Conflict-Driven XOR-Clause Learning

Laitinen, Tero; Junttila, Tommi; Niemelä, Ilkka

doi:10.1007/978-3-642-31612-8_29

Cited by 12 publications

(24 citation statements)

References 14 publications

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“…In addition to our previous work [12,14,15], also cryptominisat [11,13] can be seen to follow this framework.…”

Section: The Dpll(xor) Frameworkmentioning

confidence: 94%

“…The CDCL-part takes care of the usual unit clause propagation on the cnf-part φ or of the formula (line 4 in Fig. 1), conflict analysis and non-chronological backtracking (line [15][16][17], and heuristic selection of decision literals (lines 19-20) which extend the current partial truth assignment τ towards a total one. To handle the parity constraints in the xor-part φ xor , an xor-reasoning module M is coupled with the CDCL solver.…”

Section: The Dpll(xor) Frameworkmentioning

confidence: 99%

“…In such a case, the clause returned by the EXPLAIN method is used as the unsatisfied clause confl initiating the conflict analysis engine of the CDCL part (lines 10 and 15-17). In this paper, we study the process of deriving xor-implied literals and will not describe in detail how implying or-clauses are computed; the reader is referred to [12,14,15].…”

Section: The Dpll(xor) Frameworkmentioning

confidence: 99%

“…As we will see, this is actually the case for many "real-world" instances. The cnf-xor instances having such xor-clause conjunctions are probably best handled either by translating the xor-part into CNF or with unit propagation algorithms on parity constraints [10,11,15] instead of more complex xor-reasoning techniques.…”

Section: Unit Propagationmentioning

confidence: 99%

“…On the other hand, an instance consisting only of parity (xor) constraints can be solved in polynomial time using Gaussian elimination but CNF-based solvers relying only on basic Boolean constraint propagation tend to scale poorly on the straightforward CNF-encoding of the instance. To handle CNF instances including parity constraints, common in application domains such as circuit verification, bounded model checking, and logical cryptanalysis, several approaches have been developed [4,5,6,7,8,9,10,11,12,13,14,15]. These approaches extend CNF-level SAT solvers by implementing different forms of constraint propagation for parity constraints, ranging from plain unit propagation via equivalence reasoning to Gaussian elimination.…”

Section: Introductionmentioning

confidence: 99%

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Classifying and Propagating Parity Constraints

Laitinen

Junttila

Niemelä

2012

Lecture Notes in Computer Science

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Parity constraints, common in application domains such as circuit verification, bounded model checking, and logical cryptanalysis, are not necessarily most efficiently solved if translated into conjunctive normal form. Thus, specialized parity reasoning techniques have been developed in the past for propagating parity constraints. This paper studies the questions of deciding whether unit propagation or equivalence reasoning is enough to achieve full propagation in a given parity constraint set. Efficient approximating tests for answering these questions are developed. It is also shown that equivalence reasoning can be simulated by unit propagation by adding a polynomial amount of redundant parity constraints to the problem. It is proven that without using additional variables, an exponential number of new parity constraints would be needed in the worst case. The presented classification and propagation methods are evaluated experimentally. ⋆ The original version of the paper [1] has been presented in the 18th International Conference on Principle and Practice of Constraint Programming, CP 2012. An earlier version of the extended version has been presented for CP 2012 reviewers. This revised version uses proof techniques from [2].

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“…In addition to our previous work [12,14,15], also cryptominisat [11,13] can be seen to follow this framework.…”

Section: The Dpll(xor) Frameworkmentioning

confidence: 94%

Section: The Dpll(xor) Frameworkmentioning

confidence: 99%

Section: The Dpll(xor) Frameworkmentioning

confidence: 99%

Section: Unit Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Classifying and Propagating Parity Constraints

Laitinen

Junttila

Niemelä

2012

Lecture Notes in Computer Science

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Progress in Cryptology - AFRICACRYPT 2020

Nitaj

Youssef²

2020

Lecture Notes in Computer Science

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Logical cryptanalysis, first introduced by Massacci in 2000, is a viable alternative to common algebraic cryptanalysis techniques over boolean fields. With xor operations being at the core of many cryptographic problems, recent research in this area has focused on handling xor clauses efficiently. In this paper, we investigate solving the point decomposition step of the index calculus method for prime-degree extension fields F2n , using sat solving methods. We experimented with different sat solvers and decided on using WDSat, a solver dedicated to this specific problem. We extend this solver by adding a novel symmetry breaking technique and optimizing the time complexity of the point decomposition step by a factor of m! for the (m + 1) th summation polynomial. While asymptotically solving the point decomposition problem with this method has exponential worst time complexity in the dimension l of the vector space defining the factor base, experimental running times show that the presented sat solving technique is significantly faster than current algebraic methods based on Gröbner basis computation. For the values l and n considered in the experiments, the WDSat solver coupled with our symmetry breaking technique is up to 300 times faster than Magma's F4 implementation, and this factor grows with l and n.

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Logical Cryptanalysis with WDSat

Trimoska

Dequen

Ionica

2021

Theory and Applications of Satisfiability Testing – SAT 2021

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Over the last decade, there have been significant efforts in developing efficient XOR-enabled SAT solvers for cryptographic applications. In [22] we proposed a solver specialised to cryptographic problems, and more precisely to instances arising from the index calculus attack on the discrete logarithm problem for elliptic curve-based cryptosystems. Its most prominent feature is the module that performs an enhanced version of Gaussian Elimination. [22] is concentrated on the theoretical aspects of the new tool, but the running time-per-conflict results suggest that this module uses efficient implementation techniques as well. Thus, the first goal of this paper is to give a comprehensive exposition of the implementation details of WDSat. In addition, we show that the WDSat approach can be extended to other cryptographic applications, mainly all attacks that involve solving dense Boolean polynomial systems. We give complexity analysis for such systems and we compare different stateof-the-art SAT solvers experimentally, concluding that WDSat gives the best results. As a second contribution, we provide an original and economical implementation of a module for handling OR-clauses of any size, as WDSat currently handles OR-clauses comprised of up to four literals. We finally provide experimental results showing that this new approach does not impair the performance of the solver.⋆ We acknowledge financial support from the European Union under the 2014/2020 European Regional Development Fund (FEDER) and from the Agence Nationale de Recherche under project ANR20-ASTR-0011.

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Conflict-Driven XOR-Clause Learning

Cited by 12 publications

References 14 publications

Classifying and Propagating Parity Constraints

Classifying and Propagating Parity Constraints

Progress in Cryptology - AFRICACRYPT 2020

Logical Cryptanalysis with WDSat

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