69 lines
2.8 KiB
Rust
69 lines
2.8 KiB
Rust
//! Pure Rust implementation of group operations on secp521r1.
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//!
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//! Curve parameters can be found in [NIST SP 800-186] § 3.2.1.5: P-521.
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//!
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//! [NIST SP 800-186]: https://csrc.nist.gov/publications/detail/sp/800-186/final
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pub(crate) mod field;
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#[cfg(feature = "hash2curve")]
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mod hash2curve;
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pub(crate) mod scalar;
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mod util;
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pub use self::scalar::Scalar;
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use self::field::FieldElement;
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use crate::NistP521;
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use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
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use primeorder::{point_arithmetic, PrimeCurveParams};
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/// Elliptic curve point in affine coordinates.
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pub type AffinePoint = primeorder::AffinePoint<NistP521>;
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/// Elliptic curve point in projective coordinates.
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pub type ProjectivePoint = primeorder::ProjectivePoint<NistP521>;
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impl CurveArithmetic for NistP521 {
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type AffinePoint = AffinePoint;
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type ProjectivePoint = ProjectivePoint;
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type Scalar = Scalar;
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}
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impl PrimeCurveArithmetic for NistP521 {
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type CurveGroup = ProjectivePoint;
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}
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/// Adapted from [NIST SP 800-186] § 3.2.1.5: P-521.
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///
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/// [NIST SP 800-186]: https://csrc.nist.gov/publications/detail/sp/800-186/final
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impl PrimeCurveParams for NistP521 {
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type FieldElement = FieldElement;
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type PointArithmetic = point_arithmetic::EquationAIsMinusThree;
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/// a = -3 (0x1ff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff
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/// ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff
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/// ffffffff ffffffff ffffffff fffffffc)
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const EQUATION_A: FieldElement = FieldElement::from_u64(3).neg();
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/// b = 0x051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b 99b315f3
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/// b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd 3bb1bf07
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/// 3573df88 3d2c34f1 ef451fd4 6b503f00
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const EQUATION_B: FieldElement =
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FieldElement::from_hex("0000000000000051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00");
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/// Base point of P-521.
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///
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/// ```text
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/// Gₓ = 0x0c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 053fb521
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/// f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 a2ffa8de
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/// 3348b3c1 856a429b f97e7e31 c2e5bd66
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/// Gᵧ = 0x118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 579b4468
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/// 17afbd17 273e662c 97ee7299 5ef42640 c550b901 3fad0761
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/// 353c7086 a272c240 88be9476 9fd16650
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/// ```
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const GENERATOR: (FieldElement, FieldElement) = (
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FieldElement::from_hex("00000000000000c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66"),
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FieldElement::from_hex("000000000000011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650"),
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);
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}
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