On the Accuracy of Statistical Estimations of SAT Partitionings Effectiveness in Application to Discrete Function Inversion Problems

In this paper we study the problem of estimating the time required to process decompositions of hard SAT instances encoding inversion problems of some cryptographic functions. In particular, we consider one type of SAT decompositions, usually referred to as SAT partitioning. The effectiveness of a specific SAT parititioning is the total time required to solve all SAT instances from this partitioning. In the paper we construct statistical estimations of effectiveness of SAT partitionings with the help of computational scheme of the Monte Carlo method. We discuss the problem of accuracy of such estimations that arises because of drastic difference between the sizes of random samples, that can be processed in reasonable time, and the size of statistical population. We propose the method for improving constructed statistical estimations by using sets of random samples of increasing size followed by the extrapolation of obtained relation to the size of statistical population.