Dynamics Data Encryption Based on Chaotic Functions and Elliptic Curves: Application to Text Data

Abstract

Background: Given the vast amount of data generated daily on the Internet, numerous cryptosystems have been developed to ensure data confidentiality using symmetric, asymmetric, or hybrid encryption techniques. However, many of these systems suffer from limitations such as slow execution times and large key sizes. Objective: This paper presents a novel cryptosystem for text data encryption that integrates elliptic curve cryptography with chaotic functions to enhance data confidentiality and security. Methods: The proposed system utilizes elliptic curve points and pseudo-random numbers generated from a hybrid chaotic map (a fusion of the logistic map, sine map, and piecewise linear chaotic map) to derive short key sizes. Various analyses, including frequency histograms, correlation coefficients, and key sensitivity tests, are conducted to demonstrate the system’s robustness and reliability. Results: The analyses confirm that the fusion of chaotic functions makes the system highly sensitive to initial conditions, thus providing strong protection against unauthorized access. Conclusions: By integrating elliptic curve cryptography with chaotic functions, the proposed cryptosystem effectively addresses the limitations of existing systems, offering enhanced data confidentiality and security through the use of short key sizes and strong sensitivity to initial conditions.

Keywords

• Elliptic curve cryptography
• Chaotic functions
• Data encryption
• Hybrid cryptosystems
• Key sensitivity analysis