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 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 applications in number theory, computer algebra and cryptography. In this paper, we provide an implementation of the LLL algorithm. Both its soundness and its polynomial running-time have been verified using Isabelle/HOL. Our implementation is nearly as fast as an implementation in a commercial computer algebra system, and its efficiency can be further increased by connecting it with fast untrusted lattice reduction algorithms and certifying their output. We additionally integrate one application of LLL, namely a verified factorization algorithm for univariate integer polynomials which runs in polynomial time.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
