Image Encryption Using Elliptic Curves and Rossby/Drift Wave Triads
This work addresses image security for applications like data protection, but it appears incremental as it builds on existing encryption methods with new mathematical constructs.
The paper tackles image encryption by proposing a scheme using quasi-resonant Rossby/drift wave triads and Mordell elliptic curves to generate pseudo-random numbers and dynamic substitution boxes for diffusion and confusion, achieving high security and outperforming other popular schemes in tests on the USC-SIPI image database.
We propose an image encryption scheme based on quasi-resonant Rossby/drift wave triads (related to elliptic surfaces) and Mordell elliptic curves (MECs). By defining a total order on quasi-resonant triads, at a first stage we construct quasi-resonant triads using auxiliary parameters of elliptic surfaces in order to generate pseudo-random numbers. At a second stage, we employ an MEC to construct a dynamic substitution box (S-box) for the plain image. The generated pseudo-random numbers and S-box are used to provide diffusion and confusion, respectively, in the tested image. We test the proposed scheme against well-known attacks by encrypting all gray images taken from the USC-SIPI image database. Our experimental results indicate the high security of the newly developed scheme. Finally, via extensive comparisons we show that the new scheme outperforms other popular schemes.