FAST EXPONENTIATION IN GALOIS FIELDS USING PRECOMPUTATION
Authors
Rusanova Olga Veniaminovna
National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Ukraine
Kot Olga Sergeevna
National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Ukraine
Al-Mrayat Ghassan Abdel Jalil Halil
National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Ukraine
Abstract
The article proposes an approach to speed up the calculation of the exponent in Galois fields - the basic operation of a wide range of cryptographic algorithms. The properties of the polynomial square and the Montgomery group reduction with precomputations are used as the main reserve for improving the performance. A mathematical justification is given, a procedure for fast squaring on Galois fields is described. The presentation is illustrated with a numerical example. It has been shown that the proposed approach makes it possible peed up computations up to 3 times.
Keywords: exponentiation in Galois field, Montgomery reduction, precomputations.
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