Fast quantum image encryption scheme based on multilayer short memory fractional order Lotka-Volterra system and dual-scale triangular map

Abstract

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The Caputo fractional order Lotka-Volterra system is time-consuming in practical applications, since its starting point is fixed. To tackle this problem, a short memory fractional order Lotka-Volterra system (SMFrLVS) is proposed, where the chaotic attractor of the short memory fractional order Lotka-Volterra system is achieved by the predictor-corrector method. Then, a multilayer fractional order Lotka-Volterra system with short memory (MSMFrLVS) is introduced, whose chaotic behaviors are explored via Poincare sections and frequency power spectra. A quantum image encryption algorithm is proposed by combining MSMFrLVS with quantum dual-scale triangular map. A quantum circuit of the dual-scale triangular map is designed with ADDER-MOD2n. At the permutation stage, the plaintext image is transformed into quantum form with the generalized quantum image representation model. The resulting quantum image is divided into sub-blocks and scrambled by the quantum dual-scale triangular map. Subsequently, the intra and the inter permutation operations on bit-planes are realized by sorting pseudo-random sequence and by quantum Gray code, respectively. At the diffusion stage, the initial values of the MSMFrLVS are generated with a plaintext correlation mechanism. The ciphertext image can be acquired by carrying out three-level diffusion operations. It is demonstrated that the proposed quantum image encryption algorithm performs better than some typical image encryption algorithm in terms of security, robustness, computational complexity and encryption speed.

Keywords

• quantum image encryption
• fractional order differential equation
• Lotka-Volterra system
• predictor-corrector method
• quantum dual-scale triangular map