Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval

We propose a method to encrypt two covert images into an overt image based on phase-truncated Fourier transforms and phase retrieval. In this method, the two original images are self-encoded in the manner that one of the two images is directly separated into two phase masks (PMs) and used as keys for encryption, and then multiplied by a PM which is generated by using phase retrieval algorithm. At last, the whole encryption process is completed by a Fourier transform operation. In the decryption process, the image without a separation and the two PMs used as keys for encryption are all treated as encoded data. The cryptosystem is asymmetric which means the keys for encryption are different from those for decryption. Numerical simulations are presented to show the viability and good performance of the proposed method.

Research highlights► A new method to realize double-image self-encoding and hiding has been proposed based on phase substitution and phase retrieval. ► Two original images are self-encoded in the manner that one of the two images is directly separated into two PMs and used as keys for encryption. ► For the sake of linearity removal by phase truncation, high robustness could be achieved in this cryptosystem. ► In the decryption process the image without a separation and the two PMs used as keys for encryption are all treated as encoded data. ► In this cryptosystem the keys for encryption are different from those for decryption.