THE EMPLOYMENT OF MONTGOMERY REDUCTION FORACCELERATION OF EXPONENT ON GALOISE FIELDS CALCULATION
Keywords:
Galois fields, public key cryptographic algorithms, Montgomery reductionAbstract
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
Markovskyy, O.P Galois fields algebra utilization for implementation of the conception of zero-knowledge under identification and authentication of remote users/Zacharioudakis Leftherios, Maksymuk V.R.. // Electronic modeling. Collection of scientific works: V 6(39).- 2017.- P.33-45.
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.