Related papers: Close to Uniform Prime Number Generation With Fewe…
Self-testing and Semi-Device Independent protocols are becoming the preferred choice for quantum technologies, being able to certify their quantum nature with few assumptions and simple experimental implementations. In particular for…
Random bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require "strong" RBGs that produce high-entropy bit…
This article introduces a new approach to principled and practical random variate generation with formal guarantees. The key idea is to first specify the desired probability distribution in terms of a finite-precision numerical program that…
We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and…
It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the…
We address the problem of detecting deviations of binary sequence from randomness,which is very important for random number (RNG) and pseudorandom number generators (PRNG). Namely, we consider a null hypothesis $H_0$ that a given bit…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…
We suggest other models of sieve generated sequences like the Sieve of Eratosthenes to explain randomness properties of the prime numbers, like the twin prime conjecture, the lim sup conjecture, the Riemann conjecture, and the prime number…
The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However,…
There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we study similar notions for finite and profinite associative…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
We give a linear-time algorithm that approximately uniformly generates a random simple graph with a power-law degree sequence whose exponent is at least 2.8811. While sampling graphs with power-law degree sequence of exponent at least 3 is…
We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be…
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
We describe a methodology and standard of proof for experimental claims of quantum random number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations,…
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…
A study of certain Hamiltonian systems has lead Y. Long to conjecture the existence of infinitely many primes of the form $p=2[\alpha n]+1$, where $1<\alpha<2$ is a fixed irrational number. An argument of P. Ribenboim coupled with classical…
E. Bach, following an idea of T. Itoh, has shown how to build a small set of numbers modulo a prime p such that at least one element of this set is a generator of $\pF{p}$\cite{Bach:1997:sppr,Itoh:2001:PPR}. E. Bach suggests also that at…
In this work we show that the prime distribution is deterministic. Indeed the set of prime numbers P can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The prime…
Within context of quantum logic, it is possible to assign dispersion-free probabilities to experimental propositions pertaining to qubits. This makes qubits distinct from the rest of quantum systems since the latter do not admit…