Algorithm for finding partitionings of hard variants of boolean satisfiability problem with application to inversion of some cryptographic functions

In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a...

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Bibliographic Details
Published in:SpringerPlus Vol. 5; no. 1; p. 554
Main Authors: Semenov, Alexander, Zaikin, Oleg
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 30.04.2016
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Humanities and Social Sciences
Monte Carlo simulation
multidisciplinary
Science
Science (multidisciplinary)
Monte Carlo method
Boolean satisfiability problem
Partitioning
Tabu search
SAT
Simulated annealing
SAT-based cryptanalysis
SAT@home
ISSN:2193-1801, 2193-1801
Online Access:Get full text
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Summary:In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.
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ISSN:2193-1801
2193-1801
DOI:10.1186/s40064-016-2187-4