Related papers: A Discrete Logarithm-based Approach to Compute Low…
The ring and polynomial learning with errors problems (Ring-LWE and Poly-LWE) have been proposed as hard problems to form the basis for cryptosystems, and various security reductions to hard lattice problems have been presented. So far…
Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This…
A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic…
While many approaches have been proposed to analyze the problem of matrix multiplication parallel computing, few of them address the problem on heterogeneous processor platforms. It still remains an open question on heterogeneous processor…
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…
In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex…
This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
Minimal annihilating polynomials are very useful in a wide variety of algorithms in exact linear algebra. A new efficient method is proposed for calculating the minimal annihilating polynomials for all the unit vectors, for a square matrix…
The problem of devising learning strategies for discrete losses (e.g., multilabeling, ranking) is currently addressed with methods and theoretical analyses ad-hoc for each loss. In this paper we study a least-squares framework to…
We present an algorithm to estimate the configurational entropy $S$ of a polymer. The algorithm uses the statistics of coincidences among random samples of configurations and is related to the catch-tag-release method for estimation of…
This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. We first present two algorithms for the finite fields: one is based on Krylov iterates and Gaussian…
Maintaining the pair similarity relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simiple and intutive method is to utilize two identical code matrices…
A simple algorithm to compute all the zeros of a generic polynomial is proposed.
We consider binary dispatching problem originating from object oriented programming. We want to preprocess a hierarchy of classes and collection of methods so that given a function call in the run-time we are able to retrieve the most…
We perform logical and physical resource estimation for computing binary elliptic curve discrete logarithms using Shor's algorithm on fault-tolerant quantum computers. We adopt a windowed approach to design our circuit implementation of the…
We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…