Related papers: New Class of Pseudorandom D-sequences to Generate …
In 2009, Grant, Shallit, and Stoll constructed a large family of pseudorandom sequences, called generalized Rudin--Shapiro sequences, for which they established some results about the average of discrete correlation coefficients of order 2…
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
Random Numbers determine the security level of cryptographic applications as they are used to generate padding schemes in the encryption/decryption process as well as used to generate cryptographic keys. This paper utilizes the QKD to…
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…
We develop the theory of cryptographic nondeterministic-secure pseudorandomness beyond the point reached by Rudich's original work (Rudich 1997), and apply it to draw new consequences in average-case complexity and proof complexity.…
Pseudorandom binary sequences with optimal balance and autocorrelation have many applications in stream cipher, communication, coding theory, etc. It is known that binary sequences with three-level autocorrelation should have an almost…
A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating…
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but…
We propose a method for program generation based on semantic scaffolds, lightweight structures representing the high-level semantic and syntactic composition of a program. By first searching over plausible scaffolds then using these as…
Learning useful representations from unstructured data is one of the core challenges, as well as a driving force, of modern data-driven approaches. Deep learning has demonstrated the broad advantages of learning and harnessing such…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…
Quantum cryptography leverages many unique features of quantum information in order to construct cryptographic primitives that are oftentimes impossible classically. In this work, we build on the no-cloning principle of quantum mechanics…
Sequence generation applications require satisfying semantic constraints, such as ensuring that programs are correct, using certain keywords, or avoiding undesirable content. Language models, whether fine-tuned or prompted with few-shot…
In this paper, we present a universal scheme for transforming an arbitrary algorithm for biased 2-face coins to generate random bits from the general source of an m-sided die, hence enabling the application of existing algorithms to general…
This paper presents an expression to compute the exact period of a recursive random number generator based on d-sequences. Using the multi-recursive version of this generator we can produce large number of pseudorandom sequences.
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
This work studies the problem of separate random number generation from correlated general sources with side information at the tester under the criterion of statistical distance. Tight one-shot lower and upper performance bounds are…
Dynamical systems generated by iterations of multivariate polynomials with slow degree growth have proved to admit good estimates of exponential sums along their orbits which in turn lead to rather stronger bounds on the discrepancy for…