VSIS-RDPA: Verifiable Secret Image Sharing Based on Polynomial Interpolation for Resisting Dishonest Participant Attacks

To ensure the authenticity and validity of Secret Image Sharing (SIS) schemes, Verifiable Secret Image Sharing (VSIS) methods have been proposed. However, existing VSIS schemes are vulnerable to attacks from Dishonest Participant (DP). The dishonest participants may still access k-1 valid shares when they are identified, enabling them to recover the secret image. To address this issue, a VSIS based on polynomial interpolation for resisting Dishonest Participant Attacks (VSIS-RDPA) is proposed. Unlike traditional SIS schemes, where secret pixels are used as polynomial coefficients, our scheme treats secret pixel values as function values of the polynomial. On the contrary, the secret key and secret pixel values serve as inputs to reconstruct a k-2-degree polynomial using Lagrange interpolation, enhancing security against malicious participants. Authentication parameters generated by a hash function are combined with the k-2-degree polynomial to form a complete k-1-degree polynomial, which subsequently is utilized to generate shares. On the receiver end, the k-1-degree polynomial is first reconstructed, and the authentication parameters generated by the hash function are compared with those obtained from the reconstructed polynomial. If the two sets of values match, the authentication is successful, allowing for the recovery of the secret image. In addition, a modified authentication phase with ECC is also proposed to enhance the robustness of authentication. Experimental results and analysis demonstrate that the proposed schemes can resist DP attacks and ensure efficiency, verifiability, and security.