Image Encryption Using Elliptic Curves and Rossby/Drift Wave Triads

Abstract

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.

arXiv commentAccepted and published version (Entropy 2020, 22, 454)

References in corpus (6)

• On the cryptanalysis of Fridrich's chaotic image encryption scheme
• Cryptanalyzing an Image-Scrambling Encryption Algorithm of Pixel Bits
• Modulational instability of Rossby and drift waves and generation of zonal jets
• Complete classification of discrete resonant Rossby/drift wave triads on periodic domains
• Percolation transition in the kinematics of nonlinear resonance broadening in Charney-Hasegawa-Mima model of Rossby wave turbulence
• Discrete resonant Rossby/drift wave triads: an explicit parameterisation and a fast direct numerical search algorithm