Related papers: Aspects of Nonabelian Group Based Cryptography: A …
We analyze a cryptographic protocol for generating a distributed secret key from correlations that violate a Bell inequality by a sufficient amount, and prove its security against eavesdroppers, constrained only by the assumption that any…
Quantum cryptography uses techniques and ideas from physics and computer science. The combination of these ideas makes the security proofs of quantum cryptography a complicated task. To prove that a quantum-cryptography protocol is secure,…
It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a…
The thesis is mainly about the construction and implementation of cyclic mutually unbiased bases, dealing with different entanglement structures by discussing the related group structures. A recursive construction for Fermat number…
This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying…
In 1998, Blaze, Bleumer, and Strauss suggested a cryptographic primitive named proxy re-signatures where a proxy turns a signature computed under Alice's secret key into one from Bob on the same message. The semi-trusted proxy does not…
The present paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. Instead of a single black box, we consider categories of black boxes and their morphisms. This makes new…
The braid group has recently attracted much attention. This is primarily based upon the discovery of its usage in various cryptosystems [AAG],[KLCHKP]. One major focus of current research has been in solving decision problems in braid…
In this paper, we propose a blind signature scheme and three practical educed schemes based on elliptic curve discrete logarithm problem. The proposed schemes impart the GOST signature structure and utilize the inherent advantage of…
In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite…
We believe that there is no real data protection without our own tools. Therefore, our permanent aim is to have more of our own codes. In order to achieve that, it is necessary that a lot of young researchers become interested in…
We introduce the \emph{linear centralizer method}, and use it to devise a provable polynomial time solution of the Commutator Key Exchange Problem, the computational problem on which, in the passive adversary model, the security of the…
Threshold schemes exist for many cryptographic primitives like signatures, key derivation functions, and ciphers. At the same time, practical key exchange protocols based on Diffie-Hellman (DH) or ECDSA primitives are not designed or…
Recently the AAGL (Anshel-Anshel-Goldfeld-Lemieux) has been proposed which can be used for RFID tags. We give algorithms for the problem (we call the MSCSPv) on which the security of the AAGL protocol is based upon. Hence we give various…
We use matrices over bit strings as platforms for Diffie-Hellman-like public key exchange protocols. When multiplying matrices like that, we use Boolean OR operation on bit strings in place of addition and Boolean AND operation in place of…
Recently, Hwang et al. introduced a knapsack type public-key cryptosystem. They proposed a new algorithm called permutation combination algorithm. By exploiting this algorithm, they attempt to increase the density of knapsack to avoid the…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
We study a novel type of braid groups on a closed orientable surface $\Sigma$. These are fundamental groups of certain manifolds that are hybrids between symmetric products and configuration spaces of points on $\Sigma$; a class of examples…
Recently, a novel public key edcryption technique based on multiple chaotic systems has been proposed. The scheme employs m-chaotic systmes and a set of linear functions for key exchange over an insecure channel. The security of the…