A New Variant of the Diffie-Hellman Key-Exchange Protocol Based on Block Triangular Matrix Groups

Efficient authenticated key exchange is the most important part of a security system that employs cryptographic techniques in World Wide Web-based applications. In this paper, an ECC (Elliptic Curve Cryptography) version of Hughespsilas key-exchange protocol is proposed based on the matrix-based ECC by Climent et al. The basic security of the proposed scheme is based on the ECDLP (Elliptic Curve Discrete Logarithm Problem) and the DLP defined over a cyclic subgroup generated by a 2times2 block matrix consisting of two matrices with entries in an optimal extension field and one matrix whose entries are points of an elliptic curve. Analysis indicates that besides several desirable security properties this system can, by means of linear combination of elliptic curve points, get larger key spaces flexibly without having to increase the underlying elliptic curve and save the computational requirements inherent to the regeneration and revalidation of elliptic curves.