A fully dynamic secret sharing scheme

Abstract

Based on the homogeneous linear recursive equation and the Elliptic curve cryptography (ECC), a fully dynamic secret sharing scheme is proposed for the general access structure of the participants. The participants choose their own shadows by themselves. When the shared secrets are updated, the access structure is changed, and other participants are added to or deleted from the existed group, but the shadow of each participant remains unchanged. Each participant should only maintain a shadow to share the multiple secrets. Compared with the existing popular dynamic schemes, the key construction of the proposed scheme is simpler and the proposed scheme has a completely dynamic characteristic, so that it has the potential to extend its practical application scenarios. That is, the proposed scheme can improve the performances of the key management and the distributed system. The security of the scheme is based on the Shamir threshold scheme, the computational Diffie–Hellman problem (CDHP) and the discrete logarithm problem (DLP).