On the unique shortest lattice vector problem
نویسندگان
چکیده
منابع مشابه
A Note on the Shortest Lattice Vector Problem
We show that the problem of deciding whether a given rational lattice L has a vector of length less than some given value r is NP-hard under randomized reductions, even under the promise that L has exactly zero or one vector of length less than r.
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The unique Shortest Vector Problem (uSVP) gained prominence because it was the problem upon which the first provably-secure lattice-based cryptosystems were built. But it was an open problem as to whether uSVP was as hard as the standard, more general, version of the shortest vector problem. We show that there is a reduction from the approximate decision version of the shortest vector problem (...
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The Shortest lattice Vector Problem is central in lattice-based cryptography, as well as in many areas of computational mathematics and computer science, such as computational number theory and combinatorial optimisation. We present an algorithm for solving it in time 2 and space 2, where n is the lattice dimension. This improves the best previously known algorithm, by Micciancio and Voulgaris ...
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The Shortest lattice Vector Problem is central in lattice-based cryptography, as well as in many areas of computational mathematics and computer science, such as computational number theory and combinatorial optimisation. We present an algorithm for solving it in time 2 and space 2, where n is the lattice dimension. This improves the best previously known algorithm, by Micciancio and Voulgaris ...
متن کاملUnique Shortest Vector Problem for max norm is NP-hard
The unique Shortest vector problem (uSVP) in lattice theory plays a crucial role in many public-key cryptosystems. The security of those cryptosystems bases on the hardness of uSVP. However, so far there is no proof for the proper hardness of uSVP even in its exact version. In this paper, we show that the exact version of uSVP for `∞ norm is NP-hard. Furthermore, many other lattice problems inc...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2001
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(00)00387-x