Crate primeorder

Expand description

§RustCrypto: Prime Order Elliptic Curve Formulas

Pure Rust implementation of complete addition formulas for prime order elliptic curves (Renes-Costello-Batina 2015 a.k.a. RCB).

Generic over field element implementations and curve equation coefficients.

Documentation

§About

This crate provides a generic implementation of complete formulas for prime order elliptic curves which are defined by the short Weierstrass equation:

y² = x³ + ax + b

It’s used to implement the following elliptic curves:

p192: NIST P-192
p224: NIST P-224
p256: NIST P-256
p384: NIST P-384
p521: NIST P-521
sm2: ShangMi 2

§⚠️ Security Warning

The elliptic curve arithmetic contained in this crate has never been independently audited!

This crate has been designed with the goal of ensuring that secret-dependent operations are performed in constant time (using the subtle crate and constant-time formulas). However, it has not been thoroughly assessed to ensure that generated assembly is constant time on common CPU architectures.

USE AT YOUR OWN RISK!

§License

All crates licensed under either of:

at your option.

§Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.

Re-exports§

pub use crate::mul_backend::MulBackend;
pub use elliptic_curve;
pub use elliptic_curve::array;

Modules§

affine 🔒: Affine curve points.
mul_backend: Scalar multiplication backends.
point_arithmetic: Point arithmetic implementation optimised for different curve equations
projective 🔒: Projective curve points.
tables 🔒: Precomputed tables.

Structs§

AffinePoint: Point on a Weierstrass curve in affine coordinates.
BasepointTable: Precomputed lookup table of multiples of a base point, a.k.a. generator.
LookupTable: Lookup table containing precomputed values [p, 2p, 3p, ..., 8p]
ProjectivePoint: Point on a Weierstrass curve in projective coordinates.
Radix16Decomposition: Signed radix-16 decomposition of a scalar.

Enums§

ByteOrder: Byte order used when encoding/decoding field elements as bytestrings.

Traits§

ArraySize: Trait which associates a usize size and ArrayType with a typenum-provided Unsigned integer.
Double: Perform a doubling (i.e. self + self).
Field: This trait represents an element of a field.
FieldArithmetic: Access to a curve’s base field element type.
FieldExt: Extension trait for ff::Field, intended as a place to put optimizable arithmetic operations.
PrimeCurve: Marker trait for elliptic curves with prime order.
PrimeCurveParams: Parameters for elliptic curves of prime order which can be described by the short Weierstrass equation.
PrimeCurveWithBasepointTable: Trait for specifying a constant-time basepoint table for a given curve.
PrimeField: This represents an element of a non-binary prime field.
PrimeFieldExt: Extension trait for ff::PrimeField which enables specifying the endianness in which ff::PrimeField::Repr is encoded.
Retrieve: A generalization for numbers kept in optimized representations (e.g. Montgomery) that can be converted back to the original form.

Type Aliases§

FieldBytes: Byte representation of a base/scalar field element of a given curve.
Radix16Digits: Compute number of radix-16 digits for the given elliptic curve’s scalar field.
Scalar: Scalar field element for a particular elliptic curve.
U1