Expand description
An implementation of a 64-bit STARK-friendly prime field with modulus $2^{64} - 2^{32} + 1$ using Montgomery representation.
Our implementation follows https://eprint.iacr.org/2022/274.pdf and is constant-time.
This field supports very fast modular arithmetic and has a number of other attractive properties, including:
- Multiplication of two 32-bit values does not overflow field modulus.
- Field arithmetic in this field can be implemented using a few 32-bit addition, subtractions, and shifts.
- $8$ is the 64th root of unity which opens up potential for optimized FFT implementations.
Structsยง
- Base
Element - Represents base field element in the field using Montgomery representation.