论文信息 - New Practical Algorithms for the Approximate Shortest Lattice Vector

New Practical Algorithms for the Approximate Shortest Lattice Vector

We present a practical algorithm that given an LLL-reduced lattice basis of dimension n, runs in time O(n(k/6)+n) and approximates the length of the shortest, non-zero lattice vector to within a factor (k/6). This result is based on reasonable heuristics. Compared to previous practical algorithms the new method reduces the proven approximation factor achievable in a given time to less than its fourthth root. We also present a sieve algorithm inspired by Ajtai, Kumar, Sivakumar [AKS01].

Claus Peter Schnorr | C. Schnorr

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