Related papers: Problems in group theory motivated by cryptography
In this paper, we investigate the profit-driven team grouping problem in social networks. We consider a setting in which people possess different skills, and the compatibility between these individuals is captured by a social network.…
The root extraction problem in braid groups is the following: given a braid $\beta \in \mathcal{B}_n$ and a number $k\in \mathbb{N}$, find $\alpha\in \mathcal{B}_n$ such that $\alpha^k=\beta$. In the last decades, many cryptosystems such as…
Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and…
The secure instantiation of the random oracle is one of the major open problems in modern cryptography. We investigate this problem using concepts and methods of algorithmic randomness. In modern cryptography, the random oracle model is…
The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…
Lattice-based Cryptography is considered to have the characteristics of classical computers and quantum attack resistance. We will design various graphic lattices and matrix lattices based on knowledge of graph theory and topological…
In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…
In previous work, we developed a single Evolutionary Algorithm (EA) to solve random instances of the Anshel-Anshel-Goldfeld (AAG) key exchange protocol over polycyclic groups. The EA consisted of six simple heuristics which manipulated…
In this research work, security concepts are formalized in steganography, and the common paradigms based on information theory are replaced by another ones inspired from cryptography, more practicable are closer than what is usually done in…
Machine learning techniques have had a long list of applications in recent years. However, the use of machine learning in information and network security is not new. Machine learning and cryptography have many things in common. The most…
Studying corruption presents unique challenges. Recent work in the spirit of computational social science exploits newly available data and methods to give a fresh perspective on this important topic. In this chapter we highlight some of…
Extremal Combinatorics is among the most active topics in Discrete Mathematics, dealing with problems that are often motivated by questions in other areas, including Theoretical Computer Science and Information Theory. This paper contains a…
The interleaving of chaos and cryptography has been the aim of a large set of works since the beginning of the nineties. Many encryption proposals have been introduced to improve conventional cryptography. However, many proposals possess…
We show that every countable group H with solvable word problem (=computable group) can be subnormally embedded into a 2-generated group G which also has solvable word problem. Moreover, the membership problem for H < G is also solvable. We…
Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total…
This is an expository article on recent developments in the theory of group relaxations in integer programming from an algebraic perspective.
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
The algebraic structure of the group generated by the encryption functions of a block cipher depends on the key schedule algorithm used for generating the round keys. For such a reason, in general, studying this group does not appear to be…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
We give a review of some known published applications of quasigroups in cryptology.