Image encryption based on the fractional Fourier transform over finite fields

• Fractional Fourier transforms over GF(p  ), where ρ≡1(mod4), are introduced.
• The constructed transforms are used as the basis of a novel image encryption scheme.
• Security aspects of the proposed scheme are analyzed.

In this paper, we introduce fractional Fourier transforms over finite fields GF(p  ), where p≡1(mod4). 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.