@@ -13,6 +13,7 @@
 ### Features
 
 - [\#121](https://github.com/arkworks-rs/curves/pull/121) Add the ed25519 curve.
+- [\#122](https://github.com/arkworks-rs/curves/pull/122) Add the secp256k1 and secq256k1 curves.
 - [\#124](https://github.com/arkworks-rs/curves/pull/124) Add the curve25519 curve.
 
 ### Improvements

@@ -30,6 +30,9 @@
     "pallas",
     "vesta",
 
+    "secp256k1",
+    "secq256k1",
+    
     "curve25519",
     "ed25519",
 ]
@@ -59,3 +62,8 @@ lto = "thin"
 incremental = true
 debug-assertions = true
 debug = true
+
+[patch.crates-io]
+ark-ff = { git = "https://github.com/arkworks-rs/algebra/", branch = "release-0.4" }
+ark-poly = { git = "https://github.com/arkworks-rs/algebra/", branch = "release-0.4" }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra/", branch = "release-0.4" }

@@ -321,8 +321,10 @@ for limb in &mut max {
                 *limb = u64::MAX;
             }
 
-            let modulus_last_limb_bits = <C::ScalarField as PrimeField>::MODULUS_BIT_SIZE % 64;
-            *max.last_mut().unwrap() >>= 64 - modulus_last_limb_bits;
+            let modulus_num_bits_mod_64 = <C::ScalarField as PrimeField>::MODULUS_BIT_SIZE % 64;
+            if modulus_num_bits_mod_64 != 0 {
+                *max.last_mut().unwrap() >>= 64 - modulus_num_bits_mod_64;
+            }
             let scalars = [
                 C::ScalarField::rand(&mut rng)
                     .into_bigint()

@@ -0,0 +1,30 @@
+[package]
+name = "ark-secp256k1"
+version = "0.4.0-alpha.1"
+authors = [ "arkworks contributors" ]
+description = "The secp256k1 curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-secp256k1/"
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+categories = ["cryptography"]
+include = ["Cargo.toml", "src", "LICENSE-APACHE", "LICENSE-MIT"]
+license = "MIT/Apache-2.0"
+edition = "2021"
+
+[dependencies]
+ark-ff = { version = "0.4.0-alpha", default-features = false }
+ark-ec = { version = "0.4.0-alpha", default-features = false }
+ark-r1cs-std = { version = "0.4.0-alpha", default-features = false, optional = true }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+
+[dev-dependencies]
+ark-relations = { version = "0.4.0-alpha", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }
+
+[features]
+default = []
+std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
+r1cs = [ "ark-r1cs-std" ]

@@ -0,0 +1,1 @@
+../LICENSE-APACHE

@@ -0,0 +1,1 @@
+../LICENSE-MIT

@@ -0,0 +1,10 @@
+use crate::{constraints::FqVar, *};
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+/// A group element in the secp256k1 curve.
+pub type GVar = ProjectiveVar<Parameters, FqVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<Parameters, GVar>().unwrap();
+}

@@ -0,0 +1,11 @@
+use ark_r1cs_std::fields::fp::FpVar;
+
+use crate::fq::Fq;
+
+/// A variable that is the R1CS equivalent of `crate::Fq`.
+pub type FqVar = FpVar<Fq>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::fields::field_test::<_, _, FqVar>().unwrap();
+}

@@ -0,0 +1,7 @@
+//! This module implements the R1CS equivalent of `ark_secp256k1`.
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

@@ -0,0 +1,52 @@
+use ark_ec::{
+    models::CurveConfig,
+    short_weierstrass::{self as sw, SWCurveConfig},
+};
+use ark_ff::{Field, MontFp, Zero};
+
+use crate::{fq::Fq, fr::Fr};
+
+#[cfg(test)]
+mod tests;
+
+pub type Affine = sw::Affine<Parameters>;
+pub type Projective = sw::Projective<Parameters>;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct Parameters;
+
+impl CurveConfig for Parameters {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = 1
+    const COFACTOR: &'static [u64] = &[0x1];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr =  Fr::ONE;
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 7
+    const COEFF_B: Fq = MontFp!("7");
+
+    /// GENERATOR = (G_GENERATOR_X, G_GENERATOR_Y)
+    const GENERATOR: Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
+
+    #[inline(always)]
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
+        Self::BaseField::zero()
+    }
+}
+
+/// G_GENERATOR_X = 55066263022277343669578718895168534326250603453777594175500187360389116729240
+pub const G_GENERATOR_X: Fq =
+    MontFp!("55066263022277343669578718895168534326250603453777594175500187360389116729240");
+
+/// G_GENERATOR_Y = 32670510020758816978083085130507043184471273380659243275938904335757337482424
+pub const G_GENERATOR_Y: Fq =
+    MontFp!("32670510020758816978083085130507043184471273380659243275938904335757337482424");

@@ -0,0 +1,4 @@
+use crate::Projective;
+use ark_algebra_test_templates::*;
+
+test_group!(g1; Projective; sw);

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "115792089237316195423570985008687907853269984665640564039457584007908834671663"]
+#[generator = "3"]
+pub struct FqConfig;
+pub type Fq = Fp256<MontBackend<FqConfig, 4>>;

