Color Image Encryption Using Elliptic Curve Cryptography and Chaotic Maps

Abstract

Background: The regular use of connected devices on the internet by users of social media generates a large quantity of multimedia data every second, and the data concerned may be of a variable nature, such as text data, color images, video, and audio. We can confirm that online security is becoming an area that is increasingly being explored by researchers around the world to guarantee and ensure the authenticity and confidentiality of exchanged data. Objective: The goal of this article is to introduce a new dynamic cryptosystem for encrypting color images, using elliptic curves and chaotic functions. Methods: This new system serves to generate the coefficients of the curve, create the encryption keys, and create the prime number of the curve. The new system utilizes the length of the encryption keys, which encompasses all points on the curve and relates to the discrete logarithm problem of elliptic curves, thereby justifying the difficulty in uncovering hidden information. Results: The results were obtained with the assistance of several analyses, including histogram analysis, correlation coefficient analysis, differential attack analysis, and key space analysis. The results obtained confirm the robustness and reliability of the proposed cryptographic system. Conclusions: By combining the two systems (elliptic curves and chaotic functions), we obtain a new hybrid system capable of operating with reduced encryption key lengths and random values, which makes our new system sensitive to initial conditions.