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Quantum random number generator (QRNG) utilizes the intrinsic randomness of quantum systems to generate completely unpredictable and genuine random numbers, finding wide applications across many fields. QRNGs relying on the phase noise of a…
Cryptographic primitives such as stream ciphers,Pseudorandom Number Generators (PRNGs), and block cipher modes produce sequences that are designed to be statistically indistinguishable from random data. As a result, the traditional…
We study weighted pseudorandom generators (WPRGs) and derandomizations for read-once branching programs (ROBPs). Denote $n$ and $w$ as the length and the width of a ROBP. We have the following results. For standard ROBPs, we give an…
Elliptic curve cryptography has received great attention in recent years due to its high resistance against modern cryptanalysis. The aim of this article is to present efficient generators to generate substitution boxes (S-boxes) and pseudo…
In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In…
Powerful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labelled with powers $x^n$ for binary encoded numbers $n$. It is shown that polynomial identity testing for…
Random number generators (RNGs) that are crucial for cryptographic applications have been the subject of adversarial attacks. These attacks exploit environmental information to predict generated random numbers that are supposed to be truly…
Quantum random number generator (QRNG) is one of the most widely applied branches in quantum cryptography. Among all QRNG schemes, semi-device-independent (semi-DI) QRNG is quite promising, achieving high randomness generation rate with few…
Quantile-based randomized Kaczmarz (QRK) was recently introduced to efficiently solve sparsely corrupted linear systems $\mathbf{A} \mathbf{x}^*+\mathbf{\epsilon} = \mathbf{b}$ [SIAM J. Matrix Anal. Appl., 43(2), 605-637], where…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
Different flavors of quantum pseudorandomness have proven useful for various cryptographic applications, with the compelling feature that these primitives are potentially weaker than post-quantum one-way functions. Ananth, Lin, and Yuen…
A central question in derandomization is whether randomized logspace (RL) equals deterministic logspace (L). To show that RL=L, it suffices to construct explicit pseudorandom generators (PRGs) that fool polynomial-size read-once (oblivious)…
As Collatz conjecture is still to be proved, a method to arrive at the complete proof is explored here. Conceptually, the process relies on the pre-proven sequence data and the method follows the confirmation of the convergence of the…
We give the best known pseudorandom generators for two touchstone classes in unconditional derandomization: an $\varepsilon$-PRG for the class of size-$M$ depth-$d$ $\mathsf{AC}^0$ circuits with seed length $\log(M)^{d+O(1)}\cdot…
Monte Carlo simulations are an important tool in statistical physics, complex systems science, and many other fields. An increasing number of these simulations is run on parallel systems ranging from multicore desktop computers to…
Random number generation is crucial in many aspects of everyday life, as online security and privacy depend ultimately on the quality of random numbers. Many current implementations are based on pseudo-random number generators, but…
We introduce a systematic method for constructing polytope approximations to the quantum set in a variety of device-independent quantum random number generation (DI-QRNG) protocols. Our approach relies on two general-purpose algorithms that…
Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several…
Quantum technologies provide many applications for information processing tasks that are impossible to realize within classical physics. These capabilities include such fundamental resources as generating secure, i.e. private and…
The primary objective of this section is to demonstrate that the actual pseudorandom measures of our construction are significantly smaller than the theoretical upper bounds derived from the Weil theorem. Regarding the family of sequences,…