Segment LLL reduction of lattice bases using modular arithmetic (Q1662551)

Summary: 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 \(n^{0.5}\).