Related papers: Pseudorandom Generators for Sliding-Window Algorit…
The pseudo-random number generators (PRNGs), sampling algorithms, and algorithms for generating random integers in some common statistical packages and programming languages are unnecessarily inaccurate, by an amount that may matter for…
The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions…
We study the relationship between notions of pseudorandomness in the quantum and classical worlds. Pseudorandom quantum state generator (PRSG), a pseudorandomness notion in the quantum world, is an efficient circuit that produces states…
Emergence of stochastic simulations as an extensively used computational tool for scientific purposes intensified the need for more accurate ways of generating sufficiently long sequences of uncorrelated random numbers. Even though several…
We give improved pseudorandom generators (PRGs) for Lipschitz functions of low-degree polynomials over the hypercube. These are functions of the form psi(P(x)), where P is a low-degree polynomial and psi is a function with small Lipschitz…
We prove new results on the polarizing random walk framework introduced in recent works of Chattopadhyay {et al.} [CHHL19,CHLT19] that exploit $L_1$ Fourier tail bounds for classes of Boolean functions to construct pseudorandom generators…
We give the best known pseudorandom generators for two touchstone classes in unconditional derandomization: an $\varepsilon$-PRG for the class of size-$M$ depth-$d$ $\mathsf{AC}^0$ circuits with seed length $\log(M)^{d+O(1)}\cdot…
Pseudorandom bit generators (PRBG) can be designed to take the advantage of some hard number theoretic problems such as the discrete logarithm problem (DLP). Such type of generators will have good randomness and unpredictability properties…
We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: 1. We consider read-once group-products over a finite group $G$, i.e., tests of the form $\prod_{i=1}^n…
In this work, Pseudo-Random Bit Generation (PRBG) based on 2D chaotic mappings of logistic type is considered. The sequences generated with two Pseudorandom Bit Generators (PRBGs) of this type are statistically tested and the computational…
A polynomial threshold function (PTF) $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a function of the form $f(x) = \mathsf{sign}(p(x))$ where $p$ is a polynomial of degree at most $d$. PTFs are a classical and well-studied complexity class…
Cellular Automata (CA) are an interesting computational model for designing Pseudorandom Number Generators (PRNG), due to the complex dynamical behavior they can exhibit depending on the underlying local rule. Most of the CA-based PRNGs…
We revisit Nisan's classical pseudorandom generator (PRG) for space-bounded computation (STOC 1990) and its applications in streaming algorithms. We describe a new generator, HashPRG, that can be thought of as a symmetric version of Nisan's…
The ever-increasing need for random numbers is clear in many areas of computer science, from neural networks to optimization. As such, most common programming language provide easy access to Pseudorandom Number Generators. However, these…
Introduced in [CG24], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally…
In this paper, a new pseudorandom number generator (PRNG) based on the logistic map has been proposed. To prevent the system to fall into short period orbits as well as increasing the randomness of the generated sequences, the proposed…
Pseudo-random number generators (PRNGs) play an important role to ensure the security and confidentiality of image cryptographic algorithms. Their primary function is to generate a sequence of numbers that possesses unpredictability and…
A weight-$t$ halfspace is a Boolean function $f(x)=$sign$(w_1 x_1 + \cdots + w_n x_n - \theta)$ where each $w_i$ is an integer in $\{-t,\dots,t\}.$ We give an explicit pseudorandom generator that $\delta$-fools any intersection of $k$…
An equidistribution is a theoretical quality criteria that measures the uniformity of a linear pseudo-random number generator (PRNG). In this work, we first show that all existing linear cellular automaton (CA) based pseudo-random number…
The hardness vs.~randomness paradigm aims to explicitly construct pseudorandom generators $G:\{0,1\}^r \rightarrow \{0,1\}^m$ that fool circuits of size $m$, assuming the existence of explicit hard functions. A ``high-end PRG'' with seed…