GF(2^8) Matrix Multiplication Calculator

What is GF(2^8)?

GF(2^8) is a finite field with 256 elements. In this calculator, we represent elements as hexadecimal values (00-FF). Matrix multiplication in GF(2^8) follows special rules where addition is XOR and multiplication uses polynomial arithmetic modulo an irreducible polynomial.

How does GF(2⁸) multiplication work?

GF(2⁸) multiplication is a key operation in AES encryption. It follows these steps:

Convert operands to binary polynomials
Multiply the polynomials using standard polynomial multiplication
Reduce the result modulo the irreducible polynomial x⁸ + x⁴ + x³ + x + 1 (0x11B in hex)

This calculator implements the efficient "Russian Peasant Multiplication" algorithm to perform this operation.

Matrix 1

Default: AES MixColumns transformation matrix

🧮 GF(2⁸) Matrix Calculator

Matrix 1

Matrix 2

Result Matrix