In AES's Galois field, addition and XOR are the same operation

Galois Finite Fields and the Advanced Encryption Standard (AES)

A lecture walkthrough of how AES uses GF(2^8), the Galois field with 256 elements. Bytes map to polynomials over single-bit coefficients, so addition, subtraction, and XOR all collapse into one operation, and multiplication is polynomial multiplication reduced by 0x11b. The AES round then chains S-box inverses, ShiftRows, MixColumns, and key XOR—layered operations that resist the linear attacks simpler ciphers fall to.