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RustCrypto: Elliptic Curve Traits

crate Docs Apache2/MIT licensed Rust Version Project Chat Build Status

General purpose Elliptic Curve Cryptography (ECC) support, including types and traits for representing various elliptic curve forms, scalars, points, and public/secret keys composed thereof.


Minimum Supported Rust Version

Requires Rust 1.56 or higher.

Minimum supported Rust version can be changed in the future, but it will be done with a minor version bump.

SemVer Policy

  • All on-by-default features of this library are covered by SemVer
  • MSRV is considered exempt from SemVer as noted above


All crates licensed under either of

at your option.


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.


This crate provides traits for describing elliptic curves, along with types which are generic over elliptic curves which can be used as the basis of curve-agnostic code.

It’s intended to be used with the following concrete elliptic curve implementations from the RustCrypto/elliptic-curves project:

  • bp256: brainpoolP256r1 and brainpoolP256t1
  • bp384: brainpoolP384r1 and brainpoolP384t1
  • k256: secp256k1 a.k.a. K-256
  • p256: NIST P-256 a.k.a secp256r1, prime256v1
  • p384: NIST P-384 a.k.a. secp384r1

The ecdsa crate provides a generic implementation of the Elliptic Curve Digital Signature Algorithm which can be used with any of the above crates, either via an external ECDSA implementation, or using native curve arithmetic where applicable.

Type conversions

The following chart illustrates the various conversions possible between the various types defined by this crate.

Type Conversion Map

serde support

When the serde feature of this crate is enabled, Serialize and Deserialize impls are provided for the following types:

Please see type-specific documentation for more information.


pub use crypto_bigint as bigint;
pub use generic_array;
pub use rand_core;
pub use subtle;
pub use zeroize;
pub use ff;
pub use group;
pub use {{root}}::sec1::pkcs8;
pub use serde;


Type aliases for many constants.


Elliptic Curve Diffie-Hellman Support.

Traits for arithmetic operations on elliptic curve field elements.

Support for SEC1 elliptic curve encoding formats.


Elliptic curve errors.

JSON Web Key (JWK) with a kty of "EC" (elliptic curve).


Non-zero scalar type.


Elliptic curve public keys.


Generic scalar type with core functionality.

Elliptic curve secret keys.


Algorithm ObjectIdentifier for elliptic curve public key cryptography (id-ecPublicKey).


Elliptic curve with affine arithmetic implementation.

Obtain the affine x-coordinate of an elliptic curve point.

Associate an ObjectIdentifier (OID) with an elliptic curve algorithm implementation.

Elliptic curve.

Decompact an elliptic curve point from an x-coordinate.

Decompress an elliptic curve point.

This trait represents an element of a field.

This trait represents an element of a cryptographic group.

Is this scalar greater than n / 2?

Elliptic curve parameters used by JSON Web Keys.

Point compaction settings.

Point compression settings.

Marker trait for elliptic curves with prime order.

Prime order elliptic curve with projective arithmetic implementation.

This represents an element of a prime field.

Elliptic curve with projective arithmetic implementation.

Scalar arithmetic.

Type Definitions


Affine point type for a given curve with a ProjectiveArithmetic implementation.

Byte representation of a base/scalar field element of a given curve.

Size of field elements of this elliptic curve.


Projective point type for a given curve with a ProjectiveArithmetic implementation.

Result type with the elliptic-curve crate’s Error type.


Scalar field element for a particular elliptic curve.