Fractional Dual Memristive Hyperchaotic Model for Tensor Based Color Image Encryption

This paper develops a color-image encryption architecture built around a five-dimensional commensurate fractional-order dual-memristive hyperchaotic generator, tensor-level bit-plane permutation, dynamic bijective substitution boxes, and bidirectional diffusion. The dynamical model uses a Caputo derivative and two cubic memductance functions. Its construction is analyzed through explicit equilibria, the Jacobian spectrum, trajectory-conditioned divergence, bifurcation samples, and a full-memory fractional variational calculation. At the nominal order q = 0.98, the Lyapunov spectrum is (2.468949,0.396196,−0.899348,−1.386471,−21.228103), giving two positive exponents and a Kaplan-Yorke dimension of 4.0273. The cryptographic design uses a fresh public nonce, a masked SHA-512 plaintext digest, and domain-separated HKDF outputs, so the receiver can derive every session key before decryption while the plaintext digest remains concealed. Standard color image experiments result in precise decryption, ciphertexts with nearly uniform histograms, entropy value close to eight bits per channel, adjacent pixel correlation being minimal, and end-to-end plaintext sensitivity.