High performance GHASH function for long messages

Authors:
Nicolas Méloni;Christophe Négre;M. Anwar Hasan
Affiliations:
Department of Electrical and Computer Engineering, University of Waterloo, Canada;ELIAUS, University of Perpignan, France;Department of Electrical and Computer Engineering, University of Waterloo, Canada
Venue:
ACNS'10 Proceedings of the 8th international conference on Applied cryptography and network security
Year:
2010

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Abstract

This work presents a new method to compute the GHASH function involved in the Galois/Counter Mode of operation for block ciphers. If X = X1 . . . Xn is a bit string made of n blocks of 128 bits each, then the GHASH function effectively computes X1Hn+X2Hn-1+ . . . XnH, where H is an element of the binary field F2128. This operation is usually computed by using n successive multiply-add operations over F2128. In this work, we propose a method to replace all but a fixed number of those multiplications by additions on the field. This is achieved by using the characteristic polynomial of H. We present both how to use this polynomial to speed up the GHASH function and how to efficiently compute it for each session that uses a new H.