Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
An analysis of the Gaussian algorithm for lattice reduction
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Computing the sign or the value of the determinant of an integer matrix, a complexity survey
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Lattice-Based Threshold Changeability for Standard Shamir Secret-Sharing Schemes
IEEE Transactions on Information Theory
Designing low-complexity detectors based on Seysen's algorithm
IEEE Transactions on Wireless Communications
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Lattice reduction (LR) techniques have been adopted to improve the performance and/or reduce the complexity in communications and cryptography. So far, the LLL algorithm has been considered almost exclusively for LR. In this paper, we focus on Seysen's algorithm to perform LR. We show that for a lattice in two dimensions, Seysen's algorithm gives the same reduced basis as the well-known Gaussian reduction algorithm (up to signs). Furthermore, we prove that the Seysen's metric is upper bounded for lattices in two dimensions after LR with Seysen's algorithm. Finally, we relate Seysen's metric to the orthogonality deficiency for general cases.