177461911693276180"),
+        MontFp!("4183387201740296620308398334599285547820769823264541783190415909159130177461911693276181"),
     ];
 }

@@ -2,7 +2,7 @@ use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
-    fields::{models::fp6_2over3::*, quadratic_extension::QuadExtConfig, SquareRootField},
+    fields::{models::fp6_2over3::*, quadratic_extension::QuadExtConfig},
     Field, PrimeField,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -11,7 +11,7 @@ use core::ops::{AddAssign, MulAssign, SubAssign};
 
 use crate::*;
 
-generate_field_test!(mnt6_298; fq3; fq6; mont(5, 5); );
+generate_field_test!(mnt6_298; fq3; fq6_2_on_3; mont(5, 5); );
 generate_field_serialization_test!(mnt6_298;);
 
 #[test]

@@ -1,10 +1,10 @@
 use ark_ec::{
     mnt6,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::MontFp;
+use ark_ff::{Field, MontFp};
 
-use crate::{Fq, Fr, FR_ONE};
+use crate::{Fq, Fr};
 
 pub type G1Affine = mnt6::G1Affine<crate::Parameters>;
 pub type G1Projective = mnt6::G1Projective<crate::Parameters>;
@@ -13,7 +13,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -21,19 +21,18 @@ /// COFACTOR = 1
     const COFACTOR: &'static [u64] = &[1];
 
     /// COFACTOR^(-1) mod r = 1
-    const COFACTOR_INV: Fr = FR_ONE;
+    const COFACTOR_INV: Fr = Fr::ONE;
 }
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     /// COEFF_A = 11
-    const COEFF_A: Fq = MontFp!(Fq, "11");
+    const COEFF_A: Fq = MontFp!("11");
 
     /// COEFF_B = 0x7DA285E70863C79D56446237CE2E1468D14AE9BB64B2BB01B10E60A5D5DFE0A25714B7985993F62F03B22A9A3C737A1A1E0FCF2C43D7BF847957C34CCA1E3585F9A80A95F401867C4E80F4747FDE5ABA7505BA6FCF2485540B13DFC8468A
-    const COEFF_B: Fq = MontFp!(Fq, "11625908999541321152027340224010374716841167701783584648338908235410859267060079819722747939267925389062611062156601938166010098747920378738927832658133625454260115409075816187555055859490253375704728027944315501122723426879114");
+    const COEFF_B: Fq = MontFp!("11625908999541321152027340224010374716841167701783584648338908235410859267060079819722747939267925389062611062156601938166010098747920378738927832658133625454260115409075816187555055859490253375704728027944315501122723426879114");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 }
 
 // Generator of G1
@@ -41,8 +40,8 @@ // X = 3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728,
 // Y = 27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569,
 /// G1_GENERATOR_X =
 /// 3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728,
-pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728");
+pub const G1_GENERATOR_X: Fq = MontFp!("3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728");
 
 /// G1_GENERATOR_Y =
 /// 27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569,
-pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569");
+pub const G1_GENERATOR_Y: Fq = MontFp!("27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569");

@@ -1,11 +1,11 @@
 use ark_ec::{
     mnt6,
     mnt6::MNT6Parameters,
-    models::{ModelParameters, SWModelParameters},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{CubicExt, MontFp};
+use ark_ff::{Field, MontFp};
 
-use crate::{g1, Fq, Fq3, Fr, FQ_ZERO};
+use crate::{g1, Fq, Fq3, Fr};
 
 pub type G2Affine = mnt6::G2Affine<crate::Parameters>;
 pub type G2Projective = mnt6::G2Projective<crate::Parameters>;
@@ -14,7 +14,7 @@
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
     type BaseField = Fq3;
     type ScalarField = Fr;
 
@@ -50,23 +50,23 @@ ];
 
