Instructions and logic provide general purpose GF(28) SIMD cryptographic arithmetic functionality. Embodiments include a processor to decode an instruction for a SIMD affine transformation specifying a source data operand, a transformation matrix operand, and a translation vector. The transformation matrix is applied to each element of the source data operand, and the translation vector is applied to each of the transformed elements. A result of the instruction is stored in a SIMD destination register. Some embodiments also decode an instruction for a SIMD binary finite field multiplicative inverse to compute an inverse in a binary finite field modulo an irreducible polynomial for each element of the source data operand. Some embodiments also decode an instruction for a SIMD binary finite field multiplication specifying first and second source data operands to multiply each corresponding pair of elements of the first and second source data operand modulo an irreducible polynomial.