Symmetric Cipher for Grayscale Images Based on Quantum Differential Geometry

The increase in information technologies has generated the need to implement new methodologies to secure the exchange of information. This paper proposes a cryptographic algorithm based on the use of quantum differential geometry operators. These operators exhibit mathematical behaviors similar to quantum behavior, with the advantage that specialized equipment is not required to perform the encryption process. The algorithm is composed of two phases: In the first phase, a subkey is generated through an addition and multiplication process in Z_16 based on a user-defined key. In the second phase, three types of fundamental quantum operators are employed: creation, annihilation, and crossing, which are sequentially connected. The specific selection and configuration of these operators are based on their ability to avoid generating correlation between the data. The method proposed in this work is implemented using grayscale images, obtaining the Peak Signal-to-Noise Ratio (PSNR), the Structural Similarity Index Measure (SSIM), and the Correlation Value, in order to evaluate the fidelity and integrity of the recovered images.