Abstract
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.
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