On the Value of Order Number and Power in Secret Image Sharing

Shadow images generated from Shamir’s polynomial-based secret image sharing (SSIS) may leak the original secret image information, which causes a significant risk. The occurrence of this risk is closely related to the basis of secret image sharing, Shamir’s polynomial. Shamir’s polynomial plays an essential role in secret sharing, but there are relatively few studies on the power and order number of Shamir’s polynomial. In order to improve the security and effectiveness of SSIS, this paper mainly studies the utility of two parameters in Shamir’s polynomial, order number and power. Through the research of this kind of utility, the choice of order number and power can be given under different security requirements. In this process, an effective shadow image evaluation algorithm is proposed, which can measure the security of shadow images generated by SSIS. The user can understand the influence rule of the order number and power in SSIS, so that the user can choose the appropriate order number and power according to different security needs.