Hardware Implementation Computations in Finite Fields Characteristics of Two

The article substantiates the need for hardware implementation of computational procedures in finite fields of the form GF(2m) with a high rate of speed. Analysis of different forms of the field elements GF(2m) representation was performed and showed that there is a need (in the process of computation) to move from one form of presentation elements to another, namely provide isomorphism field in hardware implementation. It was specified that for Galois fields with never-exceed 220 capacities it is expedient to use tabular method of elements field storage. Group of operations which should be performed on a numerical representation, and group operations, which should be performed on exponential representation elements field were selected. Architecture of computational tools for the implementation of operations in the field GF(2m), which during the computation combines exponential and numeric representation of the field elements, was proposed and it allows carrying out basic operations set of operands in a finite field. Simulation results of performance computations in finite fields of two properties in two ways of realization operations – software and hardware were shown.

Publication year: 
2013
Issue: 
6
УДК: 
681.3.04
С. 20–27., Іл. 4. Табл. 2. Бібліогр.: 9 назв.
References: 

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References [transliteration]: 

1. Ėlementarnoe vvedenie v ėllipticheskui͡u kriptografii͡u. Algebraicheskie i algoritmicheskie osnovy / A.A. Bolotov, S.B. Gashkov, A.B. Frolov, A.A. Chasovskikh. – M.: KomKniga, 2006. – 328 s.
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6. C.-Y. Lee and P.K. Meher, “Efficient bit-parallel multipliers over finite fields GF(2m)”, Computers and Electrical Eng., vol. 36, pp. 955–968, 2010.
7. M. Morales-Sandoval et al., “An area/performance trade-off analysis of a GF(2m) multiplier architecture for elliptic curve cryptography”, Ibid, vol. 35, pp. 54–58, 2009.
8. S.S. Erdem et al., “Polynomial Basis Multiplication over GF(2m)”, Acta Appl. Math., vol. 93, is. 1-3, pp. 33–55, 2006.
9. Hyun-Sung Kim and Il-Soo Jeon, “Semi-systolic Architecture for Modular Multiplication over GF(2m)”, in Computational Sci – ICCS 2005, Atlanta, Vol. 3516, pp. 912–915, 2005.

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