This issue of Wireless Security Perspectives focuses on GSM and the December 1999 article titled Real Time Cryptanalysis of the Alleged A5/1 on a PC (preliminary draft) by Alex Biryukov and Adi Shamir. The authors describe an attack on the GSM A5/1 traffic encryption algorithm and claim that by analyzing the output of the algorithm, one can recover the cryptographic key in less than a second us...

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is furthe...

We survey two recent signature constructions that support signature aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single signature. Aggregate signatures are useful for reducing the size of certificate chains (by aggregating all signatures in the chain) and for reducing message size in secure routing protocol...

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic conver...

In this paper we describe a Parallel Performance Estimator suitable for the comparative evaluation of parallel algorithms. The Esti-mator is designed for SPMD programs written in either C or FORTRAN. Simulation is used to produce estimates of execution times for varying numbers of processors and to analyse the communication overheads. Results from the estimator are compared with actual results ...

An algorithm is presented for constructing an approximate numerical solution to a large scale Lyapunov equation in low rank factored form. The algorithm is based upon a synthesis of an approximate power method and an alternating direction implicit (ADI) method. The former is parameter free and tends to be efficient in practice, but there is little theoretical understanding of its convergence pr...

A major problem in using iterative number generators of the form xi = f(xi−1) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called sequence diversity, which generalizes the notion o...

The alternating direction method of Peaceman and Rachford is considered for elliptic difference schemes of second order and with two independent variables. An earlier result of the author's on the rapid convergence of multi-parameter noncommutative problems is described and a connection is established between that result and theorems on optimal scaling of band matrices. Simple algorithms to dec...

We present a multilevel high order ADI method for separable generalized Helmholtz equations. The discretization method we use is a onedimensional fourth order compact finite difference applied to each directional component of the Laplace operator, resulting in a discrete system efficiently solvable by ADI methods. We apply this high order difference scheme to all levels of grids, and then start...

A repetition free Longest Common Subsequence (LCS) of two sequences x and y is an LCS of x and y where each symbol may appear at most once. Let R denote the length of a repetition free LCS of two sequences of n symbols each one chosen randomly, uniformly, and independently over a k-ary alphabet. We study the asymptotic, in n and k, behavior of R and establish that there are three distinct regim...