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3BA: A Border Bases Solver with a SAT Extension

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10931)


Many search problems over Boolean variables can be formulated in terms of satisfiability of a set of clauses or solving a system of Boolean polynomials. On one hand, there exists a great variety of software coming from different areas such as commutative algebra, SAT or SMT, that can be used to tackle these instances. On the other hand, their approaches to inferring new constraints vary and seem to be complementary to each other. For instance, compare the handling of XOR constraints in SAT solvers to that in computer algebra systems. We present a C++ implementation of a platform that combines the power of the Boolean Border Basis Algorithm (BBBA) with a CDCL SAT solver in a portfolio-based fashion. Instead of building a complete fusion or a theory solver for a particular problem, both solvers work independently and interact through a communication interface. Hence a greater degree of flexibility is achieved. The SAT solver antom, which is currently used in the integration, can be easily replaced by any other CDCL solver. Altogether, this is the first open-source implementation of the BBBA and its combination with a SAT solver.


  • Boolean Border Basis Algorithm
  • Boolean polynomial
  • Cryptographic attack
  • SAT solving

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The authors are grateful to Tobias Schubert for providing us the SAT solver antom [13] and Jan Burchard for making the communication between antom and 3BA possible. John Abbott and Anna Bigatti gave us useful feedback on our C++ implementation. This work was financially supported by the DFG project “Algebraische Fehlerangriffe” [KR 1907/6-2] and partially supported by the H2020-FETOPEN-2015-CSA project \(\text {SC}^2\) (712689).

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Horáček, J., Kreuzer, M. (2018). 3BA: A Border Bases Solver with a SAT Extension. In: Davenport, J., Kauers, M., Labahn, G., Urban, J. (eds) Mathematical Software – ICMS 2018. ICMS 2018. Lecture Notes in Computer Science(), vol 10931. Springer, Cham.

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