Generic polynomial

About: Generic polynomial is a research topic. Over the lifetime, 608 publications have been published within this topic receiving 6784 citations.

Efficient gröbner basis reductions for formal verification of galois field multipliers

Abstract: Galois field arithmetic finds application in many areas, such as cryptography, error correction codes, signal processing, etc Multiplication lies at the core of most Galois field computations This paper addresses the problem of formal verification of hardware implementations of (modulo) multipliers over Galois fields of the type F 2k , using a computer-algebra/algebraic-geometry based approach The multiplier circuit is modeled as a polynomial system in F 2k [x 1 , x 2 , … , x d ] and the verification problem is formulated as a membership test in a corresponding (radical) ideal This requires the computation of a Grobner basis, which can be computationally intensive To overcome this limitation, we analyze the circuit topology and derive a term order to represent the polynomials Subsequently, using the theory of Grobner bases over Galois fields, we prove that this term order renders the set of polynomials itself a Grobner basis of this ideal - thus significantly improving verification Using our approach, we can verify the correctness of, and detect bugs in, upto 163-bit circuits in F 2 163 ; whereas contemporary approaches are infeasible