Algorithmic algebraic number theory
Algorithmic algebraic number theory
A course in computational algebraic number theory
A course in computational algebraic number theory
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th 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
Lattice Reduction in Cryptology: An Update
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Segment LLL-Reduction of Lattice Bases
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
Heuristics on lattice basis reduction in practice
Journal of Experimental Algorithmics (JEA)
An improved low-density subset sum algorithm
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
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
Partial key exposure attacks on RSA up to full size exponents
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
New attacks on RSA with small secret CRT-Exponents
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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
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In this paper we introduce an improved variant of the LLL algorithm. Using the Gram matrix to avoid expensive correction steps necessary in the Schnorr-Euchner algorithm and introducing the use of buffered transformations allows us to obtain a major improvement in reduction time. Unlike previous work, we are able to achieve the improvement while obtaining a strong reduction result and maintaining the stability of the reduction algorithm.