     /// COFACTOR^(-1) mod r =
     /// 6983081827986492233724035798540106188028451653325658178630583820170892135428517795509815627298389820236345161981341515817589065927929152555581161598204976128690232061758269440757592419606754539638220064054062394397574161203200
-    const COFACTOR_INV: Fr = MontFp!(Fr, "6983081827986492233724035798540106188028451653325658178630583820170892135428517795509815627298389820236345161981341515817589065927929152555581161598204976128690232061758269440757592419606754539638220064054062394397574161203200");
+    const COFACTOR_INV: Fr = MontFp!("6983081827986492233724035798540106188028451653325658178630583820170892135428517795509815627298389820236345161981341515817589065927929152555581161598204976128690232061758269440757592419606754539638220064054062394397574161203200");
 }
 
 /// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
 ///             = 11 * 11
 ///             = 121
-pub const MUL_BY_A_C0: Fq = MontFp!(Fq, "121");
+pub const MUL_BY_A_C0: Fq = MontFp!("121");
 
 /// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
 ///             = 11 * 11
 ///             = 121
-pub const MUL_BY_A_C1: Fq = MontFp!(Fq, "121");
+pub const MUL_BY_A_C1: Fq = MontFp!("121");
 
 /// MUL_BY_A_C2 = COEFF_A
 pub const MUL_BY_A_C2: Fq = g1::Parameters::COEFF_A;
 
-impl SWModelParameters for Parameters {
+impl SWCurveConfig for Parameters {
     const COEFF_A: Fq3 = crate::Parameters::TWIST_COEFF_A;
     // B coefficient of MNT6-753 G2 =
     // ```
@@ -78,19 +78,18 @@ //  =
     //  (2189526091197672465268098090392210500740714959757583916377481826443393499947557697773546040576162515434508768057245887856591913752342600919117433675080691499697020523783784738694360040853591723916201150207746019687604267190251,
     //  0, 0)
     // ```
-    const COEFF_B: Fq3 = CubicExt!(
-        MontFp!(Fq, "2189526091197672465268098090392210500740714959757583916377481826443393499947557697773546040576162515434508768057245887856591913752342600919117433675080691499697020523783784738694360040853591723916201150207746019687604267190251"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const COEFF_B: Fq3 = Fq3::new(
+        MontFp!("2189526091197672465268098090392210500740714959757583916377481826443393499947557697773546040576162515434508768057245887856591913752342600919117433675080691499697020523783784738694360040853591723916201150207746019687604267190251"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(elt: &Fq3) -> Fq3 {
-        CubicExt!(
+        Fq3::new(
             MUL_BY_A_C0 * &elt.c1,
             MUL_BY_A_C1 * &elt.c2,
             MUL_BY_A_C2 * &elt.c0,
@@ -98,8 +97,8 @@ )
     }
 }
 
-const G2_GENERATOR_X: Fq3 = CubicExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
-const G2_GENERATOR_Y: Fq3 = CubicExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
+const G2_GENERATOR_X: Fq3 = Fq3::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
+const G2_GENERATOR_Y: Fq3 = Fq3::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
 
