Crate sylow

Sylow: Elliptic Curve Cryptography Suite for BN254

Sylow is a Rust library implementing elliptic curve cryptography for the BN254 (alt-bn128) curve. It provides efficient implementations of finite fields, elliptic curve groups, and pairing-based cryptography, suitable for applications in a blockchain environment, in zero-knowledge proving, and in other cryptographic systems.

Quick Start

Add Sylow to your Cargo.toml:

[dependencies]
sylow = "0.1.0"

Key Features

• Finite field arithmetic (𝔽ₚ, 𝔽ₚ², 𝔽ₚ⁶, 𝔽ₚ¹²)
• Elliptic curve group operations (𝔾₁, 𝔾₂, 𝔾ₜ)
• Highly optimized optimal ate pairing
• BLS signature scheme
• Hash-to-curve functionality

Basic Usage

Here’s an example of generating a key pair, signing a message, and verifying the signature:

use sylow::{KeyPair, sign, verify};

// Generate a new key pair
let key_pair = KeyPair::generate();

// Sign a message
let message = b"Hello, Sylow!";
let signature = sign(&key_pair.secret_key, message).expect("Signing failed");

// Verify the signature
let is_valid = verify(&key_pair.public_key, message, &signature).expect("Verification failed");
assert!(is_valid, "Signature verification failed");

Core Components

• Fp, Fp2, Fp6, Fp12: Finite field implementations
• G1Projective, G2Projective: Elliptic curve group elements
• pairing(): Bilinear pairing operation
• KeyPair: BLS key pair generation
• sign, verify: BLS signature operations

Performance and Security

Sylow uses optimized algorithms and constant-time implementations to ensure both efficiency and security. It follows best practices outlined in RFC 9380 for operations like hashing to curve points.

Further Reading

For more detailed information, examples, and advanced usage, please refer to the full documentation and the GitHub repository.

Structs

• Fp
  Represents an element in the base field 𝔽ₚ or the r-torsion subgroup 𝔽ᵣ.
• Fr
  Represents an element in the base field 𝔽ₚ or the r-torsion subgroup 𝔽ᵣ.
• G2PreComputed
  Precomputed data for efficient Miller loop calculations on 𝔾₂ points.
• Gt
  Represents an element of the target group 𝔾ₜ in the BN254 pairing.
• KeyPair
  Represents a pair of secret and public keys for BLS signatures
• MillerLoopResult
  Represents the result of a Miller loop computation in pairing-based cryptography.
• XMDExpander
  Implements the XMD (Expand Message XOF) function, which produces a uniformly random byte string using a hash function that outputs a fixed-length of b bits.
• XOFExpander
  Implements the XOF (Expand Message XOF) function, which produces a uniformly random byte string using an extendable output function (XOF) H.

Enums

• GroupError
  Errors that can occur when working with group elements.

Traits

• Expander
  Defines the message expansion and conversion to field element functions
• FieldExtensionTrait
  Defines operations for field extensions in elliptic curve cryptography.
• GroupTrait
  Defines the basic operations for elliptic curve group elements.

Functions

• glued_miller_loop
  Performs a batched pairing calculation for multiple pairs of 𝔾₁ and 𝔾₂ points.
• glued_pairing
  The driver code for the glued miller loop execution, see comments above.
• pairing
  Computes the optimal ate pairing for a pair of points on the BN254 curve.
• sign
  Signs a message using the BLS signature scheme
• verify
  Verifies a BLS signature

Type Aliases

• Fp2
  Represents an element in the quadratic extension (𝔽ₚ²) of the base field (𝔽ₚ).
• Fp6
  Represents an element the sextic (𝔽ₚ⁶) extension of the base field (𝔽ₚ)
• Fp12
  Represents an element the dodecic (𝔽ₚ¹²) extension of the base field (𝔽ₚ)
• G1Affine
  Affine representation of a point in the 𝔾₁ group
• G1Projective
  Projective representation of a point in the 𝔾₁ group
• G2Affine
  Affine representation of a point in the 𝔾₂ group on the quadratic extension field
• G2Projective
  Projective representation of a point on the 𝔾₂ group on the quadratic extension field