Hard Instance Generation for SAT (Extended Abstract)

We consider the problem of generating hard instances for the Satisfying Assignment 'TechSearch Problem (in short, SAT). It is not known whether SAT is difficult on average, while it has been believed that the Factorization Problem (in short, FACT) is hard on average. Thus, one can expect to generate hard-on-average instances by using a reduction from FACT to SAT. Although the asymptotically best reduction is obtained by using the Fast Fourier Transform [SS71], its constant factor is too big in practice. Here we propose to use the Chinese Remainder Theorem for constructing efficient yet simple reductions from FACT to SAT. (In this extended abstract, most proofs are omitted; see [HW97].)