A card-gameplay-inspired color image encryption scheme driven by novel 2D hyperchaotic map

Abstract Color images, due to their rich information-carrying capacity, have become the mainstream in various visual applications. However, their large data volume and strong inter-channel correlations pose significant challenges for secure encryption. To address this issue, this paper proposes a novel hyperchaotic system named the 2D cross-embedded Cubic-Logistic map (2D-CECLM), which exhibits a wide chaotic parameter range with minimal periodic windows. Its stable hyperchaotic behavior is rigorously validated through analyses including phase trajectories, bifurcation diagrams, Lyapunov exponents, sample entropy, permutation entropy, the 0-1 test, and the NIST SP800-22 randomness test, confirming its suitability for image encryption. Based on 2D-CECLM, we further develop an encryption scheme involving shuffle permutation and turn-based diffusion for color images, inspired by the full process of card gameplay. The scheme seeds 2D-CECLM with a secret key and image-derived parameters to generate keystreams, applies permutation, and then executes multi-round plaintext-related diffusion with feedback. Inter-crossing and extraction shuffling disturb pixel positions, and the Deal-Bet-Showdown stages implement the diffusion rounds via nonlinear pixel transformations in a turn-based dueling framework. Simulations show the scheme achieves an average NPCR of 99.6091%, UACI of 33.4702%, information entropy of 7.9993, adjacent-pixel correlation close to zero, a key space that exceeds 2 512 , and an average encryption time of 1.2330s per 512 × 512 image, confirming robust attack resistance and practical efficiency for image encryption.