2018/01/01 by Jose Divasón, Sebastiaan J. C. Joosten, René Thiemann +1 · 1 citation
Computer Science · Mathematics · #Cryptography and Data Security #Logic, programming, and type systems #Cryptography and Residue Arithmetic #Lattice reduction #Lattice (music) #Algorithm #Computer science #Basis (linear algebra) #Lattice problem #Soundness #HOL #Mathematics #Discrete mathematics #Cryptography
paper · pdf · doi:10.1007/978-3-319-94821-8_10
openalex publication_date 2018/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 univariate integer polynomials which runs in polynomial time.