Related papers: Generating k-independent variables in constant tim…
We present algorithms for generating small random samples without replacement. We consider two cases. We present an algorithm for sampling a pair of distinct integers, and an algorithm for sampling a triple of distinct integers. The…
Quantum-proof randomness extraction is essential for handling quantum side information possessed by a quantum adversary, which is widely applied in various quantum cryptography tasks. In this study, we introduce a real-time two-source…
We study the problem of computing the probability that a given stochastic context-free grammar (SCFG), G, generates a string in a given regular language L(D) (given by a DFA, D). This basic problem has a number of applications in…
We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming…
This work reports on setup, characterisation and data processing of a true quantum random number generator. As a randomness source a pure quantum vacuum state of light is used, which is amplified by a laser beam. Performance and behaviour…
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…
We derive a formula for the moments and the free cumulants of the multiplication of $k$ free random variables in terms of $k$-equal and $k$-divisible non-crossing partitions. This leads to a new simple proof for the bounds of the right-edge…
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…
We present experimental results on the effects of using quantum or 'truly' random numbers, as opposed to pseudorandom numbers, in a system that exhibits computational creativity (given its ability to compose original chess problems). The…
Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…
We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems: 1. Given a Context Free Grammar $G$ over alphabet $\Sigma$, count the number of words of length exactly $n$ generated by…
We introduce and study the notion of k-divisible elements in a non-commutative probability space. A k-divisible element is a (non-commutative) random variable whose n-th moment vanishes whenever n is not a multiple of k. First, we consider…
Given any non-polynomial $G$-function $F(z)=\sum\_{k=0}^\infty A\_k z^k$ of radius of convergence $R$, we consider the $G$-functions $F\_n^{[s]}(z)=\sum\_{k=0}^\infty \frac{A\_k}{(k+n)^s}z^k$ for any integers $s\geq 0$ and $n\geq 1$. For…
We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on rational sublattice which coincides with the Galois field. The period of the trajectories increases as a function of lattice size and…
We propose and demonstrate a technique for quantum random number generation based on the random population of the output spatial modes of a beam splitter when both inputs are simultaneously fed with indistinguishable weak coherent states.…
The increasing sophistication of wind turbine design and control generates a need for high-quality data. Therefore, the relatively limited set of measured wind data may be extended with computer-generated surrogate data, e.g. to make…
Random number generation is a fundamental security primitive for RFID devices. However, even this relatively simple requirement is beyond the capacity of today's average RFID tag. A recently proposed solution, Fingerprint Extraction and…
Generative modeling has been used frequently in synthetic data generation. Fairness and privacy are two big concerns for synthetic data. Although Recent GAN [\cite{goodfellow2014generative}] based methods show good results in preserving…
Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks -- device-independent quantum random number…
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…