# A robust color image encryption algorithm based on 2D-SQSM hyperchaotic map and cyclic shift scrambling

## TL;DR

This paper introduces a new image encryption algorithm using a simplified chaotic map and techniques to enhance security and randomness in encrypted images.

## Contribution

A novel 2D-SQSM hyperchaotic map is proposed, offering better chaos performance with a simpler structure than existing maps.

## Key findings

- The 2D-SQSM map shows high Lyapunov exponents and superior chaotic characteristics compared to recent chaotic maps.
- The proposed encryption algorithm significantly reduces pixel correlation and enhances resistance to various attacks.
- Simulation results confirm the algorithm's strong statistical properties and suitability for secure image transmission.

## Abstract

This paper proposes a structurally simplified 2D quadratic sine map (2D-SQSM). This map effectively addresses the insufficient chaos performance of traditional chaotic maps while avoiding the overly complex structures of emerging chaotic maps. Evaluated using multiple chaos performance metrics, the 2D-SQSM demonstrates high Lyapunov exponents, and sample entropy, with chaotic characteristics superior to some advanced chaotic maps proposed in recent years. Based on the 2D-SQSM, this paper further designs a highly robust color image encryption algorithm. First, by introducing different hash functions multiple times, the correlation between the key and plaintext is enhanced, significantly improving resistance against brute-force attacks; second, cyclic shifting and segmentation-recombination operations are applied separately to the three RGB channels to effectively disrupt pixel distribution and significantly reduce spatial correlation between pixels; finally, the chaotic sequence generated by the 2D-SQSM is utilized for XOR diffusion, further enhancing the randomness and diffusion capability of the ciphertext. A large number of simulation results demonstrate that this algorithm can significantly enhance the image information entropy, and can effectively reduce pixel correlation, possessing good statistical properties. Furthermore, it is robust against differential attacks, noise attacks, cropping attacks, chosen plaintext attacks, etc., and is suitable for secure image transmission.