A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
A more efficient algorithm for lattice basis reduction
Journal of Algorithms
An Optimal, Stable Continued Fraction Algorithm
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Proceedings of the 11th Colloquium on Automata, Languages and Programming
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Segment LLL-Reduction of Lattice Bases
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Lattice Reduction by Random Sampling and Birthday Methods
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Segment LLL-Reduction of Lattice Bases
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Dimension Reduction Methods for Convolution Modular Lattices
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
An efficient LLL gram using buffered transformations
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
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We associate with an integer lattice basis a scaled basis that has orthogonal vectors of nearly equal length. The orthogonal vectors or the QR-factorization of a scaled basis can be accurately computed up to dimension 216 by Householder reflexions in floating point arithmetic (fpa) with 53 precision bits. We develop a highly practical fpa-variant of the new segment LLL-reduction of KOY AND SCHNORR [KS01]. The LLL-steps are guided in this algorithm by the Gram-Schmidt coefficients of an associated scaled basis. The new reduction algorithm is much faster than previous codes for LLL-reduction and performs well beyond dimension 1000.