Secure Image Encryption Based on a Novel 2D Chaotic Map and Four-Phase Scrambling
Shalini Gupta, Nitish, Anand Nayyar · 2026
Chaos-based encryption has emerged as a powerful tool for securing digital images due to its inherent properties of sensitivity to initial conditions and pseudo-randomness. Despite their potential, many existing algorithms suffer from limited complexity and key diversity because they rely on traditional one-dimensional chaotic maps. To address these limitations, this chapter proposes a novel image encryption algorithm (NIEA) based on a newly designed two-dimensional coupled chaotic map capable of generating multiple high-entropy, uncorrelated chaotic sequences. The NIEA incorporates a four-stage encryption framework comprising pixel permutation, to disrupt spatial correlations; DNA-based encoding, to introduce biologically inspired nonlinear transformations; pixel diffusion, to propagate changes across the image and amplify the avalanche effect; and bit-level reversion, to enhance entropy and eliminate residual patterns. Each stage is driven by a distinct chaotic sequence derived from a key-generation process that integrates SHA-256 hashing of the image and a secret external key, ensuring strong key sensitivity and resistance against known-plaintext and chosen-plaintext attacks. Experimental results confirm that the proposed NIEA achieves strong cryptographic performance, with measured entropy values approaching the theoretical maximum (7.9998), a high number of pixel change rate of 99.61% and a unified average changing intensity of 33.40%, indicating excellent sensitivity to plaintext changes. The encryption also results in extremely low correlation coefficients across all spatial directions (−0.0012, −0.00019, 0.0010), effectively eliminating pixel-level redundancies. With an expansive key space of https://www.w3.org/1998/Math/MathML" display="inline"> 2 655 , the NIEA offers robust protection against brute-force attacks. The algorithm successfully passes both the chi-square uniformity test and the NIST SP 800-22 randomness test suite, affirming the statistical unpredictability of the ciphertext. Additionally, robustness tests performed under common noise scenarios, such as salt-and-pepper noise, show that the NIEA maintains decryption fidelity even in the presence of transmission errors or data corruption. When benchmarked against other advanced image encryption methods, NIEA not only achieves superior security metrics but also delivers efficient encryption performance.