Signal Encryption Strategy based on Domain change of the Fractional Fourier Transform

TL;DR

This paper introduces a novel double encryption method leveraging the domain change properties of the fractional Fourier transform, enhancing signal security through a unique key based on domain invertibility and transform parameters.

Contribution

It proposes a new encryption algorithm utilizing the non-invertibility of the fractional Fourier transform and domain change, verified by simulations and audio examples.

Findings

Effective encryption demonstrated via simulations.

The method exploits domain change properties of FRFT.

Encryption robustness shown with audio signals.

Abstract

This paper provides a double encryption algorithm that uses the lack of invertibility of the fractional Fourier transform (FRFT) on $L^{1}$. One encryption key is a function, which maps a ``good" $L^{2}$-signal to a ``bad" $L^{1}$-signal. The FRFT parameter which describes the rotation associated with this operator on the time-frequency plane provides the other encryption key. With the help of approximate identities, such as of the Abel and Gauss means of the FRFT established in \cite{CFGW}, we recover the encrypted signal on the FRFT domain. This design of an encryption algorithm seems new even when using the classical Fourier transform. Finally, the feasibility of the new strategy is verified by simulation and audio examples.