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The projected belief network (PBN) is a layered generative network (LGN) with tractable likelihood function, and is based on a feed-forward neural network (FFNN). There are two versions of the PBN: stochastic and deterministic (D-PBN), and…

Commutative rings of one-dimensional difference operators of rank l>1 and their deformations are effectively constructed. Our analytical constructions are based on the so-called ''Tyurin parameters'' for the stable framed holomorphic vector…

The output of Deep Neural Networks (DNN) can be altered by a small perturbation of the input in a black box setting by making multiple calls to the DNN. However, the high computation and time required makes the existing approaches unusable.…

A Sidon set $S$ in $\mathbb{F}_2^n$ is a set such that $x+y=z+w$ has no solutions $x,y,z,w \in S$ with $x,y,z,w$ all distinct. In this paper, we prove various results on Sidon sets by using or generalizing known cryptographic results. In…

The construction of conformal blocks for the analysis of multipoint correlation functions with $N > 4$ local field insertions is an important open problem in higher dimensional conformal field theory. This is the first in a series of papers…

Any permutation polynomial is an $ n $-cycle permutation. When $n$ is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These…

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…

Deep neural network (DNN) architecture based models have high expressive power and learning capacity. However, they are essentially a black box method since it is not easy to mathematically formulate the functions that are learned within…

We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem…

We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials…

In this paper, we present secure distributed matrix multiplication (SDMM) schemes over the complex numbers with good numerical stability and small mutual information leakage by utilizing polynomial interpolation with roots of unity.…

Vision foundation models are widely used as frozen backbones across many downstream tasks, making them a single point of failure under adversarial attack. We study multi-level Floyd-Steinberg error-diffusion dithering as a lightweight,…

We construct 8 x 8 bijective cryptographically strong S-boxes. Our construction is based on using non-bijective power functions over the finite filed.

Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in…

EFRST20, the notion of $c$-differentials was introduced as a potential expansion of differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspiration from the technique of higher order differential…

Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups…

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…

Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over…

The output of Convolutional Neural Networks (CNN) has been shown to be discontinuous which can make the CNN image classifier vulnerable to small well-tuned artificial perturbations. That is, images modified by adding such perturbations(i.e.…

The use of Deep Learning hardware algorithms for embedded applications is characterized by challenges such as constraints on device power consumption, availability of labeled data, and limited internet bandwidth for frequent training on…