Symmetric diophantine systems revisited

Symmetric Modular Diophantine Inequalities

In this paper we study and characterize those Diophantine inequalities axmod b ≤ x whose set of solutions is a symmetric numerical semigroup. Given two integers a and b with b = 0 we write a mod b to denote the remainder of the division of a by b. Following the notation used in [8], a modular Diophantine inequality is an expression of the form ax mod b ≤ x. The set S(a, b) of integer solutions ...

Classical metric Diophantine approximation revisited

The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of the theory of metrical Diophantine approximation, a branch of Number Theory which draws on a rich and broad variety of mathematics. We discuss some recent progress and open problems concerning this classica...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Symmetric Key Authentication Services Revisited

Most of the symmetric key authentication schemes deployed today are based on principles introduced by Needham and Schroeder [17] more than twenty years ago. However, since then, the computing environment has evolved from a LAN-based client-server world to include new paradigms, including wide area networks, peer-to-peer networks, mobile ad-hoc networks and ubiquitous computing. Also, there are ...

Property Preserving Symmetric Encryption Revisited

At EUROCRYPT 2012 Pandey and Rouselakis introduced the notion of property preserving symmetric encryption which enables checking for a property on plaintexts by running a public test on the corresponding ciphertexts. Their primary contributions are: (i) a separation between ‘find-then-guess’ and ‘left-or-right’ security notions; (ii) a concrete construction for left-or-right secure orthogonalit...