Matrix analysis
Algorithms to construct Minkowski reduced and Hermite reduced lattice bases
Theoretical Computer Science
Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Integer least squares: sphere decoding and the LLL algorithm
Proceedings of the 2008 C3S2E conference
An Introduction to Mathematical Cryptography
An Introduction to Mathematical Cryptography
Low-dimensional lattice basis reduction revisited
ACM Transactions on Algorithms (TALG)
The LLL Algorithm: Survey and Applications
The LLL Algorithm: Survey and Applications
An Optimization Problem Related to Minkowski’s Successive Minima
Discrete & Computational Geometry
Lattice reduction algorithms: theory and practice
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
On the sphere-decoding algorithm I. Expected complexity
IEEE Transactions on Signal Processing - Part I
Mathematics of Public Key Cryptography
Mathematics of Public Key Cryptography
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The famous LLL algorithm is the first polynomial time lattice reduction algorithm which is widely used in many applications. In this paper, we present a novel weak Quasi-Jacobi lattice basis reduction algorithm based on a polynomial time algorithm, called the Jacobi method introduced by S. Qiao [24]. We also prove the convergence of the two Jacobi methods, and show that the Quasi-Jacobi method has the same complexity as the LLL algorithm. Our experimental results indicate that the two Jacobi methods outperform the LLL algorithm in not only efficiency, but also orthogonality defect of the bases they produce.