Fast implementation zero knowledge identification schemes using the Galois Fields arithmetic

This article proposes an approach that accelerates the realization of user identification schemes that follow the principle of zero knowledge. The proposed approach is based on using finite field arithmetic to replace the usual modular arithmetic approaches. The application of this efficient method that was developed using Galois Fields, renders feasible an exponential reduction of the computation time required for classical zero knowledge authentication methods, such as FFSIS, Schnorr and Guillou & Quisquater. Modifications of the relevant schemes are presented that use Galois Field multiplication operations. It is shown, both theoretically and experimentally that the proposed procedure attains a per order acceleration of the execution time required for the user authentication by 2-3 orders of magnitude, via a hardware implementation.