Dynamic and verifiable multi‐secret sharing scheme based on Hermite interpolation and bilinear maps

Abstract

(t, n) threshold secret sharing is a cryptographic mechanism to divide and disseminate information among n participants in a way that at least t(t ≤ n) of them should be present for the original data to be retrieved. This has practical applications in the protection of secure information against loss, destruction and theft. In this study, the authors propose a new multi-secret sharing scheme which is based on Hermite interpolation polynomials. Using the properties of discrete logarithm over elliptic curves and bilinear maps, they have created a verifiable scheme in which there is no need for a secure channel and every participant chooses their own share. This feature does not let the dealer cheat. The proposed method is dynamic to the changes in the number and value of the secrets as well as the threshold. In addition, it has the multi-use property which reduces the cost of secret distribution in multiple rounds of operation. The public values used in the proposed scheme are less than those of schemes providing similar features and the computations are also less complex. At the end of this study, they have compared the author's scheme with the similar ones against a comprehensive set of key features used in secret sharing.