Paper 2011/589

Impact of Intel's New Instruction Sets on Software Implementation of $GF(2)[x]$ Multiplication

Chen Su and Haining Fan

Abstract

PCLMULQDQ, a new instruction that supports $GF(2)[x]$ multiplication, was introduced by Intel in 2010. This instruction brings dramatic change to software implementation of multiplication in $GF(2^m)$ fields. In this paper, we present improved Karatsuba formulae for multiplying two small binary polynomials, compare different strategies for PCLMULQDQ-based multiplication in the five $GF(2^m)$ fields recommended by NIST and conclude the best design approaches to software implementation of $GF(2)[x]$ multiplication.

Note: Source code appended