منابع مشابه
Tuple lattice sieving
Lattice sieving is asymptotically the fastest approach for solving the shortest vector problem (SVP) on Euclidean lattices. All known sieving algorithms for solving the SVP require space which (heuristically) grows as 2, where n is the lattice dimension. In high dimensions, the memory requirement becomes a limiting factor for running these algorithms, making them uncompetitive with enumeration ...
متن کاملFaster tuple lattice sieving using spherical locality-sensitive filters
To overcome the large memory requirement of classical lattice sieving algorithms for solving hard lattice problems, Bai–Laarhoven–Stehlé [ANTS 2016] studied tuple lattice sieving, where tuples instead of pairs of lattice vectors are combined to form shorter vectors. Herold–Kirshanova [PKC 2017] recently improved upon their results for arbitrary tuple sizes, for example showing that a triple sie...
متن کاملSpeed-ups and time-memory trade-offs for tuple lattice sieving
In this work we study speed-ups and time–space trade-offs for solving the shortest vector problem (SVP) on Euclidean lattices based on tuple lattice sieving. Our results extend and improve upon previous work of Bai–Laarhoven– Stehlé [ANTS’16] and Herold–Kirshanova [PKC’17], with better complexities for arbitrary tuple sizes and offering tunable time–memory tradeoffs. The trade-offs we obtain st...
متن کاملSieving for Closest Lattice Vectors (with Preprocessing)
Lattice-based cryptography has recently emerged as a prime candidate for efficient and secure post-quantum cryptography. The two main hard problems underlying its security are the shortest vector problem (SVP) and the closest vector problem (CVP). Various algorithms have been studied for solving these problems, and for SVP, lattice sieving currently dominates in terms of the asymptotic time com...
متن کاملSome Sieving Algorithms for Lattice Problems
We study the algorithmic complexity of lattice problems based on the sieving technique due to Ajtai, Kumar, and Sivakumar [AKS01]. Given a k-dimensional subspace M ⊆ Rn and a full rank integer lattice L ⊆ Qn, the subspace avoiding problem SAP, defined by Blömer and Naewe [BN07], is to find a shortest vector in L \ M. We first give a 2O(n+k log k) time algorithm to solve the subspace avoiding pr...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2016
ISSN: 1461-1570
DOI: 10.1112/s1461157016000292