Threshold Phenomena in Random Lattices and Efficient Reduction Algorithms

Authors:
Ali Akhavi
Affiliations:
-
Venue:
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Year:
1999

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Random lattices, threshold phenomena and efficient reduction algorithms

Theoretical Computer Science

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Abstract

Two new lattice reduction algorithms are presented and analyzed. These algorithms, called the Schmidt reduction and the Gram reduction, are obtained by relaxing some of the constraints of the classical LLL algorithm. By analyzing the worst case behavior and the average case behavior in a tractable model, we prove that the new algorithms still produce "good" reduced basis while requiring fewer iterations on average. In addition, we provide empirical tests on random lattices coming from applications, that confirm our theoretical results about the relative behavior of the different reduction algorithms.