Andrew Okhrimenko

Work place: Department of System Analysis and Information Technology, Mariupol State University, 6/4, Preobrazhenska Str., Kyiv, 03037, Ukraine



Research Interests:


Andrew Okhrimenko: Senior Lecturer of the Department of system analysis and information technology of Mariupol State University, Kyiv, Ukraine. Areas of scientific interests: cryptography, large integer arithmetic’s, efficient implementation.

Author Articles
Software Implementation of Modular Reduction by Pseudo-mersenne Primes

By Mariia Kovtun Vladyslav Kovtun Oleksandr Stokipnyi Andrew Okhrimenko

DOI:, Pub. Date: 8 Aug. 2023

Modern cryptosystems allow the use of operation in prime fields with special kind of modules that can speed up the prime field operation: multiplication, squaring, exponentiation. The authors took into account in the optimizations: the CPU architecture and the multiplicity of the degree of the modulus in relation to the machine word width. As example, shown adopted module reduction algorithms hard-coded for modern CPU in special form of pseudo-Mersenne prime used in MAC algorithm Poly1305, - in electronic signature algorithm EdDSA and - in short message encryption algorithm DSTU 9041. These algorithms have been software implemented on both 32-bit and 64-bit platforms and compared with Barrett modular reduction algorithm for different pseudo-Mersenne and generalized-Mersenne modules. Timings for proposed and Barrett algorithms for different modules are presented and discussed.

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