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