Related papers: Problems in group theory motivated by cryptography
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
Two neural networks which are trained on their mutual output bits show a novel phenomenon: The networks synchronize to a state with identical time dependent weights. It is shown how synchronization by mutual learning can be applied to…
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols…
The point of this paper is to use affine automorphisms from algebraic geometry to build cryptographic multivariate mappings. We will construct groups G,H, both isomorphic to the cyclic group with a prime number of elements and multilinear…
We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their…
This paper surveys some results and methods in topological transformation groups.
This paper presents the study of an event grouping based algorithm for a university course timetabling problem. Several publications which discuss the problem and some approaches for its solution are analyzed. The grouping of events in…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
Finding groups of connected individuals in large graphs with tens of thousands or more nodes has received considerable attention in academic research. In this paper, we analyze three main issues with respect to the recent influx of papers…
This paper develops a theory of polynomial maps from commutative semigroups to arbitrary groups and proves that it has desirable formal properties when the target group is locally nilpotent. We apply this theory to solve Waring's Problem…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
The paper surveys various Waring type problems in groups, Lie algebras, and associative algebras.
We have a large number of samples and we want to find the infected ones using as few number of tests as possible. We can use group testing which tells about a small group of people whether at least one of them is infected. Group testing is…
Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…
In this paper we propose cryptosystems based on subgroup distortion in hyperbolic groups. We also include concrete examples of hyperbolic groups as possible platforms.
This paper provides a preparatory introduction to torsors, written with a view toward later applications in the author's work. Rather than aiming at a comprehensive survey, the exposition focuses on those aspects of torsors that are most…