Fuzzy approach to multimedia faulty module replacement

For non-real time multimedia systems, we present a fuzzy approach to replacing the faulty module. After analyzing the nature of the random and pseudo-random test sequences applied to a module under test, we obtain the aliasing fault coverage between the random and pseudo-random sequences. The activity probability features of intermittent faults in the module under test are discussed based on the Markov chain model. Results on real examples are presented to demonstrate the effectiveness of the proposed fuzzy replacement approac

A mechanism for randomness

We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that certain class of autonomous dynamical systems can generate random dynamics. This dynamics presents fundamental differences with the known chaotic systems. We present realphysical systems that can produce this kind of random time-series. We report theresults of real experiments with nonlinear circuits containing direct evidence for this new phenomenon. In particular, we show that a Josephson junction coupled to a chaotic circuit can generate unpredictable dynamics. Some applications are discussed.Comment: Accepted in Physics Letters A (2002). 11 figures (.eps

Pseudorandom number generators revisited

Statistical Methods;mathematische statistiek

Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets

Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear programming relaxation attack using local marginal polytope for randomly generated Goldreich's generators. We assume that $u(n)\in \omega(1)\cap o(n)$ input variables are known. In that case, we show that when $r\ge 3$, there is an exact threshold $\mu_\mathrm{c}(k,r):=\binom{k}{r}^{-1}\frac{(r-2)^{r-2}}{r(r-1)^{r-1}}$ such that for $m=\mu\frac{n^{r-1}}{u(n)^{r-2}}$, the LP relaxation can determine linearly many input variables of Goldreich's generator if $\mu>\mu_\mathrm{c}(k,r)$, and that the LP relaxation cannot determine $\frac1{r-2} u(n)$ input variables of Goldreich's generator if $\mu<\mu_\mathrm{c}(k,r)$. This paper uses characterization of LP solutions by combinatorial structures called stopping sets on a bipartite graph, which is related to a simple algorithm called peeling algorithm.Comment: 14 pages, 1 figur

Guaranteeing the diversity of number generators

A major problem in using iterative number generators of the form x_i=f(x_{i-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 of cycle-length for non-iterative generators. We then introduce the class of counter assisted generators, and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong.Comment: Small update

Evolving cellular automata to generate nonlinear sequences with desirable properties

This paper presents a new chromosomal representation and associated genetic operators for the evolution of highly nonlinear cellular automata that generate pseudorandom number sequences with desirable properties ensured. This chromosomal representation reduces the computational complexity of genetic operators to evolve valid solutions while facilitating fitness evaluation based on the DIEHARD statistical tests