Galois Field Instructions in the Sandblaster 2.0 Architectrue

Abstract EN

This paper presents a novel approach to implementing multiplication of Galois Fields with 2N.

Elements of GF(2N) can be represented as polynomials of degree less than N over GF(2).

Operations are performed modulo an irreducible polynomial of degree n over GF(2).

Our approach splits a Galois Field multiply into two operations, polynomial-multiply and polynomial-remainder over GF(2).

We show how these two operations can be implemented using the same hardware.

Further, we show that in many cases several polynomial-multiply operations can be combined before needing to a polynomial-remainder.

The Sandblaster 2.0 is a SIMD architecture.

It has SIMD variants of the poly-multiply and poly-remainder instructions.

We use a Reed-Solomon encoder and decoder to demonstrate the performance of our approach.

Our new approach achieves speedup of 11.5x compared to the standard SIMD processor of 8x.