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

Authors:
Chen Su;Haining Fan
Affiliations:
Key Laboratory for Information System Security, Ministry of Education, Beijing 100084, China and Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China and Scho ...;Key Laboratory for Information System Security, Ministry of Education, Beijing 100084, China and Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China and Scho ...
Venue:
Information Processing Letters
Year:
2012

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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.