Using the Logistic Coupled Map for Public Key Cryptography under a Distributed Dynamics Encryption Scheme

Abstract

Nowadays, there is a high necessity to create new and robust cryptosystems. Dynamical systems have promised to develop crypto-systems due to the close relationship between them and the cryptographic requirements. Distributed dynamic encryption (DDE) represents the first mathematical method to generate a public-key cryptosystem based on chaotic dynamics. However, it has been described that the DDE proposal has a weak point in the decryption process related to efficiency and practicality. In this work, we adapted the DDE to a low-dimensional chaotic system to evaluate the weakness and security of the adaption in a realistic example. Specifically, we used a non-symmetric logistic coupled map, which is known to have multiple chaotic attractors improving the shortcomings related to the simple logistic map that manifests its inadequacy for cryptographic applications. We found a full implementation with acceptable computational cost and speed for DDE, which it is essential because it provides a key cryptographic requirement for chaos-based cryptosystems.

Keywords

• public key encryption
• cryptography
• chaos
• chaotic cryptography
• logistic map
• logistic coupled map