.cargo
    audit.toml
.github
    dependabot.yml
    workflows
        bp256.yml
        bp384.yml
        k256.yml
        p256.yml
        p384.yml
        security-audit.yml
        workspace.yml
Cargo.toml
README.md
bp256
    CHANGELOG.md
    Cargo.toml
    README.md
    src
        lib.rs
        r1.rs
        r1
            ecdsa.rs
        t1.rs
        t1
            ecdsa.rs
bp384
    CHANGELOG.md
    Cargo.toml
    README.md
    src
        lib.rs
        r1.rs
        r1
            ecdsa.rs
        t1.rs
        t1
            ecdsa.rs
codecov.yml
k256
    CHANGELOG.md
    Cargo.toml
    README.md
    bench
        ecdsa.rs
        field.rs
        scalar.rs
    src
        arithmetic.rs
        arithmetic
            affine.rs
            dev.rs
            field.rs
            field
                field_10x26.rs
                field_5x52.rs
                field_impl.rs
            mul.rs
            projective.rs
            scalar.rs
            scalar
                wide32.rs
                wide64.rs
        ecdh.rs
        ecdsa.rs
        ecdsa
            normalize.rs
            recoverable.rs
            sign.rs
            verify.rs
        lib.rs
        test_vectors.rs
        test_vectors
            ecdsa.rs
            field.rs
            group.rs
p256
    CHANGELOG.md
    Cargo.toml
    README.md
    src
        arithmetic.rs
        arithmetic
            affine.rs
            field.rs
            projective.rs
            scalar.rs
            scalar
                blinded.rs
            util.rs
        ecdh.rs
        ecdsa.rs
        lib.rs
        test_vectors.rs
        test_vectors
            ecdsa.rs
            field.rs
            group.rs
    tests
        pkcs8.rs
p384
    CHANGELOG.md
    Cargo.toml
    README.md
    src
        ecdsa.rs
        lib.rs

# RustCrypto: Elliptic Curves ![Rust Version][rustc-image] [![Project Chat][chat-image]][chat-link] [![dependency status][deps-image]][deps-link]

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.

All curves reside in the separate crates and implemented using traits from
the [`elliptic-curve`](https://docs.rs/elliptic-curve/) crate.

Crates in this repo do not require the standard library (i.e. `no_std` capable)
and can be easily used for bare-metal or WebAssembly programming.

## Crates

| Name      | Curve              | `arithmetic`? | Crates.io | Documentation | Build Status |
|-----------|--------------------|---------------|-----------|---------------|--------------|
| [`bp256`] | brainpoolP256r1/t1 | 🚫 | [![crates.io](https://img.shields.io/crates/v/bp256.svg)](https://crates.io/crates/bp256) | [![Documentation](https://docs.rs/bp256/badge.svg)](https://docs.rs/bp256) | ![build](https://github.com/RustCrypto/elliptic-curves/workflows/bp256/badge.svg?branch=master&event=push) |
| [`bp384`] | brainpoolP384r1/t1 | 🚫 | [![crates.io](https://img.shields.io/crates/v/bp384.svg)](https://crates.io/crates/bp384) | [![Documentation](https://docs.rs/bp384/badge.svg)](https://docs.rs/bp384) | ![build](https://github.com/RustCrypto/elliptic-curves/workflows/bp384/badge.svg?branch=master&event=push) |
| [`k256`]  | [secp256k1]        | ✅ | [![crates.io](https://img.shields.io/crates/v/k256.svg)](https://crates.io/crates/k256) | [![Documentation](https://docs.rs/k256/badge.svg)](https://docs.rs/k256) | ![build](https://github.com/RustCrypto/elliptic-curves/workflows/k256/badge.svg?branch=master&event=push) |
| [`p256`]  | [NIST P-256]       | ✅ | [![crates.io](https://img.shields.io/crates/v/p256.svg)](https://crates.io/crates/p256) | [![Documentation](https://docs.rs/p256/badge.svg)](https://docs.rs/p256) | ![build](https://github.com/RustCrypto/elliptic-curves/workflows/p256/badge.svg?branch=master&event=push) |
| [`p384`]  | [NIST P-384]       | 🚫 | [![crates.io](https://img.shields.io/crates/v/p384.svg)](https://crates.io/crates/p384) | [![Documentation](https://docs.rs/p384/badge.svg)](https://docs.rs/p384) | ![build](https://github.com/RustCrypto/elliptic-curves/workflows/p384/badge.svg?branch=master&event=push) |

NOTE: Some crates contain field/point arithmetic implementations gated under the
`arithmetic` cargo feature as noted above.

