Generating Powerful Encryption Keys for Image Cryptography With Chaotic Maps by Incorporating Collatz Conjecture

Abstract

In recent years, the chaotic logistic map key (CLMK) has been widely used for image encryption due to its ability to generate random and unpredictable sequences of numbers. The CLMK algorithm uses the chaotic logistic map to generate a key stream, which is then used to encrypt the plaintext image. This study proposes an image encryption scheme based on CLMK, Collatz Conjecture, and indexing techniques; it uses a private key of a 15-digit size that is parsed in a novel way to generate a considerable keyspace reaches up to 297. The Collatz Conjecture generator is used to create variable length sequences that are used to generate the Chaotic parameters $r_{1}$ , $r_{2}$ , $x_{1}$ , and $x_{2}$ ; these parameters are used to create a 2D CLMK for encrypting each color channel and a 1D vector that is used for permeation, both confusion and diffusion are performed in four consecutive rounds to ensure the robustness of the proposed approach. The random sequences generated by the Collatz Conjecture were tested for randomness using the NIST benchmark randomness test suit, and they passed most tests. The proposed method is robust against all the well-known attacks, including differential attacks, white Gaussian noise attacks, Salt-and-pepper noise attacks, clipping attacks, occlusion attacks, and known plaintext attacks. Various experiments were conducted to evaluate the performance of the proposed method in terms of encryption time, throughput, and several image quality metrics. The results indicate that the proposed method is efficient regarding encryption time, and throughput enhancement can reach up to 3.34 times the state-of-the-art chaotic encryption methods.

Keywords

• Chaotic logistic map
• chaotic logistic map key
• chaotic parameter
• Collatz conjecture
• cryptography