Module gf256 

Arithmetic in GF(2⁸) — the Galois field with 256 elements.

Uses the standard AES irreducible polynomial: p(x) = x⁸ + x⁴ + x³ + x + 1 (0x11b)

Operations

• add — addition = XOR (free)
• mul — multiplication via Russian-peasant (8 iterations, no lookup tables)
• inv — multiplicative inverse via Fermat: a⁻¹ = a²⁵⁴
• div — division = mul(a, inv(b))

Element 0 is the additive identity. Element 1 is the multiplicative identity. Calling inv or div with b=0 panics (division by zero).

Functions

add

Addition in GF(2⁸) — identical to XOR.

div

Division in GF(2⁸): a / b = a · b⁻¹.

inv

Multiplicative inverse of a via Fermat’s little theorem: a⁻¹ = a^254.

mul

Multiplication in GF(2⁸) using the Russian-peasant algorithm. Runs in exactly 8 iterations regardless of input values.

mul_acc

acc[i] ^= coeff * symbol[i] over GF(2⁸) — the inner loop of RLNC encoding.