Fast Exponential Method on Galois Fields for Cryptographic Applications

A method for accelerated calculation of the exponent on Galois fields is proposed and investigated in relation to its use in cryptography. Acceleration is achieved through the use of precomputations that depend on the generating polynomial and the number over which the exponentiation is performed. Special procedures have been developed for fast squaring and multiplication by a constant number on Galois fields, based on the use of precalculations. It has been theoretically and experimentally proven that the developed method allows an 8-fold increase in the speed of calculating the exponent on Galois fields compared to known methods.