Related papers: Combinatorial group theory and public key cryptogr…
Motivated by a desire to test the security of the pubic key exchange protocol of I. Anshel, M. Anshel, and D. Goldfeld, (``An Algebraic Method for Public-Key Cryptography'', Mathematical Research Letters, vol. 6, pp. 1-5, 1999), we study…
Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…
This paper presents a novel methodology to test the security of the Diffie-Hellman public key exchange protocol. The security of many cryptographic schemes rely on the hardness of this problem. We are presenting a purely statistical test to…
The conjugacy search problem in a group $G$ is the problem of recovering an $x \in G$ from given $g \in G$ and $h=x^{-1}gx$. The alleged computational hardness of this problem in some groups was used in several recently suggested public key…
Ensuring security is something that is not easily done as many of the demands of network security conflict with the demands of mobile networks, majorly because of the nature of the mobile devices (e.g. low power consumption, low processing…
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.…
The main goal of this work is to propose the design of secret sharing schemes based on hard-on-average problems. It includes the description of a new multiparty protocol whose main application is key management in networks. Its…
Conjugacy is not the only possible primitive for designing braid-based protocols. To illustrate this principle, we describe a Fiat--Shamir-style authentication protocol that be can be implemented using any binary operation that satisfies…
In this paper, a new key-agreement scheme is proposed and analyzed. In addition to being provably secure in shared secret key indistinguishability model, the scheme has an interesting feature: while using exponentiation over a cyclic…
We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.
Braids groups provide an alternative to number theoretic public cryptography and can be implemented quite efficiently. The paper proposes five signature schemes: Proxy Signature, Designated Verifier, Bi-Designated Verifier, Designated…
Traditional methods in public key cryptography are based on number theory, and suffer from problems such as dealing with very large numbers, making key creation cumbersome. Here, we propose a new public key cryptosystem based on strings…
The need of totally secure online auction has led to the invention of many auction protocols. But as new attacks are developed, auction protocols also require corresponding strengthening. We analyze the auction protocol based on the…
There are recent cryptographic protocols that are based on Multiple Simultaneous Conjugacy Problems in braid groups. We improve an algorithm, due to Sang Jin Lee and Eonkyung Lee, to solve these problems, by applying a method developed by…
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which…
In this paper, we investigate properties of some multi-particle entangled states and, from the properties applying the secret sharing present a new type of quantum key distribution protocols as generalization of quantum key distribution…
In this paper,we propose a modified Anshel-Anshel-Goldfeld(AAG) key exchange scheme. The hardness assumption underlying this modified construction is based on the membership problem for Mihailova subgroups of the braid group, a problem that…
In this paper a secret sharing scheme based on the word problem in groups is introduced. The security of the scheme and possible variations are discussed in section 2. The article concludes with the suggestion of two categories of platform…
We present several quantum public-key encryption (QPKE) protocols designed with conjugate coding single-photon string, thus may be realized in laboratory with nowadays techniques. Two of these schemes are orienting one-bit message, and are…
Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect…