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Oleg Zaikin

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4 papers

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AAAI Conference 2026 Conference Paper

Using Constraint Solvers to Construct Binary Codes with Good Error Correction Performance

Stepan Kochemazov
Oleg Zaikin
Grigorii Trofimiuk
Kirill Antonov
Alexander Semenov

In recent years, constraint solvers show increasing use in solving various open combinatorial problems, e.g., from Ramsey theory or synthesis of combinatorial designs. The similar approach can be applied to some problems related to binary linear codes, which form one of the largest families of error correcting codes used both in coding theory and in various practical applications. Thanks to a simple algebraic structure of such codes it is possible to study them using a wide range of methods. Note that even codes with the same basic parameters (length n, dimension k, minimum code distance d) can show different error correction performance, i.e., the ability to correct errors which appear in a noisy channel. In the paper, we formulate the problem of finding binary linear codes with good error correction performance as a constraint optimization problem and explore the effectiveness of modern constraint solvers on it, including SAT, MaxSAT, and CP solvers. Using the respective solvers and parallel computing, for several values of n, k, d we found the codes which are significantly better than the known in terms of their practical performance.

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JAIR Journal 2024 Journal Article

Inverting Cryptographic Hash Functions via Cube-and-Conquer

Oleg Zaikin

MD4 and MD5 are fundamental cryptographic hash functions proposed in the early 1990s. MD4 consists of 48 steps and produces a 128-bit hash given a message of arbitrary finite size. MD5 is a more secure 64-step extension of MD4. Both MD4 and MD5 are vulnerable to practical collision attacks, yet it is still not realistic to invert them, i.e., to find a message given a hash. In 2007, the 39-step version of MD4 was inverted by reducing to SAT and applying a CDCL solver along with the so-called Dobbertin’s constraints. As for MD5, in 2012 its 28-step version was inverted via a CDCL solver for one specified hash without adding any extra constraints. In this study, Cube-and-Conquer (a combination of CDCL and lookahead) is applied to invert step-reduced versions of MD4 and MD5. For this purpose, two algorithms are proposed. The first one generates inverse problems for MD4 by gradually modifying the Dobbertin’s constraints. The second algorithm tries the cubing phase of Cube-and-Conquer with different cutoff thresholds to find the one with the minimum runtime estimate of the conquer phase. This algorithm operates in two modes: (i) estimating the hardness of a given propositional Boolean formula; (ii) incomplete SAT solving of a given satisfiable propositional Boolean formula. While the first algorithm is focused on inverting step-reduced MD4, the second one is not area-specific and is therefore applicable to a variety of classes of hard SAT instances. In this study, 40-, 41-, 42-, and 43-step MD4 are inverted for the first time via the first algorithm and the estimating mode of the second algorithm. Also, 28-step MD5 is inverted for four hashes via the incomplete SAT solving mode of the second algorithm. For three hashes out of them, it is done for the first time.

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IJCAI Conference 2022 Conference Paper

Inverting 43-step MD4 via Cube-and-Conquer

Oleg Zaikin

MD4 is a prominent cryptographic hash function proposed in 1990. The full version consists of 48 steps and produces a hash of size 128 bits given a message of an arbitrary finite size. In 2007, its truncated 39-step version was inverted via reducing to SAT and applying a CDCL solver. Since that time, several attempts have been made but the 40-step version still remains unbroken. In this study, 40-, 41-, 42-, and 43-step versions of MD4 are successfully inverted. The problems are reduced to SAT and solved via the Cube-and-Conquer approach. Two algorithms are proposed for this purpose. The first one generates inversion problems for MD4 by adding special constraints. The second one is aimed at finding a proper threshold for the cubing phase of Cube-and-Conquer. While the first algorithm is focused on inverting MD4 and similar cryptographic hash functions, the second one is not area specific and so is applicable to a variety of classes of hard SAT instances.

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AAAI Conference 2018 Conference Paper

On Cryptographic Attacks Using Backdoors for SAT

Alexander Semenov
Oleg Zaikin
Ilya Otpuschennikov
Stepan Kochemazov
Alexey Ignatiev

Propositional satisﬁability (SAT) is at the nucleus of state-ofthe-art approaches to a variety of computationally hard problems, one of which is cryptanalysis. Moreover, a number of practical applications of SAT can only be tackled efﬁciently by identifying and exploiting a subset of formula’s variables called backdoor set (or simply backdoors). This paper proposes a new class of backdoor sets for SAT used in the context of cryptographic attacks, namely guess-and-determine attacks. The idea is to identify the best set of backdoor variables subject to a statistically estimated hardness of the guess-anddetermine attack using a SAT solver. Experimental results on weakened variants of the renowned encryption algorithms exhibit advantage of the proposed approach compared to the state of the art in terms of the estimated hardness of the resulting guess-and-determine attacks.

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