A quantum reversible color-to-grayscale conversion scheme via image encryption based on true random numbers and two-dimensional quantum walks

Reversible Color-to-Grayscale Conversion (RCGC) is a method for converting color images to grayscale while retaining sufficient information to reconstruct the original color image when needed. This study proposes a Quantum RCGC (QRCGC) scheme that integrates quantum encryption techniques. The scheme first uses a finite number of true random numbers as seeds, which are then extended using a two-dimensional quantum walks system to generate sufficiently large random matrices for performing bitwise XOR operations with the original image. Subsequently, a quantum confusion technique is proposed, combining quantum block Arnold scrambling, cyclic shifts, and subsequence exchanges, which enhances the complexity of the relationship between the keys and the ciphertext in parallel. Additionally, a quantum diffusion technique is designed, efficiently generating hash values via a two-dimensional quantum walks system to verify image integrity. These hash values are used as content-based key inputs in a chaotic system to generate quantum secure matrices for diffusing the image information. Finally, a quantum bidirectional conversion operation is designed to achieve lossless reversible conversion between color and grayscale images. Experimental results show that the QRCGC scheme demonstrates significant advantages in terms of security, efficiency, and information retention.