A key exchange protocol using matrices over group ring

Abstract

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

A Secure Key Exchange Protocol and a Public Key Cryptosystem for Healthcare Systems

“…In this section, DLP, FP, DLPFP, Centralizer, and Semiring are defined [30,33,34], and the model, structure, flow, and security goals of the system are given.…”

“…[29] claims that the "semi-simple algebra" structure of group rings can decipher the key exchange protocols based on DLP. [30] suggests a Factorization Discrete Logarithm Problem (FDLP)-based key exchange protocol and analyses the security and complexity. Also, an ElGamal cryptosystem is proposed.…”

“…However, to our best knowledge, a few of them have provided these protocols based on ElGamal cryptosystems and mathematical hard problems. In [30], a protocol based on the group of invertible matrices over group rings is presented. Semiring is a generalized concept of group rings.…”

An Application of Twisted Group Rings in Secure Group Communications

“…In the context of SAP, we proposed in [4] a new setting, and some protocols. In our case, the platform is a twisted group ring, a new proposal in the context of group rings, that have also been recently used in cryptography in works like [3,6,5,7]. And the action proposed is the two-sided multiplication in a twisted group ring, so the problem is a variation in the twisted case of the so-called Decomposition Problem (DP), which is a generalization of the Conjugate Search Problem (CSP).…”

A New Digital Signature Scheme Using Tribonacci Matrices

“…However, the security of these schemes is still a problem to be tackled. Currently, we find many new schemes [4], [5], [6], [7], [8] designed by using algebraic structures, linear groups, non-abelian groups like matrices and polynomials which are claimed to be more secure and efficient than the existing schemes. It is observed that the size of keys and storage space can be reduced by representing the plain text message as a matrix [9], [10], [11] without compromising the security.…”