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "115792089237316195423570985008687907852837564279074904382605163141518161494337"]
+#[generator = "7"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;

@@ -0,0 +1,8 @@
+pub mod fq;
+pub use self::fq::*;
+
+pub mod fr;
+pub use self::fr::*;
+
+#[cfg(test)]
+mod tests;

@@ -0,0 +1,5 @@
+use crate::{Fq, Fr};
+use ark_algebra_test_templates::*;
+
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);

@@ -0,0 +1,27 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the secp256k1 curve.
+//! Source: <https://en.bitcoin.it/wiki/Secp256k1>
+//!
+//! Curve information:
+//! * Base field: q =
+//!   115792089237316195423570985008687907853269984665640564039457584007908834671663
+//! * Scalar field: r =
+//!   115792089237316195423570985008687907852837564279074904382605163141518161494337
+//! * Curve equation: y^2 = x^3 + 7
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

@@ -0,0 +1,31 @@
+[package]
+name = "ark-secq256k1"
+version = "0.4.0-alpha.1"
+authors = [ "arkworks contributors" ]
+description = "The secq256k1 curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-secp256k1/"
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+categories = ["cryptography"]
+include = ["Cargo.toml", "src", "LICENSE-APACHE", "LICENSE-MIT"]
+license = "MIT/Apache-2.0"
+edition = "2021"
+
+[dependencies]
+ark-ff = { version = "0.4.0-alpha", default-features = false }
+ark-ec = { version = "0.4.0-alpha", default-features = false }
+ark-r1cs-std = { version = "0.4.0-alpha", default-features = false, optional = true }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-secp256k1 = { path = "../secp256k1" }
+
+[dev-dependencies]
+ark-relations = { version = "0.4.0-alpha", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }
+
+[features]
+default = []
+std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
+r1cs = [ "ark-r1cs-std" ]

@@ -0,0 +1,1 @@
+../LICENSE-APACHE

@@ -0,0 +1,1 @@
+../LICENSE-MIT

@@ -0,0 +1,10 @@
+use crate::{constraints::FqVar, *};
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+/// A group element in the secq256k1 curve.
+pub type GVar = ProjectiveVar<Parameters, FqVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<Parameters, GVar>().unwrap();
+}

@@ -0,0 +1,11 @@
+use ark_r1cs_std::fields::fp::FpVar;
+
+use crate::fq::Fq;
+
+/// A variable that is the R1CS equivalent of `crate::Fq`.
+pub type FqVar = FpVar<Fq>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::fields::field_test::<_, _, FqVar>().unwrap();
+}

@@ -0,0 +1,7 @@
+//! This module implements the R1CS equivalent of `ark_secq256k1`.
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

@@ -0,0 +1,52 @@
+use ark_ec::{
+    models::CurveConfig,
+    short_weierstrass::{self as sw, SWCurveConfig},
+};
+use ark_ff::{Field, MontFp, Zero};
+
+use crate::{fq::Fq, fr::Fr};
+
+#[cfg(test)]
+mod tests;
+
+pub type Affine = sw::Affine<Parameters>;
+pub type Projective = sw::Projective<Parameters>;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct Parameters;
+
+impl CurveConfig for Parameters {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = 1
+    const COFACTOR: &'static [u64] = &[0x1];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr =  Fr::ONE;
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 7
+    const COEFF_B: Fq = MontFp!("7");
+
+    /// GENERATOR = (G_GENERATOR_X, G_GENERATOR_Y)
+    const GENERATOR: Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
+
+    #[inline(always)]
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
+        Self::BaseField::zero()
+    }
+}
+
+/// G_GENERATOR_X = 53718550993811904772965658690407829053653678808745171666022356150019200052646
+pub const G_GENERATOR_X: Fq =
+    MontFp!("53718550993811904772965658690407829053653678808745171666022356150019200052646");
+
+/// G_GENERATOR_Y = 28941648020349172432234515805717979317553499307621291159490218670604692907903
+pub const G_GENERATOR_Y: Fq =
+    MontFp!("28941648020349172432234515805717979317553499307621291159490218670604692907903");

@@ -0,0 +1,4 @@
+use crate::Projective;
+use ark_algebra_test_templates::*;
+
+test_group!(g1; Projective; sw);

@@ -0,0 +1,2 @@
+pub use ark_secp256k1::Fr as Fq;
+pub use ark_secp256k1::FrConfig as FqConfig;

@@ -0,0 +1,2 @@
+pub use ark_secp256k1::Fq as Fr;
+pub use ark_secp256k1::FqConfig as FrConfig;

@@ -0,0 +1,5 @@
+pub mod fq;
+pub use self::fq::*;
+
+pub mod fr;
+pub use self::fr::*;

@@ -0,0 +1,27 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the secq256k1 curve.
+//! Source: <https://moderncrypto.org/mail-archive/curves/2018/000992.html>
+//!
+//! Curve information:
+//! * Base field: q =
+//!   115792089237316195423570985008687907852837564279074904382605163141518161494337
+//! * Scalar field: r =
+//!   115792089237316195423570985008687907853269984665640564039457584007908834671663
+//! * Curve equation: y^2 = x^3 + 7
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;