Related papers: Producing Quality Pseudorandomness with a Generali…
Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider…
Randomness extractors, which extract high quality (almost-uniform) random bits from biased random sources, are important objects both in theory and in practice. While there have been significant progress in obtaining near optimal…
Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences,…
In this article we study a renormalization scheme with which we find all semi-regular continued fractions of a number in a natural way. We define two maps, T_slow and T_fast: these maps are defined for (x,y) in [0,1], where x is the number…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
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…
In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of…
Mean value and cross-covariance function of chaotic binary sequences are evaluated for chaotic maps with specific properties. We also take into account the effect of fixed- and floating-point representations on statistical properties of…
Pseudo-random number generators (PRNG) are a fundamental element of many security algorithms. We introduce a novel approach to their implementation, by proposing the use of generative adversarial networks (GAN) to train a neural network to…
This paper explores the development and viability of an alternative pseudorandom number generator (PRNG) that leverages the chaotic dynamics of multiple pendulum systems. Some traditional PRNGs, notably the one implemented in the…
We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new…
Kernel methods have recently attracted resurgent interest, showing performance competitive with deep neural networks in tasks such as speech recognition. The random Fourier features map is a technique commonly used to scale up kernel…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…
After a brief introduction to a new chaotic stream cipher Mmohocc which utilizes the fundamental chaos characteristics of mixing, unpredictability, and sensitivity to initial conditions, we conducted the randomness statistical tests against…
Conventional random number generators provide the speed but not necessarily the high quality output streams needed for large-scale stochastic simulations. Cryptographically-based generators, on the other hand, provide superior quality…
Deep learning models are vulnerable to adversarial perturbations, raising important concerns for safety-critical deployment. Empirical defenses can achieve strong robustness in practice, but lack formal guarantees, motivating the need for…
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…
Based on Restricted Boltzmann Machines (RBMs), an improved pseudo-stochastic sequential cipher generator is proposed. It is effective and efficient because of the two advantages: this generator includes a stochastic neural network that can…
The existence of pseudorandom unitaries (PRUs) -- efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries -- has been a central open question, with significant implications for cryptography,…