 // Generator of G2
 // These are three Fq elements each because X and Y (and Z) are elements of Fq^3
@@ -109,10 +108,10 @@ // 36955296703808958167583270646821654948157955258947892285629161090141878438357164213613114995903637211606408001037026832604054121847388692538440756596264746452765613740820430501353237866984394057660379098674983614861254438847846,
 // Y = 2540920530670785421282147216459500299597350984927286541981768941513322907384197363939300669100157141915897390694710534916701460991329498878429407641200901974650893207493883271892985923686300670742888673128384350189165542294615,
 // 7768974215205248225654340523113146529854477025417883273460270519532499370133542215655437897583245920162220909271982265882784840026754554720358946490360213245668334549692889019612343620295335698052097726325099648573158597797497,
 // 21014872727619291834131369222699267167761185012487859171850226473555446863681002782100371394603357586906967186931035615146288030444598977758226767063525819170917389755555854704165900869058188909090444447822088242504281789869689,
-pub const G2_GENERATOR_X_C0: Fq = MontFp!(Fq, "27250797394340459586637772414334383652934225310678303542554641987990991970766156209996739240400887081904395745019996048910447071686918567661896491214767494514394154061111870331668445455228882471000120574964265209669155206168252");
-pub const G2_GENERATOR_X_C1: Fq = MontFp!(Fq, "35762481056967998715733586393399457882827322353696313323665483142561285210083843314423554450886956650265947502285422529615273790981238406393402603210224104850580302463396274854098657541573494421834514772635884262388058080180368");
-pub const G2_GENERATOR_X_C2: Fq = MontFp!(Fq, "36955296703808958167583270646821654948157955258947892285629161090141878438357164213613114995903637211606408001037026832604054121847388692538440756596264746452765613740820430501353237866984394057660379098674983614861254438847846");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("27250797394340459586637772414334383652934225310678303542554641987990991970766156209996739240400887081904395745019996048910447071686918567661896491214767494514394154061111870331668445455228882471000120574964265209669155206168252");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("35762481056967998715733586393399457882827322353696313323665483142561285210083843314423554450886956650265947502285422529615273790981238406393402603210224104850580302463396274854098657541573494421834514772635884262388058080180368");
+pub const G2_GENERATOR_X_C2: Fq = MontFp!("36955296703808958167583270646821654948157955258947892285629161090141878438357164213613114995903637211606408001037026832604054121847388692538440756596264746452765613740820430501353237866984394057660379098674983614861254438847846");
 
-pub const G2_GENERATOR_Y_C0: Fq = MontFp!(Fq, "2540920530670785421282147216459500299597350984927286541981768941513322907384197363939300669100157141915897390694710534916701460991329498878429407641200901974650893207493883271892985923686300670742888673128384350189165542294615");
-pub const G2_GENERATOR_Y_C1: Fq = MontFp!(Fq, "7768974215205248225654340523113146529854477025417883273460270519532499370133542215655437897583245920162220909271982265882784840026754554720358946490360213245668334549692889019612343620295335698052097726325099648573158597797497");
-pub const G2_GENERATOR_Y_C2: Fq = MontFp!(Fq, "21014872727619291834131369222699267167761185012487859171850226473555446863681002782100371394603357586906967186931035615146288030444598977758226767063525819170917389755555854704165900869058188909090444447822088242504281789869689");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("2540920530670785421282147216459500299597350984927286541981768941513322907384197363939300669100157141915897390694710534916701460991329498878429407641200901974650893207493883271892985923686300670742888673128384350189165542294615");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("7768974215205248225654340523113146529854477025417883273460270519532499370133542215655437897583245920162220909271982265882784840026754554720358946490360213245668334549692889019612343620295335698052097726325099648573158597797497");
+pub const G2_GENERATOR_Y_C2: Fq = MontFp!("21014872727619291834131369222699267167761185012487859171850226473555446863681002782100371394603357586906967186931035615146288030444598977758226767063525819170917389755555854704165900869058188909090444447822088242504281789869689");

@@ -1,8 +1,8 @@
 use ark_ec::models::{
     mnt6::{MNT6Parameters, MNT6},
-    SWModelParameters,
+    short_weierstrass::SWCurveConfig,
 };
-use ark_ff::{biginteger::BigInteger768, BigInt, CubicExt, Fp3, MontFp};
+use ark_ff::{biginteger::BigInteger768, BigInt, Field, Fp3};
 
 use crate::{Fq, Fq3Config, Fq6Config, Fr};
 
