We present a Monte Carlo algorithm for testing multivariate polynomial identities over any field using fewer random bits than other methods. To test if a polynomial P(x1 ::: xn) ...
We say a polynomial P over ZZM strongly M -represents a Boolean function F if F(x) ≡ P(x) (mod M) for all x ∈ {0, 1}n . Similarly, P one-sidedly M -represents F if F(x) = 0 ⇐...
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials ...
When outsourcing data to an untrusted database server, the data should be encrypted. When using thin clients or low-bandwidth networks it is best to perform most of the work at the...
We study the link between the complexity of a polynomial and that of its coefficient functions. Valiant’s theory is a good setting for this, and we start by generalizing one of V...
We present an iterative algorithm for calculating approximate greatest common divisor (GCD) of univariate polynomials with the real coefficients. For a given pair of polynomials a...