Impact of Intel's new instruction sets on software implementation of GF(2)[x] multiplication

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.

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