Please see our [tracking issue for additional elliptic curves][other-curves]
if you are interested in curves beyond the ones listed here.

## Minimum Supported Rust Version

All crates in this repository support 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.

## License

All crates licensed under either of

 * [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
 * [MIT license](http://opensource.org/licenses/MIT)

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.

[//]: # (badges)

[rustc-image]: https://img.shields.io/badge/rustc-1.56+-blue.svg
[chat-image]: https://img.shields.io/badge/zulip-join_chat-blue.svg
[chat-link]: https://rustcrypto.zulipchat.com/#narrow/stream/260040-elliptic-curves
[deps-image]: https://deps.rs/repo/github/RustCrypto/elliptic-curves/status.svg
[deps-link]: https://deps.rs/repo/github/RustCrypto/elliptic-curves

[//]: # (crates)

[`bp256`]: https://github.com/RustCrypto/elliptic-curves/tree/master/bp256
[`bp384`]: https://github.com/RustCrypto/elliptic-curves/tree/master/bp384
[`k256`]: https://github.com/RustCrypto/elliptic-curves/tree/master/k256
[`p256`]: https://github.com/RustCrypto/elliptic-curves/tree/master/p256
[`p384`]: https://github.com/RustCrypto/elliptic-curves/tree/master/p384

[//]: # (curves)

[secp256k1]: https://en.bitcoin.it/wiki/Secp256k1
[NIST P-256]: http://oid-info.com/get/1.2.840.10045.3.1.7
[NIST P-384]: http://oid-info.com/get/1.3.132.0.34

[//]: # (general links)

[other-curves]: https://github.com/RustCrypto/elliptic-curves/issues/114
# RustCrypto: NIST P-384 (secp384r1) elliptic curve

[![crate][crate-image]][crate-link]
[![Docs][docs-image]][docs-link]
![Apache2/MIT licensed][license-image]
![Rust Version][rustc-image]
[![Project Chat][chat-image]][chat-link]
[![Build Status][build-image]][build-link]

NIST P-384 elliptic curve (a.k.a. secp384r1) types implemented in terms of
traits from the [`elliptic-curve`] crate.

[Documentation][docs-link]

## About P-384

NIST P-384 is a Weierstrass curve specified in FIPS 186-4: Digital Signature
Standard (DSS):

<https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf>

Also known as secp384r1 (SECG), it's included in the US National Security
Agency's "Suite B" and is widely used in protocols like TLS and the associated
X.509 PKI.

## Minimum Supported Rust Version

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

## License

All crates licensed under either of

 * [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
 * [MIT license](http://opensource.org/licenses/MIT)

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.

[//]: # (badges)

[crate-image]: https://img.shields.io/crates/v/p384.svg
[crate-link]: https://crates.io/crates/p384
[docs-image]: https://docs.rs/p384/badge.svg
[docs-link]: https://docs.rs/p384/
[license-image]: https://img.shields.io/badge/license-Apache2.0/MIT-blue.svg
[rustc-image]: https://img.shields.io/badge/rustc-1.56+-blue.svg
[chat-image]: https://img.shields.io/badge/zulip-join_chat-blue.svg
[chat-link]: https://rustcrypto.zulipchat.com/#narrow/stream/260040-elliptic-curves
[build-image]: https://github.com/RustCrypto/elliptic-curves/workflows/p384/badge.svg?branch=master&event=push
[build-link]: https://github.com/RustCrypto/elliptic-curves/actions?query=workflow%3Ap384

[//]: # (general links)

[`elliptic-curve`]: https://github.com/RustCrypto/traits/tree/master/elliptic-curve
# RustCrypto: Brainpool P-384 elliptic curves

[![crate][crate-image]][crate-link]
[![Docs][docs-image]][docs-link]
![Apache2/MIT licensed][license-image]
![Rust Version][rustc-image]
[![Project Chat][chat-image]][chat-link]
[![Build Status][build-image]][build-link]

Brainpool P-384 (brainpoolP384r1 and brainpoolP384t1) elliptic curve types
implemented in terms of traits from the [`elliptic-curve`] crate.

[Documentation][docs-link]

## Minimum Supported Rust Version

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

## License

All crates licensed under either of

 * [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
 * [MIT license](http://opensource.org/licenses/MIT)

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.

