  We discuss the use of elliptic curves in cryptography on high-dimensional
surfaces. In particular, instead of a Diffie-Hellman key exchange protocol
written in the form of a bi-dimensional row, where the elements are made up
with 256 bits, we propose a key exchange protocol given in a matrix form, with
four independent entries each of them constructed with 64 bits. Apart from the
great advantage of significantly reducing the number of used bits, this
methodology appears to be immune to attacks of the style of Western, Miller,
and Adleman, and at the same time it is also able to reach the same level of
security as the cryptographic system presently obtained by the Microsoft
Digital Rights Management. A nonlinear differential equation (NDE) admitting
the elliptic curves as a special case is also proposed. The study of the class
of solutions of this NDE is in progress.