@@ -22,7 +22,7 @@
 pub struct Parameters;
 
 impl MNT6Parameters for Parameters {
-    const TWIST: Fp3<Self::Fp3Config> = CubicExt!(FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const TWIST: Fp3<Self::Fp3Config> = Fp3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
     // A coefficient of MNT6-753 G2 =
     // ```
     // mnt6753_twist_coeff_a = mnt6753_Fq3(mnt6753_Fq::zero(), mnt6753_Fq::zero(),
@@ -30,7 +30,7 @@ //                                  mnt6753_G1::coeff_a);
     //  = (ZERO, ZERO, A_COEFF);
     // ```
     const TWIST_COEFF_A: Fp3<Self::Fp3Config> =
-        CubicExt!(FQ_ZERO, FQ_ZERO, g1::Parameters::COEFF_A,);
+        Fp3::new(Fq::ZERO, Fq::ZERO, g1::Parameters::COEFF_A);
 
     // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt6753.ml
     const ATE_LOOP_COUNT: &'static [u64] = &[
@@ -66,8 +66,3 @@ type Fp6Config = Fq6Config;
     type G1Parameters = self::g1::Parameters;
     type G2Parameters = self::g2::Parameters;
 }
-
-pub const FQ_ZERO: Fq = MontFp!(Fq, "0");
-pub const FQ_ONE: Fq = MontFp!(Fq, "1");
-pub const FR_ZERO: Fr = MontFp!(Fr, "0");
-pub const FR_ONE: Fr = MontFp!(Fr, "1");

@@ -1,6 +1,6 @@
 use ark_algebra_test_templates::{
     curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test,
-    generate_product_of_pairings_test, groups::*, msm::*,
+    generate_product_of_pairings_test, msm::*,
 };
 use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
 use ark_ff::{Field, One, PrimeField, UniformRand};

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp3::{Fp3, Fp3Config},
-    CubicExt, MontFp,
+    Field, MontFp,
 };
 
-use crate::{fq::Fq, FQ_ONE, FQ_ZERO};
+use crate::fq::Fq;
 
 pub type Fq3 = Fp3<Fq3Config>;
 
@@ -12,7 +12,7 @@
 impl Fp3Config for Fq3Config {
     type Fp = Fq;
 
-    const NONRESIDUE: Fq = MontFp!(Fq, "11");
+    const NONRESIDUE: Fq = MontFp!("11");
 
     const TWO_ADICITY: u32 = 30;
 
@@ -56,10 +56,10 @@ 3114545746551080,
     ];
 
     /// (11^T, 0, 0)
-    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = CubicExt!(
-        MontFp!(Fq, "22168644070733283197994897338612733221095941481265408161807376791727499343083607817089033595478370212662133368413166734396127674284827734481031659015434501966360165723728649019457855887066657739809176476252080335185730833468062"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("22168644070733283197994897338612733221095941481265408161807376791727499343083607817089033595478370212662133368413166734396127674284827734481031659015434501966360165723728649019457855887066657739809176476252080335185730833468062"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     // Coefficients for the Frobenius automorphism.
@@ -67,14 +67,14 @@ // c1[0] = 1,
     // c1[1] = 24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132
     // c1[2] = 17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868,
     const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        FQ_ONE,
-        MontFp!(Fq, "24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132"),
-        MontFp!(Fq, "17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868"),
+        Fq::ONE,
+        MontFp!("24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132"),
+        MontFp!("17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868"),
     ];
 
     // c2 = {c1[0], c1[2], c1[1]}
     const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
-        FQ_ONE,
+        Fq::ONE,
         Self::FROBENIUS_COEFF_FP3_C1[2],
         Self::FROBENIUS_COEFF_FP3_C1[1],
     ];

@@ -1,9 +1,9 @@
 use ark_ff::{
     fields::fp6_2over3::{Fp6, Fp6Config},
-    CubicExt, MontFp,
+    Field, MontFp,
 };
 
-use crate::{Fq, Fq3, Fq3Config, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq3, Fq3Config};
 
 pub type Fq6 = Fp6<Fq6Config>;
 
@@ -12,7 +12,7 @@
 impl Fp6Config for Fq6Config {
     type Fp3Config = Fq3Config;
 
