On Nearly Orthogonal Lattice Bases

On Nearly Orthogonal Lattice Bases and Random Lattices

We study lattice bases where the angle between any basis vector and the linear subspace spanned by the other basis vectors is at least π 3 radians; we denote such bases as “nearly orthogonal.” We show that a nearly orthogonal lattice basis always contains a shortest lattice vector. Moreover, we prove that if the basis vector lengths are “nearly equal,” then the basis is the unique nearly orthog...

Minkowski and KZ reduction of nearly orthogonal lattice bases

We prove that if a lattice basis is nearly orthogonal (the angle between any basis vector and the linear subspace spanned by the other basis vectors is at least π3 radians), then a KZ-reduced basis can be obtained from it in polynomial time. We also show that if a nearly orthogonal lattice basis has nearly equal vector lengths (within a certain constant factor of one another), then the basis is...

Improving BDD Cryptosystems in General Lattices

A prime goal of Lattice-based cryptosystems is to provide an enhanced security assurance by remaining secure with respect to quantum computational complexity, while remaining practical on conventional computer systems. In this paper, we define and analyze a superclass of GGH-style nearly-orthogonal bases for use in private keys, together with a subclass of Hermite Normal Forms for use in Miccia...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Development of Nonlinear Lattice-Hammerstein Filters for Gaussian Signals

In this paper, the nonlinear lattice-Hammerstein filter and its properties are derived. It is shown that the error signals are orthogonal to the input signal and also backward errors of different stages are orthogonal to each other. Numerical results confirm all the theoretical properties of the lattice-Hammerstein structure.