On Methods for Implementation of Arithmetic Operations in Cryptographic Systemsстатья
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Дата последнего поиска статьи во внешних источниках: 26 ноября 2015 г.
Аннотация:Modifications of classical algorithms for multiplication and division of polynomials, which are effi-
cient for a small number of nonzero coefficients of one factor or of the divisor, respectively, are considered.
Ahybrid algorithm for multiplication of polynomials in GF(2n) that involves a modification of the classical
algorithm or of the Karatsuba method, depending on the form of the factors, and a method for reduction to the
standard basis with respect to an irreducible polynomial with a small number of nonzero coefficients are con-
structed. A modification of a known method and a new method for raising polynomials to a power and inverting
them are described. The complexity estimates for these methods and the results of experiments on the corre-
sponding software as applied to the problems of elliptic curve cryptography are analyzed.