Distributed Nonlinear-Polynomial Computing Based on a Group of Polynomials over a Galois Field in the FPGA Architecture

A technique is proposed for performing distributed nonlinear-polynomial (NP) computing over Galois field. The technique is based on representing this polynomial by a group of similar polynomials over a Galois field, the power of which will be considerably lower than that of the field, over which the initial polynomial was defined. Due to the joint computation of elementary polynomials for a group of polynomials, the estimates of the NP computational complexity were reduced. Moreover, distributed computation of a group of similar polynomials allows adjusting the NP computation process to the predefined hardware basis. This also includes adjusting to the basis of field-programmable gate arrays (FPGAs), which also comprises logic and storage devices.