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Organization of fast exponentiation on galois fields for cryptographic data protection systems
(National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 2022) Halil, Al-Mrayt Ghassan Abdel Jalil; Markovskiy, Oleksandr; Stupak, Alona
The article proposes the organization of accelerated execution of the basic operation of a wide range of cryptographic algorithms with a public key - exponentiation on finite Galois fields GF(2n ). Acceleration of the computational implementation of this operation is achieved by organizing the processing of several bits of the code at once during squaring on Galois fields. This organization is based on the use of polynomial squared properties, Montgomery group reduction, and extensive use of previous calculations. Procedures for performing basic operations of exponentiation on Galois fields are developed in detail, the work of which is illustrated by numerical examples. It has been proved that the proposed organization can increase the computational speed of this operation by 2.4 times, which is significant for cryptographic applications.