We consider the binary-LWE problem, which is the learning with errors problem when the entries of the secret vector are chosen from {0, 1} or {−1, 0, 1} (and the error vector is sampled from a discrete Gaussian distribution). Our main result is an improved lattice decoding algorithm for binary-LWE which first translates the problem to the inhomogeneous short integer solution (ISIS) problem, and...

We give deterministic Õ(2)-time algorithms to solve all the most important computational problems on point lattices in NP, including the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), and Shortest Independent Vectors Problem (SIVP). This improves the n running time of the best previously known algorithms for CVP (Kannan, Math. Operation Research 12(3):415-440, 1987) and SIVP (Micc...

A closer look is taken at the well-known divide-andconquer algorithm for finding the closest pair of a set of points in the plane under the Euclidean distance. An argument is made that it is sufficient, and sometimes necessary, to check only the next three points following the current point associated with the y-sorted array in the combine phase of the algorithm.

The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries such as k nearest neighbor (kNN), reverse kNN, and closest pair. Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space for their specifi...

The closest string problem is an NP-hard problem, which arises in computational molecular biology and coding theory. Its task is to find a string that minimizes maximum Hamming distance to a given set of strings. This problem can be reduced to an integer program (IP). However, to date, there exists no known polynomial-time algorithm for integer programs. In 2004, Meneses et al. introduced a bra...

Lattice enumeration algorithms are the most basic algorithms for solving hard lattice problems such as the shortest vector problem and the closest vector problem, and are often used in public-key cryptanalysis either as standalone algorithms, or as subroutines in lattice reduction algorithms. Here we revisit these fundamental algorithms and show that surprising exponential speedups can be achie...

In Crypto 97, a public key cryptosystem based on the closest vector problem was suggested by Goldreich, Goldwasser and Halevi [4]. In this paper, we propose a public key cryptosystem applying representations of polynomials to the GGH encryption scheme. Its key size is much smaller than the GGH system so that it is a quite practical and efficient lattice based cryptosystem.