Neural algorithms of data performing in finite fields GF(2m )

Neural networks realizing finite-field arithmetic are presented. The neural algorithms of addition and multiplication are exploited to develop a neural network realizing Zhegalkin´s polynomial of the Boolean function. Neural algorithms for addition and exponentiation computation were used for solving linear equation systems and for evaluating logarithms in finite fields. The author presents the operations´ run-time expressions in finite fields with neural networks and a comparative estimation of existing multiplication and exponentiation algorithms