Watermarking of SAT using combinatorial isolation lemmas

Watermarking of hardware and software designs is an effective mechanism for intellectual property protection (IPP). Two important criteria for watermarking schemes are credibility and fairness. In this paper, we present the unique solution-based watermarking technique which provides, in a sense, the ultimate answer to both credibility and fairness requirements. Leveraging on a combinatorial theorem of Valiant and Vazirani, we demonstrate how ultimate credibility and complete fairness can almost always be achieved with high probability during the watermarking of the solution of the satisfiability (SAT) problem. The effectiveness of the technique is demonstrated on both specially created examples where the number of solutions is known, as well as on common CAD and operation research SAT instances.