Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Finding smooth integers in short intervals using CRT decoding
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Proceedings of the 11th Colloquium on Automata, Languages and Programming
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
The Complexity of Some Lattice Problems
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Lattice Reduction in Cryptology: An Update
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Segment LLL-Reduction with Floating Point Orthogonalization
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Attacking the Chor-Rivest cryptosystem by improved lattice reduction
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Lattice Reduction by Random Sampling and Birthday Methods
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Dimension Reduction Methods for Convolution Modular Lattices
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Segment LLL-Reduction with Floating Point Orthogonalization
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Explicit Hard Instances of the Shortest Vector Problem
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Journal of Global Optimization
An LLL-reduction algorithm with quasi-linear time complexity: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
Lattice reduction algorithms: theory and practice
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
I forgot your password: randomness attacks against PHP applications
Security'12 Proceedings of the 21st USENIX conference on Security symposium
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 present an efficient variant of LLL-reduction of lattice bases in the sense of LENSTRA, LENSTRA, LOVáSZ. We organize LLL-reduction in segments of size k. Local LLL-reduction of segments is done using local coordinates of dimension k. We introduce segment LLL-reduced bases, a variant of LLL-reduced bases achieving a slightly weaker notion of reducedness, but speeding up the reduction time of lattices of dimension n by a factor n. We also introduce a variant of LLL-reduction using iterated segments. The resulting reduction algorithm runs in O(n3 log2 n) arithmetic steps for integer lattices of dimension n with basis vectors of length 2n.