-    const NONRESIDUE: Fq3 = CubicExt!(FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
     // Coefficients for the Frobenius automorphism.
     // c1[0] = 1,
@@ -22,11 +22,11 @@ // c1[3] = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160000
     // c1[4] = 17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868
     // c1[5] = 17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107869
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        FQ_ONE,
-        MontFp!(Fq, "24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052133"),
-        MontFp!(Fq, "24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132"),
-        MontFp!(Fq, "41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160000"),
-        MontFp!(Fq, "17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868"),
-        MontFp!(Fq, "17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107869"),
+        Fq::ONE,
+        MontFp!("24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052133"),
+        MontFp!("24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132"),
+        MontFp!("41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160000"),
+        MontFp!("17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868"),
+        MontFp!("17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107869"),
     ];
 }

@@ -2,7 +2,7 @@ use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
 use ark_ff::{
-    fields::{models::fp6_2over3::*, quadratic_extension::QuadExtConfig, SquareRootField},
+    fields::{models::fp6_2over3::*, quadratic_extension::QuadExtConfig},
     Field, PrimeField,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -11,7 +11,7 @@ use core::ops::{AddAssign, MulAssign, SubAssign};
 
 use crate::*;
 
-generate_field_test!(mnt6_753; fq3; fq6; mont(12, 12); );
+generate_field_test!(mnt6_753; fq3; fq6_2_on_3; mont(12, 12); );
 generate_field_serialization_test!(mnt6_753;);
 
 #[test]

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_pallas`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,8 +1,8 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
 };
-use ark_ff::{MontFp, Zero};
+use ark_ff::{Field, MontFp, Zero};
 
 use crate::{fq::Fq, fr::Fr};
 
@@ -12,7 +12,7 @@
 #[derive(Copy, Clone, Default, PartialEq, Eq)]
 pub struct PallasParameters;
 
-impl ModelParameters for PallasParameters {
+impl CurveConfig for PallasParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -20,22 +20,21 @@ /// COFACTOR = 1
     const COFACTOR: &'static [u64] = &[0x1];
 
     /// COFACTOR_INV = 1
-    const COFACTOR_INV: Fr = MontFp!(Fr, "1");
+    const COFACTOR_INV: Fr = Fr::ONE;
 }
 
-pub type Affine = GroupAffine<PallasParameters>;
-pub type Projective = GroupProjective<PallasParameters>;
+pub type G1Affine = Affine<PallasParameters>;
+pub type G1Projective = Projective<PallasParameters>;
 
-impl SWModelParameters for PallasParameters {
+impl SWCurveConfig for PallasParameters {
     /// COEFF_A = 0
-    const COEFF_A: Fq = MontFp!(Fq, "0");
+    const COEFF_A: Fq = Fq::ZERO;
 
     /// COEFF_B = 5
-    const COEFF_B: Fq = MontFp!(Fq, "5");
+    const COEFF_B: Fq = MontFp!("5");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G_GENERATOR_X, G_GENERATOR_Y);
+    const GENERATOR: G1Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -44,7 +43,7 @@ }
 }
 
 /// G_GENERATOR_X = -1
-pub const G_GENERATOR_X: Fq = MontFp!(Fq, "-1");
+pub const G_GENERATOR_X: Fq = MontFp!("-1");
 
 /// G_GENERATOR_Y = 2
-pub const G_GENERATOR_Y: Fq = MontFp!(Fq, "2");
+pub const G_GENERATOR_Y: Fq = MontFp!("2");

@@ -1,29 +1,17 @@
-use ark_algebra_test_templates::{
-    curves::{curve_tests, sw_tests},
-    groups::group_test,
-};
+use ark_algebra_test_templates::curves::{curve_tests, sw_tests};
 use ark_ec::AffineCurve;
-use ark_std::{rand::Rng, test_rng};
 
-use crate::{Affine, PallasParameters, Projective};
+use crate::{G1Affine, G1Projective, PallasParameters};
 
 #[test]
 fn test_projective_curve() {
-    curve_tests::<Projective>();
+    curve_tests::<G1Projective>();
     sw_tests::<PallasParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a: Projective = rng.gen();
-    let b: Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
 fn test_generator() {
-    let generator = Affine::prime_subgroup_generator();
+    let generator = G1Affine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
 }

@@ -1,7 +1,7 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};

@@ -1,7 +1,7 @@
 //! This module implements the R1CS equivalent of `ark_vesta`.
 //!
 //! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
+//! and group variables for `crate::Projective`.
 //!
 //! The field underlying these constraints is `crate::Fq`.
 //!

