Progressive secret image sharing based on Boolean operations and polynomial interpolations

With the expansion of network bandwidth and the rise of social networks, image sharing on open networks has become a trend. The ensuing privacy leakage events have aroused widespread concerns. Therefore, image sharing that protects privacy is desired. Progressive Secret Image Sharing (PSIS), a multilevel privacy protection technology for images, offers a promising solution. However, the progressivity of the majority of PSIS schemes depends on the preprocessing of a secret image, which increases the calculation costs. In addition, a block-based PSIS may have information leakage security risks when processing highly confidential images. Many existing PSIS schemes use a single operation to share secret images, which makes the schemes inflexible and limits the application scenarios. Therefore, we propose a PSIS based on Boolean operations and Polynomial interpolations (PSIS-BP). The proposed scheme divides the bit-plane of the pixel into two parts. One part is utilized to perform the Boolean operation, and the other part is used to perform the polynomial interpolation. Different assignment strategies can produce different progressive reconstruction levels and expand the application scenarios of the scheme. Theoretical analyses and experimental results demonstrate that the proposed scheme is secure, low-cost, and flexible.