This library provides efficient and flexible implementations of various halo2-friendly elliptic curves, originally implementing the BN256 curve with traits from the zkcrypto ecosystem,

• zkcrypto/ff
• zkcrypto/group
• zkcrypto/pairing

The implementations were originally ported from matterlabs/pairing and zkcrypto/bls12-381, but have been extended and optimized to cover a broader set of curves and use cases. Since its initial release, the library has expanded to include additional curves, along with the following features:

• secp256k1, secp256r1, and grumpkin curves, enhancing its usability across a range of cryptographic protocols.
• Assembly optimizations leading to significantly improved performance.
• Various features related to serialization and deserialization of curve points and field elements.
• Curve-specific optimizations and benchmarking capabilities.

Benchmarking is supported through the use of Rust's built-in test framework. Benchmarks can be run without assembly optimizations:

$ cargo test --profile bench test_field -- --nocapture

or with assembly optimizations:

$ cargo test --profile bench test_field --features asm -- --nocapture

1. Derivation of Serialize/Deserialize: The library supports Serde's Serialize and Deserialize traits for field and group elements, making it easier to integrate curve operations into serialization-dependent workflows.

2. Hash to Curve: For the bn256::G1 and grumpkin::G1 curves, hash_to_curve is implemented, enabling more efficient hash-and-sign signature schemes.

3. Lookup Table: A pre-computed lookup table is available for bn256::Fr, accelerating conversion from u16 to montgomery representation.

The library's top-level directories are organized as follows:

• benches: Contains benchmarking tests.
• script: Contains utility scripts.
• src: Contains the source code of the library, further subdivided into modules for each supported curve (bn256, grumpkin, secp256k1, secp256r1, pasta) and additional functionalities (derive, tests).