Application of minimally redundant modular arithmetic to perform the cryptographic transformations in RSA-system

The article presents the methodological and algorithmic means of implementation of cryptographic RSA-transformations with the usage of minimally redundant modular arithmetic. Proposed solution contains redundant modular arithmetic algorithm of multiplication with squaring for exponentiation on a modular of cryptosystem and synthesis algorithm for evaluation of denormalization coefficient of computing scheme for this operation. Described exponentiation algorithm is based on optimized multiplicative minimally redundant modular arithmetic procedure of Montgomery multi-plication. Cryptographic transformation realized by proposed solution takes about 0.56…5.67 seconds for modules with digital capacity 1024…2048 bits under PC with processor Intel Core i5 (2,27 HHz). We developed new multiplicative-substractive method for denormalization coefficient calculation and fast and simple algorithm that takes nor more 13.3 minutes by conventional PC.