A Three-Factor Authenticated Mobile Key Exchange Protocol Using Matrices Over Group Ring Structure

Firstly, we know that the RSA/Discrete Logarithm assumptions don’t support devices with low computing. The factorization with discrete logarithm assumption uses only simple algebraic operations such as matrix multiplications, vector-matrix multiplications, and scalar matrix multiplications. Secondly, even if we’re still years away from having real quantum computers their ability is a significant threat to the cryptographic community. Therefore, we must be ready for future threats and computation complexity for low computing devices. In this article, we have introduced an advanced password-based anonymous authenticated exchange of keys protocol over a group ring structure over a non-commutative semigroup. As far as we are aware, this is the first authenticated exchange of keys protocol over a group ring structure over a non-commutative semigroup. The safety depends upon the toughness of factoring utilizing discrete logarithm assumption. Additionally, we analyzed both the complexity and security of the proposed protocol. This scheme is very efficient and includes only simple algebraic operations, matrix additions, and multiplications.