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Flexible secp256k1 curve math library.

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# `secp`

A flexible and secure secp256k1 elliptic curve math library, with constant-time support, and superb ergonomics.

`secp` takes full advantage of Rust's `std::ops` traits to make elliptic curve cryptography code easy to read, easy to write, succinct, readable, and secure.

## Example

Here's an implementation of simple Schnorr signatures using the `secp` crate.

```rust
use secp::{MaybeScalar, Point, Scalar};
use sha2::{Digest, Sha256};

fn compute_challenge(nonce_point: &Point, pubkey: &Point, msg: &[u8]) -> MaybeScalar {
    let hash: [u8; 32] = Sha256::new()
        .chain_update(&nonce_point.serialize())
        .chain_update(&pubkey.serialize())
        .chain_update(msg)
        .finalize()
        .into();
    MaybeScalar::reduce_from(&hash)
}

fn random_scalar() -> Scalar {
    // In an actual implementation this would produce a scalar value
    // sampled from a CSPRNG.
    Scalar::two()
}

fn schnorr_sign(secret_key: Scalar, message: &[u8]) -> (Point, MaybeScalar) {
    let nonce = random_scalar();
    let nonce_point = nonce.base_point_mul();
    let pubkey = secret_key.base_point_mul();

let e = compute_challenge(&nonce_point, &pubkey, message);
    let s = nonce + secret_key * e;
    (nonce_point, s)
}

fn schnorr_verify(public_key: Point, signature: (Point, MaybeScalar), message: &[u8]) -> bool {
    let (r, s) = signature;
    let e = compute_challenge(&r, &public_key, message);
    s.base_point_mul() == r + e * public_key
}

let secret_key: Scalar = "0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef"
    .parse()
    .unwrap();
let public_key = secret_key.base_point_mul();

let message = b"I am the dragon!";

let signature = schnorr_sign(secret_key, message);
assert!(schnorr_verify(public_key, signature, message));
```

## Choice of Backbone

This crate does not implement elliptic curve point math directly. Instead we depend on one of two reputable elliptic curve cryptography libraries:

- C bindings to [`libsecp256k1`](https://github.com/bitcoin-core/secp256k1), via [the `secp256k1` crate](https://crates.io/crates/secp256k1), maintained by the Bitcoin Core team.
- A pure-rust implementation via [the `k256` crate](https://crates.io/crates/k256), maintained by the [RustCrypto](https://github.com/RustCrypto) team.

**One or the other can be used.** By default, this crate prefers to rely on `libsecp256k1`, as this is the most vetted and publicly trusted implementation of secp256k1 curve math available anywhere. However, if you need a pure-rust implementation, you can install this crate without it, and use the pure-rust `k256` crate instead.

```notrust
cargo add secp --no-default-features --features k256
```

If both `k256` and `secp256k1` features are enabled, then we default to using `libsecp256k1` bindings for the actual math, but still provide trait implementations to make this crate interoperable with `k256`.

## Documentation

To see the API documentation, [head on over to docs.rs](https://docs.rs/secp).

## CLI

This crate also offers a CLI tool for computing secp256k1 curve operations in your shell. Build it with `make cli`. A binary will be built at `target/release/secp`.

```not_rust
Usage:

-- Scalar operations --
  secp scalar gen                           Generate a random scalar.
  secp scalar add <scalar> [<scalar>...]    Sum two or more scalars.
  secp scalar mul <scalar> [<scalar>...]    Multiply two or more scalars.
  secp scalar inv <scalar>                  Multiplicative inverse of a scalar mod n.

-- Point operations --
  secp scalar gen                           Generate a random point.
  secp point add <point> [<point>...]       Sum two or more points.
  secp point mul <point> [<scalar>...]      Multiply a point by one or more scalars.

-- Formats --

Points are represented in 65-byte compressed hex format. Example:

02eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Scalars are represented in 32-byte hex format. Example:

e8c23ee3c98e040adea5dc92c5c381d6be93615f289ec2d505909657368a0c8f

Prepending a minus sign '-' in front of a point or scalar will negate it. Example:

-02eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

-- Special values --

- The values '0', '1', or '-1' may be substituted for any scalar.
- The value 'G' may be substituted for any point to represent the secp256k1 base point.
- The value '0' may be substituted for any point to represent the additive identity point (infinity).
```

Example usage:

```console
s1=`secp scalar gen`
s2=`secp scalar gen`
p1=`secp point mul G $s1`
p2=`secp point mul G $s2`
p3=`secp point add $p1 $p2`
p4=`secp point add $p1 -$p2`
```

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