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The paper study counter-dependent pseudorandom generators; the latter are generators such that their state transition function (and output function) is being modified dynamically while working: For such a generator the recurrence sequence…
Empirical tests for pseudorandom number generators based on the use of processes or physical models have been successfuly used and are considered as complementary to theoretical test of randomness. In this work a statistical methodology for…
This paper presents an expression to compute the exact period of a recursive random number generator based on d-sequences. Using the multi-recursive version of this generator we can produce large number of pseudorandom sequences.
The paper study counter-dependent pseudorandom number generators based on $m$-variate ($m>1$) ergodic mappings of the space of 2-adic integers $\Z_2$. The sequence of internal states of these generators is defined by the recurrence law…
We investigate the periodic structure of the exponential pseudorandom number generator obtained from the map $x\mapsto g^x\pmod p$ that acts on the set $\{1, \ldots, p-1\}$.
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…
The behavior of a family of dissipative dynamical systems representing transformations of two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying…
The authors prove that the probability of choosing a nonlinear filter of m-sequences with optimal properties, that is, maximum period and maximum linear complexity, tends assymptotically to 1 as the linear feedback shift register length…
We introduce several classes of pseudorandom sequences which represent a natural extension of classical methods in random number generation. The sequences are obtained from constructions on labeled binary trees, generalizing the well-known…
An approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness…
We present a new approach to constructing unconditional pseudorandom generators against classes of functions that involve computing a linear function of the inputs. We give an explicit construction of a pseudorandom generator that fools the…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
Iteration of the modular l-th power function f(x) = x^l (mod n) provides a common pseudorandom number generator (known as the Blum-Blum-Shub generator when l=2). The period of this pseudorandom number generator is closely related to…
We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and…
Let $\mu$ be the geometric realization on $[0,1]$ of a Gibbs measure on $\Sigma=\{0,1\}^{\mathbb{N}}$ associated with a H\"older potential. The thermodynamic and multifractal properties of $\mu$ are well known to be linked via the…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
Pseudorandom number generators have been widely used in Monte Carlo methods, communication systems, cryptography and so on. For cryptographic applications, pseudorandom number generators are required to generate sequences which have good…
In this paper, we focus on analyzing the period distribution of the inversive pseudorandom number generators (IPRNGs) over finite field $({\rm Z}_{N},+,\times)$, where $N>3$ is a prime. The sequences generated by the IPRNGs are transformed…