To protect a cryptographic algorithm against Differential Power Analysis, a general method consists in masking all intermediate data with a random value. When a cryptographic algorithm combines boolean operations with arithmetic operations, it is then necessary to perform conversions between boolean masking and arithmetic masking. A very efficient method was proposed by Louis Goubin in [6] to c...

Abstract. Topological tools, such as Conley index theory, have inspired rigorous computational methods for studying dynamics. These methods rely on the construction of an outer approximation, a combinatorial representation of the system that incorporates small, bounded error. In this work, we present an automated approach for constructing outer approximations for systems in a class of integrodi...

A method for ray casting implicit surfaces, defined with procedural noise models, is presented. The method is robust in that it is able to guarantee correct intersections at all image pixels and for all types of implicit surfaces. This robustness comes from the use of an affine arithmetic representation for the quantity that expresses the variation of the implicit function along a ray. Affine a...

The purpose is to study the strength of Ramsey’s Theorem for pairs restricted to recursive assignments of k-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number k ≥ 2, Ramsey’s Theorem for pairs and recursive assignments of k colors is equivalent to the Limited Lesser Principle of Omniscience for Σ 3 formulas over Heyting Arithmetic. Alternative...

ÐThis note relates to a recently published partly tutorial article that presents some discussion of the polynomial form of Boolean functions and its applications based on the literature published in English and German. We show that a lot of the research in this area has also been done in Eastern Europe, and this note aims to present these unknown developments. The most recent work in this area ...

We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.

We are interested in accurate numerical solutions of ill-conditioned linear systems using floating-point arithmetic. Recently, we proposed a preconditioning method to reduce the condition numbers of coefficient matrices. The method utilizes an LU factorization obtained in working precision arithmetic and requires matrix multiplication in quadruple precision arithmetic. In this note, we aim to a...

Positive solutions of systems of Hammerstein integral equations are studied by using the theory of the fixed-point index for compact maps defined on cones in Banach spaces. Criteria for the fixed-point index of the Hammerstein integral operators being 1 or 0 are given. These criteria are generalizations of previous results on a single Hammerstein integral operator. Some of criteria are new and ...

In this paper we compare the performance of several range arithmetic methods in evaluating problems in symbolicnumeric circuit analysis. Symbolic-numeric circuit analysis involves solving systems of linear equations in order to obtain the values of currents and voltages in a given circuit. Symbolic circuit expressions contain a large number of product terms and long chains of arithmetic operati...