A novel approach for silhouette-free image encryption based on interference is proposed using discrete multiple-parameter fractional Fourier transform (DMPFrFT), which generalizes from fractional Fourier transform. An original image is firstly applied by chaotic pixel scrambling (CPS) and then encoded into the real part of a complex signal. Using interference principle, the complex signal generates three phase-only masks in DMPFrFT domain. The silhouette of the original image cannot be extracted using one or two of the three phase-only masks. The parameters of both CPS and DMPFrFT can also serve as encryption keys to extend the key space, which further enhance the level of cryptosystem security. Numerical simulations are demonstrated to show the feasibility and validity of this approach.

Silhouette-free image encryption using interference in the multiple-parameter fractional Fourier transform domain.

In recent years, several special multiple-parameter discrete fractional transforms (MPDFRTs) have been proposed, and their advantages have been demonstrated in the fields of communication systems and information security. However, the general theoretical framework of MPDFRTs has not yet been established. In this paper, we propose two separate theoretical frameworks called the type I and II MPDFRT that can include existing multiple-parameter transforms as special cases. The properties of the type I and II MPDFRT have been analyzed in detail and their high-dimensional operators have been defined. Under the theoretical frameworks, we can construct new types of transforms that may be useful in signal processing and information security. Finally, we perform two applications about image encryption and image feature extraction in the type I and II MPDFRT domain. The simulation results demonstrate that the typical transforms constructed under the proposed theoretical frameworks yield promising results in these applications.

Multiple-Parameter Discrete Fractional Transform and its Applications

A Comprehensive Survey on Fractional Fourier Transform

We present for the first time an optical encrypting–decrypting protocol for recovering messages without speckle noise. This is a digital holographic technique using a 2f scheme to process QR codes entries. In the procedure, letters used to compose eventual messages are individually converted into a QR code, and then each QR code is divided into portions. Through a holographic technique, we store each processed portion. After filtering and repositioning, we add all processed data to create a single pack, thus simplifying the handling and recovery of multiple QR code images, representing the first multiplexing procedure applied to processed QR codes. All QR codes are recovered in a single step and in the same plane, showing neither cross-talk nor noise problems as in other methods. Experiments have been conducted using an interferometric configuration and comparisons between unprocessed and recovered QR codes have been performed, showing differences between them due to the involved processing. Recovered QR codes can be successfully scanned, thanks to their noise tolerance. Finally, the appropriate sequence in the scanning of the recovered QR codes brings a noiseless retrieved message. Additionally, to procure maximum security, the multiplexed pack could be multiplied by a digital diffuser as to encrypt it. The encrypted pack is easily decoded by multiplying the multiplexing with the complex conjugate of the diffuser. As it is a digital operation, no noise is added. Therefore, this technique is threefold robust, involving multiplexing, encryption, and the need of a sequence to retrieve the outcome.

https://iopscience.iop.org/article/10.1088/2040-8978/17/8/085702/pdf

Optimized and secure technique for multiplexing QR code images of single characters: application to noiseless messages retrieval

Multiple-image encryption using spectral cropping and spatial multiplexing

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method.

https://iopscience.iop.org/article/10.1088/2040-8978/16/12/125404/pdf

Yujie Zhang

Papers

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform