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Theoretical Computer Science
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FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
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CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
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FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fast LLL-type lattice reduction
Information and Computation
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PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
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ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
Fast LLL-type lattice reduction
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CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
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CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
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ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
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CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
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We present a novel practical algorithm that given a lattice basis b1, ..., bn finds in O(n2(k/6)k/4) average time a shorter vector than b1 provided that b1 is (k/6)n/(2k) times longer than the length of the shortest, nonzero lattice vector. We assume that the given basis b1, ..., bn has an orthogonal basis that is typical for worst case lattice bases. The new reduction method samples short lattice vectors in high dimensional sublattices, it advances in sporadic big jumps. It decreases the approximation factor achievable in a given time by known methods to less than its fourth-th root. We further speed up the new method by the simple and the general birthday method.