Galois Finite Fields and the Advanced Encryption Standard (AES)
Summary
The article introduces GF(2^8), the finite field used by AES, and explains how arithmetic in this field is performed using polynomials, binary representations, and a reduction polynomial (0x11b). It then outlines AES operations—S-box, ShiftRows, MixColumns, and round key addition—highlighting how finite-field arithmetic underpins the cipher’s invertibility and security. The piece includes illustrative tables and examples to visualize field multiplication and AES-related computations, making it a solid educational resource on cryptographic foundations.