Related papers: The root extraction problem in braid group-based c…
We construct a one-dimensional deformation retract of the unordered k-point configuration space of a star S. This retract suggests an explicit set of free generators Beta_k for the corresponding braid group of the star B_k and shows that…
The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…
Cryptographic Self-Selection is a paradigm employed by modern Proof-of-Stake consensus protocols to select a block-proposing "leader." Algorand [Chen and Micali, 2019] proposes a canonical protocol, and Ferreira et al. [2022] establish…
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
In 2020 Sala, Sogiorno and Taufer have been able to find the private keys of some Bitcoin addresses, thus being able to spend the cryptocurrency linked to them. This result was unexpected, since the recovery of non-trivial private keys for…
This paper introduces a new method of Blockchain formation for reliable storage of personal data of ID-card holders. In particular, the model of the information system is presented, the new structure of smart ID-cards and information on…
Mobile devices have become an indispensable component of modern life. Their high storage capacity gives these devices the capability to store vast amounts of sensitive personal data, which makes them a high-value target: these devices are…
In the Best-$K$ identification problem (Best-$K$-Arm), we are given $N$ stochastic bandit arms with unknown reward distributions. Our goal is to identify the $K$ arms with the largest means with high confidence, by drawing samples from the…
It was recently observed in [1], that in index coding, learning the coding matrix used by the server can pose privacy concerns: curious clients can extract information about the requests and side information of other clients. One approach…
Let $G$ be a group endowed with a solution to the conjugacy problem and with an algorithm which computes the centralizer in $G$ of any element of $G$. Let $H$ be a subgroup of $G$. We give some conditions on $H$, under which we provide a…
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time…
In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…
The theory of Engel groups plays an important role in group theory since these groups are closely related to the Burnside problems. In this survey we consider several classical and novel algorithmic problems for Engel groups and propose…
The Bad Triangle Transversal (BTT) problem asks for the smallest set of edges that need to be removed from a given signed graph, so that the resulting graph does not have a bad triangle. Here, a bad triangle is a triangle with exactly one…
Prior research has shown that cryptography is hard to use for developers. We aim to understand what cryptography issues developers face in practice. We clustered 91954 cryptography-related questions on the Stack Overflow website, and…
We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used…
The group generated by the round functions of a block ciphers is a widely investigated problem. We identify a large class of block ciphers for which such group is easily guaranteed to be primitive. Our class includes the AES and the…
Most modern cryptographic systems, such as RSA and the Diffie-Hellman Key Exchange, rely on "trapdoor" mathematical functions that are presumed to be computationally difficult with existing tools. However, quantum computers will be able to…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…