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Participants Increasing for Shamir’s Polynomial-Based Secret Image Sharing Scheme

In Shamir's polynomial-based secret sharing scheme, a secret image is generated into n shadow images and distributed to n associated participants. The secret image can be recovered by collecting any k or more shadow images. Unfortunately, the previous Shamir's scheme neglected the situation of participants increasing. However, in some applications, some new shadow images need to be generated because some new participants join in the secret sharing. In this paper, we consider a new participant increasing issue as well as propose a participant increasing method only from the n original shadow images generated by previous Shamir'spolynomial-based scheme. Without knowing the original secret image, a new shadow image can be obtained from the original n shadow images. As a result, the Shamir's polynomial-based (n, n) threshold scheme is extended to a (n, n + 1) threshold scheme. Theoretical analysis and experiments are conducted to evaluate the security and efficiency of the proposed scheme.