Publication

Improved hardness results for unique shortest vector problem

Divesh Aggarwal
2016
Journal Articles

Abstract

The unique shortest vector problem on a rational lattice is the problem of finding the shortest non-zero vector under the promise that it is unique (up to multiplication by -1). We give several incremental improvements on the known hardness of the unique shortest vector problem (uSVP) using standard techniques. This includes a deterministic reduction from the shortest vector problem to the uSVP, the NP-hardness of uSVP on (1 + 1/poly(n))-unique lattices, and a proof that the decision version of uSVP defined by Cai [4] is in co-NP for n(1/4)-unique lattices. (C) 2016 Published by Elsevier B.V.

Official source

https://infoscience.epfl.ch/entities/publication/e15d571a-f468-4e48-b6a5-24612e0a552d

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Divesh Aggarwal
2016
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e15d571a-f468-4e48-b6a5-24612e0a552d

About this result

Related concepts (19)

Decision problem

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.

NP (complexity)

In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine.

Lattice problem

In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: Lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic algorithms. In addition, some lattice problems which are worst-case hard can be used as a basis for extremely secure cryptographic schemes.

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