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Hash-based sampling and estimation are common themes in computing. Using hashing for sampling gives us the coordination needed to compare samples from different sets. Hashing is also used when we want to count distinct elements. The quality…
Digital circuits based on residue number systems have been considered to produce a pseudo-random behavior. The present work is an initial step towards the complete implementation of those systems for similar applications using quantum…
This article proposes the use of pseudorandom decimal sequences that have gone through an additional random mapping for the design of cryptographic keys. These sequences are generated by starting with inverse prime expansions in base 3 and…
The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
We describe the use of quasiperiodic oscillators for computation and control of robots. We also describe their relationship to central pattern generators in simple organisms and develop a group theory for describing the dynamics of these…
Randomness extraction is an essential post-processing step in practical quantum cryptography systems. When statistical fluctuations are taken into consideration, the requirement of large input data size could heavily penalise the speed and…
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash…
We show how to construct pseudorandom permutations (PRPs) that remain secure even if the adversary can query the permutation, both in the forward and reverse directions, on a quantum superposition of inputs. Such quantum-secure PRPs have…
Let $H$ and $L$ be quantum groupoids. If $H$ has a quasitriangular structure, then we show that $L$ induces a Hopf algebra $C_{L}(L_s)$ in the category $_{H}\mathcal{M}$, which generalizes the transmutation theory introduced by Majid.…
In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct…
By modeling quantum chaotic dynamics with ensembles of random operators, we explore howmachine learning learning algorithms can be used to detect pseudorandom behavior in qubit systems.We analyze samples consisting of pieces of correlation…
This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using…
Pseudorandmness plays an important role in number theory, complexity theory and cryptography. Our aim is to use models of arithmetic to explain pseudorandomness by randomness. To this end we construct a set of models $\cal M$, a common…
This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
Random numbers are a fundamental and useful resource in science and engineering with important applications in simulation, machine learning and cyber-security. Quantum systems can produce true random numbers because of the inherent…