Welcome to the resource topic for 2009/636
Title:
Obtaining More Karatsuba-Like Formulae over The Binary Field
Authors: Haining Fan, Ming Gu, Jiaguang Sun, Kwok-Yan Lam
Abstract:The aim of this paper 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. We first generalize the division algorithm, and then present a generalized definition of the remainder of integer division. Finally, a previously generalized Chinese remainder theorem is used to achieve our initial goal. As a by-product of the generalized remainder of integer division, we rediscover Montgomery’s N-residue and present a systematic interpretation of definitions of Montgomery’s multiplication and addition operations.
ePrint: https://eprint.iacr.org/2009/636
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