In this semitutorial paper, a comprehensive survey of closest point search methods for
lattices without a regular structure is presented. The existing search strategies are described …

The latest quantum computers have the ability to solve incredibly complex classical
cryptography equations particularly to decode the secret encrypted keys and making the …

In this chapter we describe some of the recent progress in lattice-based cryptography.
Lattice-based cryptographic constructions hold a great promise for post-quantum …

Lattices are geometric objects that can be pictorially described as the set of intersection
points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices …

We prove the Minimum Vertex Cover problem to be NP-hard to approximate to within a
factor of 1.3606, extending on previous PCP and hardness of approximation technique. To …

We give deterministic~ O (22n+ o (n))-time algorithms to solve all the most important
computational problems on point lattices in NP, including the Shortest Vector Problem …

The generalized knapsack function is defined as fa (x)=∑ iai· xi, where a=(a 1,..., am)
consists of m elements from some ring R, and x=(x 1,..., xm) consists of m coefficients from a …

We show that approximating the shortest vector problem (in any \ell_p norm) to within any
constant factor less than \sqrtp2 is hard for NP under reverse unfaithful random reductions …

Let p> 1 be any fixed real. We show that assuming NP⊈ RP, there is no polynomial time
algorithm that approximates the Shortest Vector Problem (SVP) in ℓ p norm within a constant …

We investigate the average-case complexity of a generalization of the compact knapsack
problem to arbitrary rings: given m (random) ring elements a 1,..., am∈ R and a (random) …