Related papers: Using Quasigroups for Generating Pseudorandom Numb…
Random numbers form an intrinsic part of modern day computing with applications in a wide variety of fields. But due to their limitations, the use of pseudo random number generators (PRNGs) is certainly not desirable for sensitive…
A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, "mathematical" refers to the fact that to construct that generator it is not necessary to resort to a physical phenomenon, such as the thermal noise of an…
Pseudo-random number generators (PRNGs) are essential in a wide range of applications, from cryptography to statistical simulations and optimization algorithms. While uniform randomness is crucial for security-critical areas like…
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…
Efficiently sampling a quantum state that is hard to distinguish from a truly random quantum state is an elementary task in quantum information theory that has both computational and physical uses. This is often referred to as pseudorandom…
We introduce new families of enhanced chaotic number generators in order to compute very fast long series of pseudorandom numbers. The key feature of these generators being the use of chaotic numbers themselves for sampling chaotic…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
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…
In this paper, we identify many important properties and develop criteria for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of subquasigroup of…
This paper presents a new methodology to count the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius…
Quantum Random Number Generators (QRNGs) emerged as a promising solution for generating truly random numbers. In the present article, we give an overview of QRNGs highlighting the merits and demerits of various strategies briefly. Then…
Chung and Graham define quasirandom subsets of $\mathbb{Z}_n$ to be those with any one of a large collection of equivalent random-like properties. We weaken their definition and call a subset of $\mathbb{Z}_n$ $\epsilon$-balanced if its…
The Ziggurat Algorithm is a very fast rejection sampling method for generating PseudoRandom Numbers (PRNs) from common statistical distributions. The algorithm divides a distribution into rectangular layers that stack on top of each other…
Quasirandomness is a general mathematical concept meant to encapsulate several characteristics usually satisfied by random combinatorial objects, and which we regard as describing when a given object 'looks random'. In this survey we…
A few conventions for thinking about and writing quantum pseudocode are proposed. The conventions can be used for presenting any quantum algorithm down to the lowest level and are consistent with a quantum random access machine (QRAM) model…
With the widespread use of communication technologies, cryptosystems are therefore critical to guarantee security over open networks as the Internet. Pseudo-random number generators (PRNGs) are fundamental in cryptosystems and information…
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…
We introduce the notion of numerical semigroups generated by concatenation of arithmetic sequences and show that this class of numerical semigroups exhibit multiple interesting behaviours.
Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of…
We demonstrate quantum algorithms to implement pseudo-random operators that closely reproduce statistical properties of random matrices from the three universal classes: unitary, symmetric, and symplectic. Modified versions of the…