Time complexity of multipliers for Galois fields

Abstract

Multipliers for binary Galois field GF (2n) hardware complexity allows to implement in FPGA an operational device with multiple multipliers. But because of large structural complexity for some combinations of large degrees n of field and the multipliers number to make it is practically impossible. One of the possible choices of this problem solving is the move to using Galois fields with the base d, greater than 2. Multipliers for such extended Galois field GF (dm) with approximately the same number of elements dm  2n are estimated in the article in terms of their time complexity to determine the fields in which the multiplier will have the least time complexity.