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Generative Adversarial Networks (GANs) have become the gold standard when it comes to learning generative models for high-dimensional distributions. Since their advent, numerous variations of GANs have been introduced in the literature,…

In symmetric cryptography, maximum distance separable (MDS) matrices with computationally simple inverses have wide applications. Many block ciphers like AES, SQUARE, SHARK, and hash functions like PHOTON use an MDS matrix in the diffusion…

Bent functions are of great importance in both mathematics and information science. The $\mathcal{P}\mathcal{S}$ class of bent functions was introduced by Dillon in 1974, but functions belonging to this class that can be explicitly…

Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…

In this work, we use the notion of ``symmetry'' of functions for an extension $K/L$ of finite fields to produce extensions of a function field $F/K$ in which almost all places of degree one split completely. Then we introduce the notion of…

There exists a dichotomy between classical probabilistic graphical models, such as Bayesian networks (BNs), and modern tractable models, such as sum-product networks (SPNs). The former generally have intractable inference, but provide a…

We consider the following problem: estimate the size of a nonempty set $S\subseteq\left[ N\right] $, given both quantum queries to a membership oracle for $S$, and a device that generates equal superpositions $\left\vert S\right\rangle $…

Proving super-polynomial size lower bounds for syntactic multilinear Algebraic Branching Programs(smABPs) computing an explicit polynomial is a challenging problem in Algebraic Complexity Theory. The order in which variables in…

The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in which one often wishes to solve PDEs in regimes far beyond…

We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom…

In this paper, we present a black-box attack against API call based machine learning malware classifiers, focusing on generating adversarial sequences combining API calls and static features (e.g., printable strings) that will be…

We study the relation among some security parameters for vectorial Boolean functions which prevent attacks on the related block cipher. We focus our study on a recently-introduced security criterion, called weak differential uniformity,…

Arithmetic circuit complexity studies the complexity of computing polynomials using only arithmetic operations such as addition, multiplication, subtraction, and division. Polynomials over rings of integers model counting problems.…

Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models.…

The inverse function $x \mapsto x^{-1}$ on $\mathbb{F}_{2^n}$ is one of the most studied functions in cryptography due to its widespread use as an S-box in block ciphers like AES. In this paper, we show that, if $n\geq 5$, every function…

Quantum state preparation, also known as encoding or embedding, is a crucial initial step in many quantum algorithms and often constrains theoretical quantum speedup in fields such as quantum machine learning and linear equation solvers.…

Advanced Encryption Standard(AES) is one of the most widely used block ciphers nowadays, and has been established as an encryption standard in 2001. Here we design AES-128 and the sample-AES(S-AES) quantum circuits for deciphering. In the…

In this work, we analyze the combinatorial properties of cylinders and subdivisions of augmented semi-simplicial sets. These constructions are obtained as particular cases of a certain action from a co-semi-simplicial set on an augmented…

One of the major open problems in symmetric cryptanalysis is to discover new specif i c types of invariant properties which can hold for a larger number of rounds of a block cipher. We have Generalised Linear Cryptanalysis (GLC) and…

We propose a semiclassical approach to calculate multiparticle cross sections in scalar theories, which have been strongly argued to have the exponential form $\exp(\lambda^{-1}F(\lambda n,\epsilon))$ in the regime $\lambda\to0$, $\lambda…