Related papers: Black Box White Arrow
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
Clustering algorithms are used in a large number of applications and play an important role in modern machine learning-- yet, adversarial attacks on clustering algorithms seem to be broadly overlooked unlike supervised learning. In this…
In 2008, the author proposed a version of duality theory for (not necessarily, Abelian) complex Lie groups, based on the idea of using the Arens-Michael envelope of topological algebra and having an advantage over existing theories in that…
Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…
We are used to the availability of big data generated in nearly all fields of science as a consequence of technological progress. However, the analysis of such data possess vast challenges. One of these relates to the explainability of…
Here is a more detailed description of the algorithm proposed in [1]. This algorithm simultaneously uses two cryptographic procedures: encryption using a generalization of the Markovski algorithm [2] and encryption using a system of…
As Machine Learning (ML) is now widely applied in many domains, in both research and industry, an understanding of what is happening inside the black box is becoming a growing demand, especially by non-experts of these models. Several…
Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
As the number of hacking events and cyber threats keeps going up, it is getting harder and harder to communicate securely and keep personal information safe on the Internet. Cryptography is a very important way to deal with these problems…
The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems…
In the last decade, deep neural networks have proven to be very powerful in computer vision tasks, starting a revolution in the computer vision and machine learning fields. However, deep neural networks, usually, are not robust to…
This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent…
Polycyclic groups are natural generalizations of cyclic groups but with more complicated algorithmic properties. They are finitely presented and the word, conjugacy, and isomorphism decision problems are all solvable in these groups.…
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…
Adversarial robustness is one of the essential safety criteria for guaranteeing the reliability of machine learning models. While various adversarial robustness testing approaches were introduced in the last decade, we note that most of…
In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…
Topological Coding consists of two different kinds of mathematics: topological structure and mathematical relation. The colorings and labelings of graph theory are main techniques in topological coding applied in asymmetric encryption…
Machine Learning (ML) and Deep Learning (DL) models have achieved state-of-the-art performance on multiple learning tasks, from vision to natural language modelling. With the growing adoption of ML and DL to many areas of computer science,…
Black-box optimization (BBO) can be used to optimize functions whose analytic form is unknown. A common approach to realising BBO is to learn a surrogate model which approximates the target black-box function which can then be solved via…