A Formalization of the LLL Basis Reduction Algorithm

## Authors: Jose Divasón, Sebastiaan Joosten, René Thiemann and Akihisa Yamada

## Paper Information

Title: | A Formalization of the LLL Basis Reduction Algorithm |

Authors: | Jose Divasón, Sebastiaan Joosten, René Thiemann and Akihisa Yamada |

Proceedings: | ITP Papers |

Editors: | Jeremy Avigad and Assia Mahboubi |

Keywords: | Basis Reduction, Polynomial Factorization, Isabelle/HOL |

Abstract: | ABSTRACT. The LLL basis reduction algorithm was the first polynomial-time algorithm to compute a reduced basis of a given lattice, and hence also a short vector in the lattice. It thereby approximates an NP-hard problem where the approximation quality solely depends on the dimension of the lattice, but not the lattice itself. The algorithm has several applications in number theory, computer algebra and cryptography. In this paper, we develop the first mechanized soundness proof of the LLL algorithm using Isabelle/HOL. We additionally integrate one application of LLL, namely a verified factorization algorithm for integer polynomials which runs in polynomial time. |

Pages: | 17 |

Talk: | Jul 10 11:00 (Session 54C) |

Paper: |