Related papers: Pseudorandom Vector Generation Using Elliptic Curv…
This paper studies the problem of discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator, particularly in the non-translational case. Two families of results are obtained. First, in a…
We describe a uniformly fast algorithm for generating points \vec{x} uniformly in a hypercube with the restriction that the difference between each pair of coordinates is bounded. We discuss the quality of the algorithm in the sense of its…
The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in…
Given a prime $p$, an elliptic curve $\E/\F_p$ over the finite field $\F_p$ of $p$ elements and a binary \lrs\ $\(u(n)\)_{n =1}^\infty$ of order~$r$, we study the distribution of the sequence of points $$ \sum_{j=0}^{r-1} u(n+j)P_j, \qquad…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…
Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the…
Major controversy surrounds the use of Elliptic Curves in finite fields as Random Number Generators. There is little information however concerning the "randomness" of different procedures on Elliptic Curves defined over fields of…
In this paper we study the kaleidoscopic pseudo-randomness of finite Euclidean graphs using probabilistic methods. Roughly speaking, we show that sufficiently large subsets of d-dimensional vector spaces over finite fields contain every…
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…
Pseudorandom bit generators (PRBG) can be designed to take the advantage of some hard number theoretic problems such as the discrete logarithm problem (DLP). Such type of generators will have good randomness and unpredictability properties…
The Deligne-Ogus-Shioda theorem guarantees the existence of isomorphisms between products of supersingular elliptic curves over finite fields. In this paper, we present methods for explicitly computing these isomorphisms in polynomial time,…
We describe an explicit method for constructing pseudo-automorphisms of a space $X$ which is obtained by blowing up points of $P^k$ (or a product $P^k \times \cdots \times P^k$). The centers of blowup are chosen to lie on an elliptic normal…
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…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…
Let $\E$ be an elliptic curve over a finite field $\F_{q}$ of $q$ elements, with $\gcd(q,6)=1$, given by an affine Weierstra\ss\ equation. We also use $x(P)$ to denote the $x$-component of a point $P = (x(P),y(P))\in \E$. We estimate…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…