A nonlinear elliptic curve cryptosystem based on matrices

We propose a new mathematical problem that is applicable to public key cryptography. Based on the Discrete Logarithm Problem (DLP), it uses certain elements formed by two matrices with elements in a finite field and a matrix whose elements are points of an elliptic curve. With this system, we get a larger key space without increasing the underlying elliptic curve and, consequently, without the computational requirements inherent to the set up of elliptic curves at random. Also, we expose the Diffie-Hellman key agreement protocol with this system acting as the underlying mathematical problem.