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Obtaining more Karatsuba-like formulae over the binary field

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4 Author(s)
Fan, H. ; Key Lab. for Inf. Syst. Security, Tsinghua Univ., Beijing, China ; Gu, M. ; Sun, J. ; Lam, K.-Y.

The aim of this study is to find more Karatsuba-like formulae for a fixed set of moduli polynomials in GF(2)[x]. To this end, a theoretical framework is established. The authors first generalise the division algorithm, and then present a generalised definition of the remainder of integer division. Finally, a generalised Chinese remainder theorem is used to achieve their initial goal. As a by-product of the generalised remainder of integer division, the authors rediscover Montgomery's N-residue and present a systematic interpretation of definitions of Montgomery's multiplication and addition operations.

Published in:

Information Security, IET  (Volume:6 ,  Issue: 1 )