More NIST curves (#142)

Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>

Cargo.toml

@@ -31,6 +31,8 @@ members = [
     "vesta",
 
     "secp256k1",
+    "secp256r1",
+    "secp384r1",
     "secq256k1",
     
     "curve25519",
@@ -69,4 +71,4 @@ ark-ec = { git = "https://github.com/arkworks-rs/algebra/" }
 ark-poly = { git = "https://github.com/arkworks-rs/algebra/" }
 ark-serialize = { git = "https://github.com/arkworks-rs/algebra/" }
 ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra/" }
-ark-r1cs-std = { git = "https://github.com/arkworks-rs/r1cs-std/" }
+ark-r1cs-std = { git = "https://github.com/arkworks-rs/r1cs-std/" }

secp256r1/Cargo.toml

@@ -0,0 +1,30 @@
+[package]
+name = "ark-secp256r1"
+version = "0.4.0-alpha"
+authors = [ "arkworks contributors" ]
+description = "The secp256r1 curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-secp256r1/"
+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" ]

secp256r1/LICENSE-APACHE

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

secp256r1/LICENSE-MIT

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

secp256r1/src/constraints/curves.rs

@@ -0,0 +1,10 @@
+use crate::{constraints::FqVar, *};
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+/// A group element in the secp256r1 curve.
+pub type GVar = ProjectiveVar<Config, FqVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<Config, GVar>().unwrap();
+}

secp256r1/src/constraints/fields.rs

@@ -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();
+}

secp256r1/src/constraints/mod.rs

@@ -0,0 +1,7 @@
+//! This module implements the R1CS equivalent of `ark_secp256r1`.
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

secp256r1/src/curves/mod.rs

@@ -0,0 +1,50 @@
+use ark_ec::{
+    models::CurveConfig,
+    short_weierstrass::{self as sw, SWCurveConfig},
+};
+use ark_ff::{Field, MontFp};
+
+use crate::{fq::Fq, fr::Fr};
+
+#[cfg(test)]
+mod tests;
+
+pub type Affine = sw::Affine<Config>;
+pub type Projective = sw::Projective<Config>;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    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 Config {
+    /// COEFF_A = -3
+    const COEFF_A: Fq = MontFp!("-3");
+
+    /// COEFF_B = 41058363725152142129326129780047268409114441015993725554835256314039467401291
+    const COEFF_B: Fq =
+        MontFp!("41058363725152142129326129780047268409114441015993725554835256314039467401291");
+
+    /// GENERATOR = (G_GENERATOR_X, G_GENERATOR_Y)
+    const GENERATOR: Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
+}
+
+/// G_GENERATOR_X =
+/// 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
+pub const G_GENERATOR_X: Fq =
+    MontFp!("48439561293906451759052585252797914202762949526041747995844080717082404635286");
+
+/// G_GENERATOR_Y =
+/// 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
+pub const G_GENERATOR_Y: Fq =
+    MontFp!("36134250956749795798585127919587881956611106672985015071877198253568414405109");

secp256r1/src/curves/tests.rs

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

secp256r1/src/fields/fq.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "115792089210356248762697446949407573530086143415290314195533631308867097853951"]
+#[generator = "2"]
+pub struct FqConfig;
+pub type Fq = Fp256<MontBackend<FqConfig, 4>>;

secp256r1/src/fields/fr.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "115792089210356248762697446949407573529996955224135760342422259061068512044369"]
+#[generator = "11"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;

secp256r1/src/fields/mod.rs

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

secp256r1/src/fields/tests.rs

@@ -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);

secp256r1/src/lib.rs

@@ -0,0 +1,29 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the secp256r1 curve.
+//! Source: <https://neuromancer.sk/std/secg/secp256r1>
+//!
+//! Curve information:
+//! * Base field: q =
+//!   0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
+//! * Scalar field: r =
+//!   0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
+//! * a = -3
+//! * b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
+//! * Curve equation: y^2 = x^3 + ax + b
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

secp384r1/Cargo.toml

@@ -0,0 +1,30 @@
+[package]
+name = "ark-secp384r1"
+version = "0.4.0-alpha"
+authors = [ "arkworks contributors" ]
+description = "The secp384r1 curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-secp384r1/"
+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" ]

secp384r1/LICENSE-APACHE

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

secp384r1/LICENSE-MIT

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

secp384r1/src/constraints/curves.rs

@@ -0,0 +1,10 @@
+use crate::{constraints::FqVar, *};
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+/// A group element in the secp384r1 curve.
+pub type GVar = ProjectiveVar<Config, FqVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<Config, GVar>().unwrap();
+}

secp384r1/src/constraints/fields.rs

@@ -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();
+}

secp384r1/src/constraints/mod.rs

@@ -0,0 +1,7 @@
+//! This module implements the R1CS equivalent of `ark_secp384r1`.
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

secp384r1/src/curves/mod.rs

@@ -0,0 +1,50 @@
+use ark_ec::{
+    models::CurveConfig,
+    short_weierstrass::{self as sw, SWCurveConfig},
+};
+use ark_ff::{Field, MontFp};
+
+use crate::{fq::Fq, fr::Fr};
+
+#[cfg(test)]
+mod tests;
+
+pub type Affine = sw::Affine<Config>;
+pub type Projective = sw::Projective<Config>;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    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 Config {
+    /// COEFF_A = -3
+    const COEFF_A: Fq = MontFp!("-3");
+
+    /// COEFF_B = 27580193559959705877849011840389048093056905856361568521428707301988689241309860865136260764883745107765439761230575
+    const COEFF_B: Fq =
+        MontFp!("27580193559959705877849011840389048093056905856361568521428707301988689241309860865136260764883745107765439761230575");
+
+    /// GENERATOR = (G_GENERATOR_X, G_GENERATOR_Y)
+    const GENERATOR: Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
+}
+
+/// G_GENERATOR_X =
+/// 26247035095799689268623156744566981891852923491109213387815615900925518854738050089022388053975719786650872476732087
+pub const G_GENERATOR_X: Fq =
+    MontFp!("26247035095799689268623156744566981891852923491109213387815615900925518854738050089022388053975719786650872476732087");
+
+/// G_GENERATOR_Y =
+/// 8325710961489029985546751289520108179287853048861315594709205902480503199884419224438643760392947333078086511627871
+pub const G_GENERATOR_Y: Fq =
+    MontFp!("8325710961489029985546751289520108179287853048861315594709205902480503199884419224438643760392947333078086511627871");

secp384r1/src/curves/tests.rs

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

secp384r1/src/fields/fq.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319"]
+#[generator = "2"]
+pub struct FqConfig;
+pub type Fq = Fp384<MontBackend<FqConfig, 6>>;

secp384r1/src/fields/fr.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643"]
+#[generator = "2"]
+pub struct FrConfig;
+pub type Fr = Fp384<MontBackend<FrConfig, 6>>;

secp384r1/src/fields/mod.rs

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

secp384r1/src/fields/tests.rs

@@ -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);

secp384r1/src/lib.rs

@@ -0,0 +1,29 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the secp384r1 curve.
+//! Source: <https://neuromancer.sk/std/nist/P-384>
+//!
+//! Curve information:
+//! * Base field: q =
+//!   0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
+//! * Scalar field: r =
+//!   0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973
+//! * a = -3
+//! * b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
+//! * Curve equation: y^2 = x^3 + ax + b
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;