Quantum Image Encryption Based on Iterative Framework of Frequency-Spatial Domain Transforms

A novel quantum image encryption and decryption algorithm based on iteration framework of frequency-spatial domain transforms is proposed. In this paper, the images are represented in the flexible representation for quantum images (FRQI). Previous quantum image encryption algorithms are realized by spatial domain transform to scramble the position information of original images and frequency domain transform to encode the color information of images. But there are some problems such as the periodicity of spatial domain transform, which will make it easy to recover the original images. Hence, we present the iterative framework of frequency-spatial domain transforms. Based on the iterative framework, the novel encryption algorithm uses Fibonacci transform and geometric transform for many times to scramble the position information of the original images and double random-phase encoding to encode the color information of the images. The encryption keys include the iterative time t of the Fibonacci transform, the iterative time l of the geometric transform, the geometric transform matrix G i which is n × n matrix, the classical binary sequences K (\(k_{0}k_{1}{\ldots } k_{2^{2n}-1}\)) and \(D(d_{0}d_{1}{\ldots } d_{2^{2n}-1}\)). Here the key space of Fibonacci transform and geometric transform are both estimated to be 2²⁶. The key space of binary sequences is (2 ^n×n ) × (2 ^n×n ). Then the key space of the entire algorithm is about \(2^{2{n^{2}}+52}\). Since all quantum operations are invertible, the quantum image decryption algorithm is the inverse of the encryption algorithm. The results of numerical simulation and analysis indicate that the proposed algorithm has high security and high sensitivity.