Elliptic-Curves Cryptography on High-Dimensional Surfaces
This work addresses cryptographic efficiency and security for data protection systems, but appears incremental as it builds on existing elliptic-curve methods with a new matrix-based approach.
The paper tackles the problem of reducing bit usage in elliptic-curve cryptography by proposing a key exchange protocol in matrix form with four 64-bit entries, which significantly cuts bits and claims immunity to certain attacks while matching the security of Microsoft Digital Rights Management.
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.