@@ -1,9 +1,9 @@
 use crate::{fq::Fq, fr::Fr};
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
 };
-use ark_ff::{MontFp, Zero};
+use ark_ff::{Field, MontFp, Zero};
 
 #[cfg(test)]
 mod tests;
@@ -11,7 +11,7 @@
 #[derive(Copy, Clone, Default, PartialEq, Eq)]
 pub struct VestaParameters;
 
-impl ModelParameters for VestaParameters {
+impl CurveConfig for VestaParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 
@@ -19,22 +19,21 @@ /// COFACTOR = 1
     const COFACTOR: &'static [u64] = &[0x1];
 
     /// COFACTOR_INV = 1
-    const COFACTOR_INV: Fr = MontFp!(Fr, "1");
+    const COFACTOR_INV: Fr = Fr::ONE;
 }
 
-pub type Affine = GroupAffine<VestaParameters>;
-pub type Projective = GroupProjective<VestaParameters>;
+pub type G1Affine = Affine<VestaParameters>;
+pub type G1Projective = Projective<VestaParameters>;
 
-impl SWModelParameters for VestaParameters {
+impl SWCurveConfig for VestaParameters {
     /// COEFF_A = 0
-    const COEFF_A: Fq = MontFp!(Fq, "0");
+    const COEFF_A: Fq = Fq::ZERO;
 
     /// COEFF_B = 5
-    const COEFF_B: Fq = MontFp!(Fq, "5");
+    const COEFF_B: Fq = MontFp!("5");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G_GENERATOR_X, G_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
 
     #[inline(always)]
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
@@ -44,8 +43,8 @@ }
 
 /// G_GENERATOR_X = -1
 /// Encoded in Montgomery form, so the value here is -R mod p.
-pub const G_GENERATOR_X: Fq = MontFp!(Fq, "-1");
+pub const G_GENERATOR_X: Fq = MontFp!("-1");
 
 /// G_GENERATOR_Y = 2
 /// Encoded in Montgomery form, so the value here is 2R mod p.
-pub const G_GENERATOR_Y: Fq = MontFp!(Fq, "2");
+pub const G_GENERATOR_Y: Fq = MontFp!("2");

@@ -1,29 +1,17 @@
-use ark_algebra_test_templates::{
-    curves::{curve_tests, sw_tests},
-    groups::group_test,
-};
+use ark_algebra_test_templates::curves::{curve_tests, sw_tests};
 use ark_ec::AffineCurve;
-use ark_std::{rand::Rng, test_rng};
 
-use crate::{Affine, Projective, VestaParameters};
+use crate::{G1Affine, G1Projective, VestaParameters};
 
 #[test]
 fn test_projective_curve() {
-    curve_tests::<Projective>();
+    curve_tests::<G1Projective>();
     sw_tests::<VestaParameters>();
 }
 
 #[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a: Projective = rng.gen();
-    let b: Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
 fn test_generator() {
-    let generator = Affine::prime_subgroup_generator();
+    let generator = G1Affine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
 }

@@ -1,7 +1,7 @@
 use ark_algebra_test_templates::{
     fields::*, generate_field_serialization_test, generate_field_test,
 };
-use ark_ff::{Field, One, PrimeField, SquareRootField, UniformRand, Zero};
+use ark_ff::{Field, One, PrimeField, UniformRand, Zero};
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
 use ark_std::{rand::Rng, test_rng};
 use core::ops::{AddAssign, MulAssign, SubAssign};