A common key encryption algorithm using N-dimensional Hilbert curves

Abstract

There are a lot of previous works on common key encryptions such as DES, AES, etc, In this paper, a new common key encryption algorithm is proposed using Hilbert curves which are a one-to-one mapping between N-dimensional (N-D) spaces and 1-D space (a line). This is based on a property having a sharp rise in the number of Hilbert curve patterns in N-D spaces. In the case of N = 2, there are only four patterns, while if N is 5, the number of the patterns is more than 1 billions. Operations of addition and multiplication are denned on a curve, based on a mapping of a point in N-D spaces to a point on a line. In order to realize a cryptosystem, the algorithm utilizes Hilbert ordered point addresses, which is expressed as the coordinates of the points in N-dimensional space.