An encryption protocol for NEQR images based on one-particle quantum walks on a circle

Quantum walks are generalizations of random walks that have extensive applications in various fields including cryptography, quantum algorithms, and quantum networking. Discrete quantum walks can be seen as nonlinear mappings between quantum states and position probability distributions, and this mathematical property may be thought of as an imprint of chaotic behavior and consequently used to generate encryption keys. In this paper, we introduce encryption and decryption algorithms for NEQR images based on discrete quantum walks on a circle. We present full quantum circuits of proposed encryption and decryption algorithms together with digital computer simulations of most common attacks on encrypted images. Our numerical results show that our quantum image encryption and decryption scheme has high efficiency and high security with high large key space.