A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
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LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
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Transactions on computational science X
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IWCC'11 Proceedings of the Third international conference on Coding and cryptology
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CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
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Security and Communication Networks
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TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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Despite their popularity, lattice reduction algorithms remain mysterious in many ways. It has been widely reported that they behave much more nicely than what was expected from the worst-case proved bounds, both in terms of the running time and the output quality. In this article, we investigate this puzzling statement by trying to model the average case of lattice reduction algorithms, starting with the celebrated Lenstra-Lenstra-Lovász algorithm (L3). We discuss what is meant by lattice reduction on the average, and we present extensive experiments on the average case behavior of L3, in order to give a clearer picture of the differences/similarities between the average and worst cases. Our work is intended to clarify the practical behavior of L3 and to raise theoretical questions on its average behavior.