Related papers: Pseudorandomness via the discrete Fourier transfor…
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…
There is a large body of work studying what forms of computational hardness are needed to realize classical cryptography. In particular, one-way functions and pseudorandom generators can be built from each other, and thus require equivalent…
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…
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…
We introduce a novel family of expander-based error correcting codes. These codes can be sampled with randomness linear in the block-length, and achieve list-decoding capacity (among other local properties). Our expander-based codes can be…
Pseudorandom generators (PRGs) for low-degree polynomials are a central object in pseudorandomness, with applications to circuit lower bounds and derandomization. Viola's celebrated construction gives a PRG over the binary field, but with…
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…
In a recent work, O'Donnell, Servedio and Tan (STOC 2019) gave explicit pseudorandom generators (PRGs) for arbitrary $m$-facet polytopes in $n$ variables with seed length poly-logarithmic in $m,n$, concluding a sequence of works in the last…
We introduce the Romu family of pseudo-random number generators (PRNGs) which combines the nonlinear operation of rotation with the linear operations of multiplication and (optionally) addition. Compared to conventional linear-only PRNGs,…
"A generator is a parser of randomness." This perspective on generators for random data structures is well established as folklore in the programming languages community, but it has apparently never been formalized, nor have its…
NIST SP800-22 (2010) proposes the state of art testing suite for (pseudo) random generators to detect deviations of a binary sequence from randomness. On the one hand, as a counter example to NIST SP800-22 test suite, it is easy to…
Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin…
A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open…
A central approach to algorithmic derandomization is to construct probability distributions with small support that "fool" randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
We have introduced in former work the concept of Deep Randomness and its interest to design Unconditionally Secure communication protocols. We have in particular given an example of such protocol and introduced how to design a Deep Random…
In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In…
The aim of this paper is to present a new design for a pseudorandom number generator (PRNG) that is cryptographically secure, passes all of the usual statistical tests referenced in the literature and hence generates high quality random…
We propose a novel pseudorandom number generator based on R\"ossler attractor and bent Boolean function. We estimated the output bits properties by number of statistical tests. The results of the cryptanalysis show that the new pseudorandom…
A simple construction of pseudorandom generator is appear.This pseudorandom generator is always passed by NIST statistical test.This paper reports a pseudorandom number generator which has good property is able to construct using only…