## Abstract

Tropical linear algebra has been recently put forward by Grigoriev and Shpilrain as a promising platform for implementation of protocols of Diffie-Hellman and Stickel type. Based on the CSR expansion of tropical matrix powers, we suggest a simple algorithm for the following tropical discrete logarithm problem: “Given that

*A = V ⊗ F*for a unique t and matrices^{⊗t }*A, V, F*of appropriate dimensions, find this*t*.” We then use this algorithm to suggest a simple attack on a protocol based on the tropical semidirect product. The algorithm and the attack are guaranteed to work in some important special cases and are shown to be efficient in our numerical experiments.Original language | English |
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Pages (from-to) | 861-879 |

Number of pages | 19 |

Journal | Communications in Algebra |

Volume | 50 |

Issue number | 2 |

Early online date | 20 Sept 2021 |

DOIs | |

Publication status | Published - 1 Feb 2022 |

### Bibliographical note

Funding Information:We would like to thank the anonymous referee of our paper for their careful reading, useful comments and appreciation of our work.

Publisher Copyright:

© 2021 Taylor & Francis Group, LLC.

## Keywords

- Cryptanalysis
- matrix powers
- semidirect product
- tropical algebra

## ASJC Scopus subject areas

- Algebra and Number Theory