A threshold secret-sharing scheme for multiple quantum images based on a hybrid two-layer access structure

To address the lack of differentiated access control between master-key shares and image shares in existing multiple quantum image secret-sharing schemes, as well as the increase in the color-register width of an individual quantum image with the number of secret images, this paper presents a hybrid two-layer secret-sharing design integrating established threshold-sharing techniques with block-based novel enhanced quantum representation (NEQR) encoding. First, key-derived images and a cyclic XOR structure are used to establish associations among multiple secret images, while an anchor image is introduced to enable recursive reconstruction and closed-loop consistency verification. Shamir threshold sharing is then applied separately to the master key and the image information, forming a role-separated two-layer access structure. Furthermore, complete finite-field shares are partitioned into blocks and prepared as quantum images using the NEQR model, thereby reducing the register size of each individual quantum image. Simulation results show that the secret images can be correctly reconstructed only when the authorized participant set simultaneously satisfies both threshold conditions. The resulting block quantum images effectively conceal the visual and statistical characteristics of the original images, while the scheme provides flexible access control with a reasonable trade-off in quantum resource overhead.