Related papers: On the Evolution of Boomerang Uniformity in Crypto…
Recent studies on binomials of the form $F_r(x) = x^r(1 + \chi(x))$ over $\mathbb{F}_{p^n}$ have shown that these functions can exhibit very low boomerang uniformity. In this paper, we focus on the specific behavior of such binomials in…
We define a new framework that unifies the filtration and mapper approaches from TDA, and present efficient algorithms to compute it. Termed the box filtration of a PCD, we grow boxes (hyperrectangles) that are not necessarily centered at…
In modern engineering, computer simulations are a popular tool to analyse, design, and optimize systems. Furthermore, concepts of uncertainty and the related reliability analysis and robust design are of increasing importance. Hence, an…
After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies. The optimal cloner is realized by quantum channels with memory, and greately outperforms…
Deep learning has demonstrated state-of-the-art performance for a variety of challenging computer vision tasks. On one hand, this has enabled deep visual models to pave the way for a plethora of critical applications like disease…
The construction of asymmetric error correcting codes is a topic that was studied extensively, however, the existing approach for code construction assumes that every codeword should tolerate $t$ asymmetric errors. Our main observation is…
As deep neural networks (DNNs) have become increasingly important and popular, the robustness of DNNs is the key to the safety of both the Internet and the physical world. Unfortunately, some recent studies show that adversarial examples,…
In adversarial machine learning, neural networks suffer from a significant issue known as robust overfitting, where the robust test accuracy decreases over epochs (Rice et al., 2020). Recent research conducted by Xing et al.,2021; Xiao et…
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.…
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…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
Deep Learning (DL) algorithms have gained popularity owing to their practical problem-solving capacity. However, they suffer from a serious integrity threat, i.e., their vulnerability to adversarial attacks. In the quest for DL…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions,…
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…
Coalescing RDMA and Persistent Memory (PM) delivers high end-to-end performance for networked storage systems, which requires rethinking the design of efficient hash structures. In general, existing hashing schemes separately optimize RDMA…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Strong, fast pulses, called ``bang-bang'' controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which…
We investigate a fundamental property of device independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that…
We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and…