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Algorithms 2010, 3(3), 224-243; doi:10.3390/a3030224
Article

Segment LLL Reduction of Lattice Bases Using Modular Arithmetic

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Received: 28 May 2010; Accepted: 29 June 2010 / Published: 12 July 2010
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
Download PDF [396 KB, uploaded 12 July 2010]
Abstract: The algorithm of Lenstra, Lenstra, and Lovász (LLL) transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n) using modular arithmetic. Koy and Schnorr developed a segment-LLL basis reduction algorithm that generates lattice basis satisfying a weaker condition than the LLL reduced basis with O(n) improvement than the LLL algorithm. In this paper we combine Storjohann’s modular arithmetic approach with the segment-LLL approach to further improve the worst case complexity of the segment-LLL algorithms by a factor of n0.5.
Keywords: Lattice; LLL basis reduction; reduced basis; successive minima; segments; modular arithmetic; fast matrix multiplication Lattice; LLL basis reduction; reduced basis; successive minima; segments; modular arithmetic; fast matrix multiplication
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Mehrotra, S.; Li, Z. Segment LLL Reduction of Lattice Bases Using Modular Arithmetic. Algorithms 2010, 3, 224-243.

AMA Style

Mehrotra S, Li Z. Segment LLL Reduction of Lattice Bases Using Modular Arithmetic. Algorithms. 2010; 3(3):224-243.

Chicago/Turabian Style

Mehrotra, Sanjay; Li, Zhifeng. 2010. "Segment LLL Reduction of Lattice Bases Using Modular Arithmetic." Algorithms 3, no. 3: 224-243.


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