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Journal Neurocomputers №10 for 2016 г.
Article in number:
Calculation of denormalizing factor for cryptographic transformations according to the RSA scheme using minimally redundant modular arithmetic
Keywords: RSA cryptosystem RSA cryptographic transformation residue number system interval-index characteristics the minimally redundant modular arithmetic Montgomery multiplication
Authors:
A.A. Kolyada - Dr.Sc. (Phys.-Math.), Associate Professor, Chief Research, Scientntict A.N. Sevchenko Institute of Applied Physics Problems of Byelorussian State University (Minsk) E-mail: razan@tut.by P.V. Kuchynski - Dr.Sc. (Phys.-Math.), Associate Professor, Director of A.N. Sevchenko Institute of Applied Physics Problems of Byelorussian State University (Minsk) E-mail: niipfp@bsu.by N.I. Chervyakov - Dr.Sc. (Eng.), Professor, Head of Department of the Applied Mathematics and Mathematical Modeling, Institute of Mathematics and Natural Sciences, North Caucasus Federal University (Stavropol) E-mail: Chervyakov@yandex.ru
Abstract:
The work is devoted to the problem of a denormalization of base transformations in the RSA cryptosystem with minimum excess modular code organization. To solve this problem we propose a new method, based on the multiplicative-subtractive calculation circuit recursive. The theoretical base of the applied approach is made by the device of interval and modular forms of numbers and interval and index characteristics. The used tools allow to reach essential simplification of the not modular operations which are a part of the synthesized procedure of calculation of denormalizing factor for cryptographic RSA transformations. These op-erations include the operations of multiplication on the modular base of the number system and bringing the accumulated works of the bases to the residue modular cryptosystem. On the set of cryptographic modules 1024-2048 digit bit time the proposed procedure on the PC with the Intel Core i5 processor (frequency of 2.27 GHz) is in the second range.
Pages: 4-12
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