galois-field-gf256

Arithmetic over the finite field GF(2^8), using the same irreducible polynomial as AES: x^8 + x^4 + x^3 + x + 1 (0x11B). Handy for building Reed-Solomon codecs, AES internals, or any bytewise finite-field code.

Zero dependencies. Pure ESM.

Install

npm install galois-field-gf256

Usage

import { gmul, mul, inverse, div, pow } from "galois-field-gf256";

gmul(0x57, 0x83); // 0xC1  (the AES spec example)
mul(0x53, inverse(0x53)); // 1
div(0x06, 0x02); // 0x03
pow(0x02, 8); // 0x1B

API

| Function | Description | | --------------- | ------------------------------------------------------------------ | | gadd(a, b) | Field addition — this is just XOR. | | gsub(a, b) | Subtraction — identical to addition in characteristic 2. | | gmul(a, b) | Carry-less multiply with on-the-fly reduction (no tables). | | mul(a, b) | Table-driven multiply. Same result as gmul, faster for hot loops.| | inverse(a) | Multiplicative inverse. Throws for a === 0. | | div(a, b) | a * inverse(b). Throws for b === 0. | | pow(a, n) | Integer power; negative n uses the inverse. | | exp(i) | generator^i where the generator is 0x03. | | log(a) | Discrete log base the generator. Throws for a === 0. |

Notes

The exp/log tables are built at import time from the primitive element 0x03. All bytes are masked to 8 bits, so passing larger integers is safe (only the low byte is used).

License

MIT