Isochronous finite fields

This crate implements finite field arithmetic on finite fields with 2⁸ elements, often denoted as GF(2⁸), in an isochronous manner. This means that it will always run in the same amount of time, no matter the input.

The implementation isochronous, because it:

• is branch free
• runs in constant time
• doesn't do table lookups

This crate uses the irreducible polynomial x⁸ + x⁴ + x³ + x + 1 for multiplication, as standardized for the AES algorithm in FIPS 197.

Example

// Add two elements of the Galois field GF(2^8) together.
assert_eq!(GF(5) + GF(12), GF(9));

// Subtract two elements of the Galois field GF(2^8).
assert_eq!(GF(32) - GF(219), GF(251));

// Multiply two elements of the Galois field GF(2^8) together.
assert_eq!(GF(175) * GF(47),  GF(83));

// Calculate the multiplicative inverse of GF(110) in the Galois field GF(2^8).
assert_eq!(GF(110).multiplicative_inverse(), GF(33));
assert_eq!(GF(110) * GF(33), GF(1));

License

This project is licensed under the MIT License - see the LICENSE file for details.