[//]: # (badges)

[crate-image]: https://img.shields.io/crates/v/bp384.svg
[crate-link]: https://crates.io/crates/bp384
[docs-image]: https://docs.rs/bp384/badge.svg
[docs-link]: https://docs.rs/bp384/
[license-image]: https://img.shields.io/badge/license-Apache2.0/MIT-blue.svg
[rustc-image]: https://img.shields.io/badge/rustc-1.56+-blue.svg
[chat-image]: https://img.shields.io/badge/zulip-join_chat-blue.svg
[chat-link]: https://rustcrypto.zulipchat.com/#narrow/stream/260040-elliptic-curves
[build-image]: https://github.com/RustCrypto/elliptic-curves/workflows/bp384/badge.svg?branch=master&event=push
[build-link]: https://github.com/RustCrypto/elliptic-curves/actions?query=workflow:bp384

[//]: # (general links)

[`elliptic-curve`]: https://github.com/RustCrypto/traits/tree/master/elliptic-curve
# RustCrypto: Brainpool P-256 elliptic curves

[![crate][crate-image]][crate-link]
[![Docs][docs-image]][docs-link]
![Apache2/MIT licensed][license-image]
![Rust Version][rustc-image]
[![Project Chat][chat-image]][chat-link]
[![Build Status][build-image]][build-link]

Brainpool P-256 (brainpoolP256r1 and brainpoolP256t1) elliptic curve types
implemented in terms of traits from the [`elliptic-curve`] crate.

[Documentation][docs-link]

## Minimum Supported Rust Version

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

## License

All crates licensed under either of

 * [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
 * [MIT license](http://opensource.org/licenses/MIT)

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.

[//]: # (badges)

[crate-image]: https://img.shields.io/crates/v/bp256.svg
[crate-link]: https://crates.io/crates/bp256
[docs-image]: https://docs.rs/bp256/badge.svg
[docs-link]: https://docs.rs/bp256/
[license-image]: https://img.shields.io/badge/license-Apache2.0/MIT-blue.svg
[rustc-image]: https://img.shields.io/badge/rustc-1.56+-blue.svg
[chat-image]: https://img.shields.io/badge/zulip-join_chat-blue.svg
[chat-link]: https://rustcrypto.zulipchat.com/#narrow/stream/260040-elliptic-curves
[build-image]: https://github.com/RustCrypto/elliptic-curves/workflows/bp256/badge.svg?branch=master&event=push
[build-link]: https://github.com/RustCrypto/elliptic-curves/actions?query=workflow:bp256

[//]: # (general links)

[`elliptic-curve`]: https://github.com/RustCrypto/traits/tree/master/elliptic-curve
# RustCrypto: NIST P-256 (secp256r1) elliptic curve

[![crate][crate-image]][crate-link]
[![Docs][docs-image]][docs-link]
![Apache2/MIT licensed][license-image]
![Rust Version][rustc-image]
[![Project Chat][chat-image]][chat-link]
[![Build Status][build-image]][build-link]

NIST P-256 elliptic curve (a.k.a. prime256v1, secp256r1) types implemented
in terms of traits from the [`elliptic-curve`] crate.

Optionally includes an [`arithmetic`] feature providing scalar and
affine/projective point types with support for constant-time scalar
multiplication, which can be used to implement protocols such as [ECDH].

[Documentation][docs-link]

## ⚠️ 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!

## Supported Algorithms

- [Elliptic Curve Diffie-Hellman (ECDH)][ECDH]: gated under the `ecdh` feature.
- [Elliptic Curve Digital Signature Algorithm (ECDSA)][ECDSA]: gated under the
  `ecdsa` feature.

## About NIST P-256

NIST P-256 is a Weierstrass curve specified in FIPS 186-4: Digital Signature
Standard (DSS):

<https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf>

Also known as prime256v1 (ANSI X9.62) and secp256r1 (SECG), it's included in
the US National Security Agency's "Suite B" and is widely used in protocols
like TLS and the associated X.509 PKI.

## Minimum Supported Rust Version

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

## License

All crates licensed under either of

 * [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
 * [MIT license](http://opensource.org/licenses/MIT)

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.

