An Image Encryption Scheme based on the 2D Hybrid Hyperchaotic Modified Lemniscate Map

Abstract

Secure image transmission is critical in today’s digital landscape. Chaotic systems, renowned for their sensitivity to initial conditions and randomness, are widely applied in encryption schemes but often encounter limitations such as weak chaos and predictable structures. To address these challenges, this paper proposes a novel image encryption scheme based on a 2D Hybrid Hyperchaotic Modified Lemniscate (2D-HHML) map. The enhanced 2D-HHML map demonstrates superior chaotic properties, evidenced by a higher maximum Lyapunov exponent of 17.350 and increased sample entropy compared to conventional chaotic maps, indicating stronger randomness and unpredictability. The encryption framework integrates a selective pixel-shuffling strategy, which disrupts the spatial relationships between adjacent pixels, and a pixel-wise diffusion process, which further enhances security by masking statistical patterns in the encrypted image. The security and performance of the proposed scheme are rigorously evaluated through multiple statistical metrics, including NPCR, UACI, Shannon entropy, correlation coefficients, encryption time, and key sensitivity. Simulation results show that the scheme achieves an average NPCR of 99.6% and an average UACI of 33.39%, with Shannon entropy values approaching the ideal value of 8, low correlation coefficients close to zero, and efficient encryption times. Additionally, resistance against various differential and statistical attacks is validated through simulated attack analyses. Overall, the results confirm that the proposed encryption method provides high security, strong key sensitivity, and excellent performance, making it a promising candidate for secure transmission of sensitive image data.