A verifiable variable threshold visual image secret sharing scheme

This paper proposes a visual image encryption algorithm based on 2D compressive sensing and variable threshold secret sharing, aiming to achieve efficient, secure, and flexible image encryption and decryption. Firstly, the plain image is compressed and encrypted using the 2D compressive sensing technique, while the measurement matrix and disordered sequence are generated through an improved chaotic system. Secondly, the shadow image is produced using the variable threshold secret sharing scheme, and a corresponding authentication signature is generated to verify the integrity and authenticity of the shadow image. Finally, the shadow image and its signature are embedded into a carrier image to generate a cipher image with visual steganography. Experimental results demonstrate that the proposed algorithm achieves excellent performance in terms of operational efficiency, visual encryption quality, and decryption performance. The encryption execution time is 0.694 s, the PSNR of decrypted images is approximately 32 dB, and the PSNR of cipher images is around 42 dB, ensuring high visual concealment and reconstruction quality while maintaining security.