THE EMPLOYMENT OF MONTGOMERY REDUCTION FORACCELERATION OF EXPONENT ON GALOISE FIELDS CALCULATION

Authors

  • Oleksandr Markovskyi National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine
  • Viktoriia Maksymuk National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine
  • Olha Kot National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine
  • Volodymyr Kuts National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine

Keywords:

Galois fields, public key cryptographic algorithms, Montgomery reduction

Abstract

The paper proposes an approach to acceleration of the calculation of the Galois field exposure operation, which is important for cryptographic data protection, based on a modification of Montgomery technology. The methods of multiplication and exponentiation in Galois fields with the Montgomery reduction of intermediate results are proposed. It is shown that the use of modified Montgomery technology allows to accelerate the calculation of the exponent in the Galois fields 5 .5 times.

References

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Montgommery P.L. Modular multiplication without trial division / P.L. Montgommery // Mathematics of Computation. — 1985— Vol. 44. — Р. 519-521.

Koc C.K. Analyzing and comparing Montgomery Multiplication Algorithms./ С.К. Кос, Acar T., Kaliski B.S. // IEEE Micro. —1996 — V.16, № 3. — Р. 26— 33.

Samofalov KG Methods of accelerated implementation of exponentiation in Galois fields in the information protection system / Markovsky OP, Sharshakov AS // Problems of information information and management. Collection of scientific works: K., NAU. - 2011. - Vol.2, № 33 - P.143-151.

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Published

2023-06-08

Issue

Section

IoT, Real Time Systems