Implementing Multi-party Key Exchange by Linear Combination of Elliptic Curve Points

Efficient authenticated multi-party key agreement is both an open problem and one of the fundamental cryptographic primitives that has to be tackled for deploying secure e-commerce in the real world. In this paper, by taking one third of the order of a generator a basic version of a multi-party key agreement scheme is proposed based on the matrix-based ECC (Elliptic Curve Cryptog-raphy) 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 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 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.