algebra

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Libraries for finite field, elliptic curve, and polynomial arithmetic

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About

Libraries for finite field, elliptic curve, and polynomial arithmetic

arkworks::algebra

The arkworks ecosystem consist of Rust libraries for designing and working with zero knowledge succinct non-interactive arguments (zkSNARKs). This repository contains efficient implementations of the key algebraic components underlying zkSNARKs: finite fields, elliptic curves, and polynomials.

This library is released under the MIT License and the Apache v2 License (see License).

WARNING: This is an academic proof-of-concept prototype, and in particular has not received careful code review. This implementation is NOT ready for production use.

Directory structure

This repository contains several Rust crates:

ark-ff: Generic abstractions for, and implementations of various kinds of finite fields
ark-ec: Generic abstractions for prime-order groups, and implementations of various kinds of (pairing-friendly and standard) elliptic curves
ark-poly: Interfaces for univariate, multivariate, and multilinear polynomials, and FFTs over finite fields
ark-serialize: Efficient interfaces for serialization and point compression for finite fields and elliptic curves

In addition, the curves repository contains concrete implementations of popular elliptic curves; see here for details.

Build guide

The library compiles on the stable toolchain of the Rust compiler (v 1.51+). For the optimized assembly backend, Rust 1.59+ is required. To install the latest version of Rust, first install rustup by following the instructions here, or via your platform's package manager. Once rustup is installed, install the Rust toolchain by invoking:

bash

rustup install stable

After that, use cargo, the standard Rust build tool, to build the libraries:

bash

git clone https://github.com/arkworks-rs/algebra.git
cd algebra
cargo build --release

Tests

This library comes with comprehensive unit and integration tests for each of the provided crates. Run the tests with:

bash

cargo test --all

Benchmarks

To run the benchmarks, install the nightly Rust toolchain, via rustup install nightly, and then run the following command:

bash

cargo +nightly bench

Assembly backend for field arithmetic

The ark-ff crate contains (off-by-default) optimized assembly implementations of field arithmetic that rely on the adcxq, adoxq and mulxq instructions. These are available on most x86_64 platforms (Broadwell onwards for Intel and Ryzen onwards for AMD). Using this backend can lead to a 30-70% speedup in finite field and elliptic curve arithmetic. To build with this backend enabled, run the following command:

bash

RUSTFLAGS="-C target-feature=+bmi2,+adx" cargo [test/build/bench] --features asm

To enable this in the Cargo.toml of your own projects, enable the asm feature flag:

toml

ark-ff = { version = "0.4", features = [ "asm" ] }

Note that using this backend requires Rust 1.59+ for stable inline assembly support.

License

The crates in this repository are licensed under either of the following licenses, at your discretion.

Apache License Version 2.0 (LICENSE-APACHE or apache.org license link)
MIT license (LICENSE-MIT or opensource.org license link)

Unless you explicitly state otherwise, any contribution submitted for inclusion in this library by you shall be dual licensed as above (as defined in the Apache v2 License), without any additional terms or conditions.

Acknowledgements

This work was supported by: a Google Faculty Award; the National Science Foundation; the UC Berkeley Center for Long-Term Cybersecurity; and donations from the Ethereum Foundation, the Interchain Foundation, and Qtum.

An earlier version of this library was developed as part of the paper "ZEXE: Enabling Decentralized Private Computation".