A new cryptosystem based on elliptic curves and polynomial matrices*

The system we propose is a mathematical problem with the necessary properties to define public key cryptosystems. It is based on the Elliptic Curve Discrete Logarithm Problem (ECDLP) and polynomial matrices. In this way, we achieve to increase the possible number of keys and, therefore, we augment the resolution complexity of the system. Also, we make a cryptanalisys of the system detecting its weaknesses and verifying that, even so, it is harder to solve than the ECDLP. Key-Words: Public key cryptography, elliptic curves, finite fields, discrete logarithm problem, linear systems, Diffie-Hellman key agreement, multiple instances, polynomial matrices.