A case study of algorithm implementation in reconfigurable hardware and software

Abstract

We present a case study of implementation of a combinatorial search problem in both reconfigurable hardware and software. The particular problem is the search for approximate solutions of overconstrained systems of equations over GF(2). The problem is of practical interest in cryptanalysis. We consider the efficient implementation of exhaustive search techniques to find the best solutions of sets of up to 1000 equations over 30 variables. Best is defined to be those variable assignments that leave the minimum number of equations unsatisfied. As we apply various techniques to speed up this computation, we find that the techniques, whether inspired by software or reconfigurable hardware, are applicable to both implementation domains. While reconfigurable hardware offers greater raw compute power than software, new microprocessor with wide datapaths and far higher clock speeds do not lag far behind. Software also benefits from faster compilation times which prove important for some optimizations.