Hermite normal form computation using modulo determinant arithmetic
Mathematics of Operations Research
Algorithmic algebraic number theory
Algorithmic algebraic number theory
Efficient reduction of quadratic forms
Proceedings of the third conference on Computers and mathematics
Improved low-density subset sum algorithms
Computational Complexity
A course in computational algebraic number theory
A course in computational algebraic number theory
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On the complexity of finding short vectors in integer lattices
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
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
New Results on Lattice Basis Reduction in Practice
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Finding a small root of a univariate modular equation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
Toward non-parallelizable client puzzles
CANS'07 Proceedings of the 6th international conference on Cryptology and network security
Approximate polynomial GCD over integers
Journal of Symbolic Computation
Improving the parallel schnorr-euchner lll algorithm
ICA3PP'11 Proceedings of the 11th international conference on Algorithms and architectures for parallel processing - Volume Part I
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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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In this paper we provide a survey on LLL lattice basis reduction in practice. We introduce several new heuristics as to speed up known lattice basis reduction methods and improve the quality of the computed reduced lattice basis in practice. We analyze substantial experimental data and to our knowledge, we are the first to present general heuristics for determining which variant of the reduction algorithm, for varied parameter choices, yields the most efficient reduction strategy for reducing a particular problem instance.