A Polynomial time Jacobi Method for Lattice Basis Reduction
نویسندگان
چکیده
Among all lattice reduction algorithms, the LLL algorithm is the first and perhaps the most famous polynomial time algorithm, and it is widely used in many applications. In 2012, S. Qiao [24] introduced another algorithm, the Jacobi method, for lattice basis reduction. S. Qiao and Z. Tian [25] improved the Jacobi method further to be polynomial time but only produces a Quasi-Reduced basis. In this paper, we present a polynomial time Jacobi method for lattice basis reduction (short as Poly-Jacobi method) that can produce a reduced basis. Our experimental results indicate that the bases produced by Poly-Jacobi method have almost equally good orthogonality defect as the bases produced by the Jacobi method.
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