Related papers: Close to Uniform Prime Number Generation With Fewe…
Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in $\{1,2,\ldots ,n\}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as…
Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This…
We propose a simple approach which, given distributed computing resources, can nearly achieve the accuracy of $k$-NN prediction, while matching (or improving) the faster prediction time of $1$-NN. The approach consists of aggregating…
We investigate, using the weighted linear sieve, the distribution of almost-primes among the residue classes (mod p) that generate the multiplicative group of reduced residue classes. We are concerned with finding an upper bound for the…
We consider the fundamental problem of communicating an estimate of a real number $x\in[0,1]$ using a single bit. A sender that knows $x$ chooses a value $X\in\set{0,1}$ to transmit. In turn, a receiver estimates $x$ based on the value of…
We present a practical high-speed quantum random number generator, where the timing of single-photon detection relative to an external time reference is measured as the raw data. The bias of the raw data can be substantially reduced…
The generation of series of random numbers is an important and difficult problem. Even the very definition of random is difficult. Appropriate measurements on entangled states have been proposed as the definitive solution to produce series…
It is a classical problem to compute a minimal set of invariant polynomial generating the invariant ring of a finite group as an algebra. We present here an algorithm for the computation of minimal generating sets in the non-modular case.…
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…
Random numbers are commonly used in many different fields, ranging from simulations in fundamental science to security applications. In some critical cases, as Bell's tests and cryptography, the random numbers are required to be both secure…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
We present an efficient method to extract the amount of true randomness that can be obtained by a Quantum Random Number Generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases,…
Let $x\ge y>0$ be integers. A positive integer is $y$-smooth if all its prime divisors are at most $y$. Let $\Psi(x,y)$ count the number of $y$-smooth integers up to $x$. We present several algorithms that will generate an integer $n\le x$…
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…
An algorithm is presented which, with optimal efficiency, solves the problem of uniform random generation of distribution functions for an n-valued random variable.
We show that once $\theta>17/30$, every sufficiently long interval $[x,x+x^\theta]$ contains many $k$-term arithmetic progressions of primes, uniformly in the starting point $x$. More precisely, for each fixed $k\ge3$ and $\theta>17/30$,…
Quantum Key Distribution(QKD) thrives to achieve perfect secrecy of One time Pad (OTP) through quantum processes. One of the crucial components of QKD are Quantum Random Number Generators(QRNG) for generation of keys. Unfortunately, these…
A new method for parallel generation of $q$-valued pseudorandom sequence based on the presentation of systems generating logical formulae by means of arithmetic polynomials is proposed. Fragment consisting of $k$-elements of $q$-valued…
Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an integer $N$, the test tries to find an…
The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which…