Symmetric Grayscale Image Encryption Based on Quantum Operators with Dynamic Matrices

Luis Olvera-Martinez, Manuel Cedillo-Hernandez (), Carlos Adolfo Diaz-Rodriguez, Leonardo Faustinos-Morales, Antonio Cedillo-Hernandez and Francisco Javier Garcia-Ugalde
Additional contact information
Luis Olvera-Martinez: Instituto Politecnico Nacional, Escuela Superior de Ingenieria Mecanica y Electrica Unidad Culhuacan, Avenida Santa Ana 1000, San Francisco Culhuacan, Culhuacan CTM V, Coyoacan, Ciudad de Mexico CP 04440, Mexico
Manuel Cedillo-Hernandez: Instituto Politecnico Nacional, Escuela Superior de Ingenieria Mecanica y Electrica Unidad Culhuacan, Avenida Santa Ana 1000, San Francisco Culhuacan, Culhuacan CTM V, Coyoacan, Ciudad de Mexico CP 04440, Mexico
Carlos Adolfo Diaz-Rodriguez: Independent Researcher, Ciudad de Mexico CP 04440, Mexico
Leonardo Faustinos-Morales: Independent Researcher, Ciudad de Mexico CP 04440, Mexico
Antonio Cedillo-Hernandez: Escuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501, Monterrey CP 64849, Mexico
Francisco Javier Garcia-Ugalde: Facultad de Ingenieria, Universidad Nacional Autonoma de Mexico (UNAM), Av. Universidad No. 3000, Ciudad Universitaria, Coyoacan, Ciudad de Mexico CP 04510, Mexico

Mathematics, 2025, vol. 13, issue 6, 1-19

Abstract: Image encryption is crucial for ensuring the confidentiality and integrity of digital images, preventing unauthorized access and alterations. However, existing encryption algorithms often involve complex mathematical operations or require specialized hardware, which limits their efficiency and practicality. To address these challenges, we propose a novel image encryption scheme based on the emulation of fundamental quantum operators from a multi-braided quantum group in the sense of Durdevich. These operators—coproduct, product, and braiding—are derived from quantum differential geometry and enable the dynamic generation of encryption values, avoiding the need for computationally intensive processes. Unlike quantum encryption methods that rely on physical quantum hardware, our approach simulates quantum behavior through classical computation, enhancing accessibility and efficiency. The proposed method is applied to grayscale images with 8-, 10-, and 12-bit depth per pixel. To validate its effectiveness, we conducted extensive experiments, including visual quality metrics (PSNR, SSIM), randomness evaluation using NIST 800-22, entropy and correlation analysis, key sensitivity tests, and execution time measurements. Additionally, comparative tests against AES encryption demonstrate the advantages of our approach in terms of performance and security. The results show that the proposed method provides a high level of security while maintaining computational efficiency.

Keywords: braided quantum groups; quantum operators; image encryption; finite fields; security analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/6/982/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/6/982/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:6:p:982-:d:1614219

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().