## Abstract

Algebraic cryptanalysis studies breaking ciphers by solving algebraic equations. Some of the promising approaches use SAT solvers for this purpose. Although the corresponding satisfiability problems are hard, their difficulty can often be lowered by choosing a set of variables to brute force over, and by solving each of the corresponding reduced problems using a SAT solver, which is called the guess-and-determine attack. In many successful cipher breaking attempts this set was chosen analytically, however, the nature of the problem makes evolutionary computation a good choice.

We investigate one particular method for constructing guess-and-determine attacks based on evolutionary algorithms. This method estimates the fitness of a particular guessed bit set by Monte-Carlo simulations. We show that using statistical tests within the comparator of fitness values, which can be used to reduce the necessary number of samples, together with a dynamic strategy for the upper limit on the number of samples, speeds up the attack by a factor of 1.5 to 4.3 even on a distributed cluster.

We investigate one particular method for constructing guess-and-determine attacks based on evolutionary algorithms. This method estimates the fitness of a particular guessed bit set by Monte-Carlo simulations. We show that using statistical tests within the comparator of fitness values, which can be used to reduce the necessary number of samples, together with a dynamic strategy for the upper limit on the number of samples, speeds up the attack by a factor of 1.5 to 4.3 even on a distributed cluster.

Original language | English |
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Title of host publication | GECCO '19 |

Subtitle of host publication | Proceedings of the Genetic and Evolutionary Computation Conference |

Editors | Manuel López-Ibáñez |

Pages | 312-320 |

Number of pages | 9 |

DOIs | |

Publication status | Published - 13 Jul 2019 |

Externally published | Yes |

Event | GECCO 2019: The Genetic and Evolutionary Computation Conference - Prague, Czech Republic Duration: 13 Jul 2019 → 17 Jul 2019 https://gecco-2019.sigevo.org |

### Conference

Conference | GECCO 2019: The Genetic and Evolutionary Computation Conference |
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Country/Territory | Czech Republic |

City | Prague |

Period | 13 Jul 2019 → 17 Jul 2019 |

Internet address |

## Keywords

- algebraic cryptanalysis
- approximate fitness evaluation
- satisfiability problems