Image encryption based on the fractional Fourier transform over finite fields

摘要

In this paper, we introduce fractional Fourier transforms over finite fields GF(p), where p=1 (mod 4). Such a definition is based on the approach given in [1], which corresponds to a finite field extension of the commuting matrix method for defining discrete fractional Fourier transforms [2]. The transforms we have constructed are then used as the basis of a novel image encryption scheme. Security aspects of such a scheme are analyzed through computer simulations and specific metrics.