Abstract
In this paper, we propose a novel simulated annealing algorithm for the shortest vector problem through y-sparse representations of short lattice vectors. A Markov analysis proves that the algorithm guarantees to converge to the shortest vector at a probability 1, under certain conditions to ensure strong ergodicity of its inhomogeneous Markov chain. After that, we propose a polynomial-time approximation version of our algorithm, and the experimental results under benchmarks in SVP challenge [27] show that the simulated annealing one outperforms the famous Kannan's algorithm in two aspects: it runs exponentially faster and it succeeds in searching the shortest vectors in lattices of higher dimensions. Therefore, our newly-proposed algorithm is a fast and efficient SVP solver and paves a completely new road for SVP algorithms.
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