Solving the Shortest Lattice Vector Problem in Time 2
نویسندگان
چکیده
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 [SODA 2010], which runs in time 2 and space 2.
منابع مشابه
Solving the Shortest Lattice Vector Problem in Time 22.465n
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 کاملSpace-efficient classical and quantum algorithms for the shortest vector problem
A lattice is the integer span of some linearly independent vectors. Lattice problems have many significant applications in coding theory and cryptographic systems for their conjectured hardness. The Shortest Vector Problem (SVP), which is to find the shortest non-zero vector in a lattice, is one of the well-known problems that are believed to be hard to solve, even with a quantum computer. In t...
متن کاملSolving the Shortest Vector Problem in Lattices Faster Using Quantum Search
By applying Grover’s quantum search algorithm to the lattice algorithms of Micciancio and Voulgaris, Nguyen and Vidick, Wang et al., and Pujol and Stehlé, we obtain improved asymptotic quantum results for solving the shortest vector problem. With quantum computers we can provably find a shortest vector in time 2, improving upon the classical time complexity of 2 of Pujol and Stehlé and the 2 of...
متن کاملApproximate Algorithms on Lattices with Small Determinant
In this paper, we propose approximate lattice algorithms for solving the shortest vector problem (SVP) and the closest vector problem (CVP) on an n-dimensional Euclidean integral lattice L. Our algorithms run in polynomial time of the dimension and determinant of lattices and improve on the LLL algorithm when the determinant of a lattice is less than 2 2/4. More precisely, our approximate SVP a...
متن کاملSolving the Shortest Vector Problem in $2^n$ Time via Discrete Gaussian Sampling
We give a randomized 2n+o(n)-time and space algorithm for solving the Shortest Vector Problem (SVP) on n-dimensional Euclidean lattices. This improves on the previous fastest algorithm: the deterministic Õ(4n)-time and Õ(2n)-space algorithm of Micciancio and Voulgaris (STOC 2010, SIAM J. Comp. 2013). In fact, we give a conceptually simple algorithm that solves the (in our opinion, even more int...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010