A nonlinear elliptic curve cryptosystem based on matrices

摘要

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.