We give polynomial-time quantum algorithms for three problems from computational algebraic number theory. The first is Pell's equation. Given a positive nonsquare integer d, ...
We describe a compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan’s (DGHV) fully homomorphic scheme over the integers from ËœO(Î...
We consider a quadratic programming (QP) problem (Π) of the form min xT Cx subject to Ax ≥ b where C ∈ Rn×n + , rank(C) = 1 and A ∈ Rm×n , b ∈ Rm . We present an FPTAS ...
We investigate equidissections of a trapezoid T(a), where the ratio of the lengths of two parallel sides is a. (An equidissection is a dissection into triangles of equal areas.) A...
Given a set of patterns and a similarity measure between them, we will present an optimization framework to approximate a small subset, known as a canonical set, whose members clo...