[//]: # (badges)

[crate-image]: https://img.shields.io/crates/v/p256.svg
[crate-link]: https://crates.io/crates/p256
[docs-image]: https://docs.rs/p256/badge.svg
[docs-link]: https://docs.rs/p256/
[license-image]: https://img.shields.io/badge/license-Apache2.0/MIT-blue.svg
[rustc-image]: https://img.shields.io/badge/rustc-1.56+-blue.svg
[chat-image]: https://img.shields.io/badge/zulip-join_chat-blue.svg
[chat-link]: https://rustcrypto.zulipchat.com/#narrow/stream/260040-elliptic-curves
[build-image]: https://github.com/RustCrypto/elliptic-curves/workflows/p256/badge.svg?branch=master&event=push
[build-link]: https://github.com/RustCrypto/elliptic-curves/actions?query=workflow%3Ap256

[//]: # (general links)

[`elliptic-curve`]: https://github.com/RustCrypto/traits/tree/master/elliptic-curve
[`arithmetic`]: https://docs.rs/p256/latest/p256/arithmetic/index.html
[ECDH]: https://en.wikipedia.org/wiki/Elliptic-curve_Diffie-Hellman
[ECDSA]: https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm
# RustCrypto: secp256k1 (K-256) elliptic curve

[![crate][crate-image]][crate-link]
[![Docs][docs-image]][docs-link]
![Apache2/MIT licensed][license-image]
![Rust Version][rustc-image]
[![Project Chat][chat-image]][chat-link]
[![Build Status][build-image]][build-link]

[secp256k1] (a.k.a. K-256) elliptic curve library written in pure Rust with
support for [ECDSA] signing/verification (including Ethereum-style signatures
with public-key recovery), Elliptic Curve Diffie-Hellman (ECDH), and general
purpose arithmetic which can be used to implement arbitrary protocols.

Uses traits and base types from the [`elliptic-curve`] crate.

Optionally includes a secp256k1 [`arithmetic`] feature providing scalar and
point types (projective/affine) with support for constant-time scalar
multiplication. Additionally, implements traits from the [`group`] crate
which can be used to generically construct group-based protocols.

[Documentation][docs-link]

## ⚠️ Security Warning

The secp256k1 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
secp256k1 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!

## Supported Algorithms

- [Elliptic Curve Diffie-Hellman (ECDH)][ECDH]: gated under the `ecdh` feature.
  Note that this is technically ephemeral secp256k1 Diffie-Hellman
  (a.k.a. ECDHE)
- [Elliptic Curve Digital Signature Algorithm (ECDSA)][ECDSA]: gated under the
  `ecdsa` feature. Support for ECDSA/secp256k1 signing and verification,
  applying [low-S normalization (BIP 0062)][BIP0062] as used in
  consensus-critical applications, and additionally supports secp256k1
  public-key recovery from ECDSA signatures (as used by e.g. Ethereum)

## About secp256k1 (K-256)

[secp256k1] is a Koblitz curve commonly used in cryptocurrency applications.
The "K-256" name follows NIST notation where P = prime fields,
B = binary fields, and K = Koblitz curves.

The curve is specified as `secp256k1` by Certicom's SECG in
"SEC 2: Recommended Elliptic Curve Domain Parameters":

<https://www.secg.org/sec2-v2.pdf>

secp256k1 is primarily notable for usage in Bitcoin and other cryptocurrencies,
particularly in conjunction with the
[Elliptic Curve Digital Signature Algorithm (ECDSA)][ECDSA].
Owing to its wide deployment in these applications, secp256k1 is one of the
most popular and commonly used elliptic curves.

## Minimum Supported Rust Version

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

## License

All crates licensed under either of

 * [Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0)
 * [MIT license](http://opensource.org/licenses/MIT)

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.

[//]: # (badges)

[crate-image]: https://img.shields.io/crates/v/k256.svg
[crate-link]: https://crates.io/crates/k256
[docs-image]: https://docs.rs/k256/badge.svg
[docs-link]: https://docs.rs/k256/
[license-image]: https://img.shields.io/badge/license-Apache2.0/MIT-blue.svg
[rustc-image]: https://img.shields.io/badge/rustc-1.56+-blue.svg
[chat-image]: https://img.shields.io/badge/zulip-join_chat-blue.svg
[chat-link]: https://rustcrypto.zulipchat.com/#narrow/stream/260040-elliptic-curves
[build-image]: https://github.com/RustCrypto/elliptic-curves/workflows/k256/badge.svg?branch=master&event=push
[build-link]: https://github.com/RustCrypto/elliptic-curves/actions?query=workflow%3Ak256

[//]: # (general links)

[secp256k1]: https://en.bitcoin.it/wiki/Secp256k1
[`elliptic-curve`]: https://github.com/RustCrypto/traits/tree/master/elliptic-curve
[`arithmetic`]: https://docs.rs/k256/latest/k256/arithmetic/index.html
[`group`]: https://github.com/zkcrypto/group
[ECDH]: https://en.wikipedia.org/wiki/Elliptic-curve_Diffie-Hellman
[ECDSA]: https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm
[BIP0062]: https://github.com/bitcoin/bips/blob/master/bip-0062.mediawiki
