RSA encryption algorithm based on torus automorphisms

We propose a public-key encryption algorithm based on torus automorphisms, which is secure, practical, and can be used for both encryption and digital signature. Software implementation and properties of the algorithm are discussed in detail. We show that our algorithm is as secure as RSA algorithm. In this paper we have generalized RSA algorithm replacing powers with matrix powers, choosing the matrix to be a matrix which defines a two-torus automorphisms, an example of strongly chaotic system.