Program and Scheme Methods of Multiplication of Polynomials for Elliptic Cryptographyстатья
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Дата последнего поиска статьи во внешних источниках: 17 декабря 2015 г.
Аннотация:An original scheme for multiplying polynomials based on Karatsuba’s method and a modification
of the method based on the Discrete Fourier Transform (DFT) are presented. Based on theoretical estimates of
the algorithm complexity it is shown that fast variants of the classical algorithm of polynomial multiplication
have advantages in runtime for polynomials in the degree range up to 100, while the computation by the sug-
gested scheme of multiplication is accomplished more quickly for the degree range of 100 to 1000 characteristic
of the cryptography of elliptic curves. For larger degrees, the advantages of using the DFT method reveal them-
selves. These conclusions are also confirmed by the results of computer tests of the developed library of arith-
metic operations in finite fields and groups of elliptic curves. The proposed scheme of multiplication allows a
hardware implementation.