Related papers: Increasing Randomness Using Permutations on Blocks
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
We provide a general framework to improve trade-offs between the number of full batch and sample queries used to solve structured optimization problems. Our results apply to a broad class of randomized optimization algorithms that…
In our previous works, we have studied quantum random walk search algorithm on hypercube, with traversing coin constructed by using generalized Householder reflection and a phase multiplier. When the same phases are used each iteration, the…
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…
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…
Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…
This work evaluates the impact of sparse matrix reordering on the performance of sparse matrix-vector multiplication across different multicore CPU platforms. Reordering can significantly enhance performance by optimizing the non-zero…
The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes. In this paper, we focus on the basic problem of correcting faulty or adversarially corrupted random oracles, so that…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
We study the regimes in which Hamiltonian simulation benefits from randomization. We introduce a sparse-QSVT construction based on composite stochastic decompositions, where dominant terms are treated deterministically and smaller…
Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model. The limited success of both methods demonstrated in…
As the mobile application landscape expands, wireless networks are tasked with supporting various connection profiles, including real-time communications and delay-sensitive traffic. Among many ensuing engineering challenges is the need to…
When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample $n$ individuals at the end of a selective sweep. If we focus on a…
Given a connected network, it can be augmented by applying a growing strategy (e.g. random or scale-free rules) over the previously existing structure. Another approach for augmentation, recently introduced, involves incorporating a direct…
Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing…
Recent work has extensively shown that randomized perturbations of neural networks can improve robustness to adversarial attacks. The literature is, however, lacking a detailed compare-and-contrast of the latest proposals to understand what…
Blockchains based on the celebrated Nakamoto consensus protocol have shown promise in several applications, including cryptocurrencies. However, these blockchains have inherent scalability limits caused by the protocol's consensus…
Frailty and resilience models provide a way to introduce random effects in hazard and reversed hazard rate modeling by random variables, called frailty and resilience random variables, respectively, to account for unobserved or unexplained…
In his Ph.D. thesis, Ira Gessel proved a reciprocity formula for noncommutative symmetric functions which enables one to count words and permutations with restrictions on the lengths of their increasing runs. We generalize Gessel's theorem…