Noir BigInt

Packages

This library provides three crates:

• biguint - custom unsigned big integer type implemented using u56 limbs
• primefield - wrapper around biguint that implements prime field operations
• curves - example elliptic curve libraries built using the primefield type

biguint

This crate provides a custom BigUint56 data type, allowing for computations on large unsigned integers. The integers are represented with a fixed number of limbs, each of which is a 56-bit unsigned integer.

We utilize u56 limbs for two primary reasons:

1. 56 is divisible by 8, simplifying conversions to/from bytes.
2. Multiplication requires a double-width intermediate value and u112 is the maximum double-width value that can be represented in Noir.

This provides various functionalities such as arithmetic operations (addition, subtraction, multiplication, division), bitwise operations (left shift, right shift), comparisons and conversions (to bytes, to bits).

primefield

This contains the PrimeField data type, which allows for efficient operations on prime field elements. This is implemented as a wrapper around the BigUint56 type and stores the values in the Montgomery form for efficient modular multiplication/reduction.

curves

This crate contains examples of the secp256k1 and the ed25519 curves implemented using the PrimeField type.

Installation

In your Nargo.toml file, add the following dependency:

[dependencies]
noir_bigint = { tag = "v0.1.0", git = "https://github.com/shuklaayush/noir-bigint" }

Testing

Tests are run using nargo:

nargo test

All tests are run as part of the CI pipeline test.yaml.

Contributing

Contributions are welcome! Please adhere to the following guidelines:

• Open a pull request with a clear description of your changes.
• Changes should aim to improve code efficiency or readability.
• Add appropriate tests, ensuring all pass before submission.

Acknowledgements

• Original noir-bigint
• Rust crypto-bigint
• Rust num-bigint

Disclaimer

This is experimental software and is provided on an "as is" and "as available" basis. We do not give any warranties and will not be liable for any losses incurred through any use of this code base.