Finding Effective SAT Partitionings Via Black-Box Optimization

Семенов, А. А.; Zaikin, Oleg; Kochemazov, Stepan

doi:10.1007/978-3-030-66515-9_11

Cited by 6 publications

(4 citation statements)

References 35 publications

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“…Future work may include the development of optimization algorithms similar to ones described in [30,35,32] for finding cubes over auxiliary variables with good statistical estimation of hardness of LEC w.r.t. the corresponding SAT partitioning.…”

Section: Discussionmentioning

confidence: 99%

Estimating the hardness of SAT encodings for Logical Equivalence Checking of Boolean circuits

Semenov¹,

Chukharev²,

Tarasov³

et al. 2022

Preprint

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In this paper we investigate how to estimate the hardness of Boolean satisfiability (SAT) encodings for the Logical Equivalence Checking problem (LEC). Meaningful estimates of hardness are important in cases when a conventional SAT solver cannot solve a SAT instance in a reasonable time. We show that the hardness of SAT encodings for LEC instances can be estimated w.r.t. some SAT partitioning. We also demonstrate the dependence of the accuracy of the resulting estimates on the probabilistic characteristics of a specially defined random variable associated with the considered partitioning. The paper proposes several methods for constructing partitionings, which, when used in practice, allow one to estimate the hardness of SAT encodings for LEC with good accuracy. In the experimental part we propose a class of scalable LEC tests that give extremely complex instances with a relatively small input size 𝑛 of the considered circuits. For example, for 𝑛 = 40, none of the state-of-the-art SAT solvers can cope with the considered tests in a reasonable time. However, these tests can be solved in parallel using the proposed partitioning methods.

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Section: Discussionmentioning

confidence: 99%

Estimating the hardness of SAT encodings for Logical Equivalence Checking of Boolean circuits

Semenov¹,

Chukharev²,

Tarasov³

et al. 2022

Preprint

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show abstract

“…The next step consists in automatizing the search for such B that yields an attack with acceptable hardness estimation (11). Here we will use the approach described in a series of works [20], [21], [22], [23]. These papers considered guessand-determine attacks which employed the SAT solvers to solve subproblems weakened by substituting into CNF formulas the values of variables from a guessed bits set.…”

Section: Construction Of Guess-and-determine Attack As a Metaheuristi...mentioning

confidence: 99%

“…specific guessed bits set B and specific algorithm A with the ability to move between different guessed bits sets using metaheuristic optimization was apparently first proposed in [20] and [74]. Later, a number of guessand-determine attacks were constructed using metaheuristic pseudo-Boolean optimization in [22], [23], and [31]. We are aware of several other works that proposed the approaches to automatic construction of guess-and-determine attacks but they are based on other principles compared to the ones used in our method (e.g.…”

Section: Related Workmentioning

confidence: 99%

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Using Linearizing Sets to Solve Multivariate Quadratic Equations in Algebraic Cryptanalysis

Semenov,

Antonov,

Kochemazov

et al. 2023

IEEE Access

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In this paper we describe a class of cryptographic guess-and-determine attacks which is based on the notion of a linearizing set. A linearizing set-based attack is applied to a system of Multivariate Quadratic equations (MQ) over GF(2) field, which encodes how a considered cryptographic function works. By substituting into such MQ system a random (in some strict sense) assignment of variables from a linearizing set we aim to transform the system into a linear one. We introduce a probability of such an event and call it a probability of linearization. Then we describe a guess-and-determine attack, the hardness of which can be expressed via a probability of linearization. To estimate the latter it is possible to use a simple Monte Carlo algorithm. Also we describe a technique that allows to augment a considered MQ system by new linear equations and to construct a new MQ system, for which the probability of linearization is usually larger than that for an original one. For this purpose we apply a SAT oracle to a Boolean formula that is naturally associated with a considered MQ system. Finally, we reduce the problem of searching for a linearizing set that yields the best effectiveness of a constructed guess-and-determine attack to a pseudo-Boolean optimization problem, which can be solved using metaheuristic optimization algorithms. The important consequence of this is that this way we can construct guess-and-determine attacks automatically by solving the corresponding optimization problem. In the computational experiments we used the proposed methodology to construct attacks on several well-known stream ciphers. The runtime estimations of some of the attacks make it possible to implement them in reasonable time.INDEX TERMS Algebraic cryptanalysis, guess-and-determine attack, system of multivariate quadratic equations, Boolean satisfiability, pseudo-Boolean optimization, evolutionary algorithm.

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Searching for Orthogonal Latin Squares via Cells Mapping and BOINC-Based Cube-and-Conquer

Vatutin

Zaikin

Manzyuk³

et al. 2021

Communications in Computer and Information Science

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Finding Effective SAT Partitionings Via Black-Box Optimization

Cited by 6 publications

References 35 publications

Estimating the hardness of SAT encodings for Logical Equivalence Checking of Boolean circuits

Estimating the hardness of SAT encodings for Logical Equivalence Checking of Boolean circuits

Using Linearizing Sets to Solve Multivariate Quadratic Equations in Algebraic Cryptanalysis

Searching for Orthogonal Latin Squares via Cells Mapping and BOINC-Based Cube-and-Conquer

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