Verifiable Multi-use Multi-secret Sharing Scheme on Monotone Span Program

Abstract

Based on the monotone span program, this paper proposes a verifiable multi-secret sharing scheme on the general access structure. Each participant can choose their own secret share and use the RSA cryptosystem to send the share to the dealer through open channels. In the secret recovery phase, the scheme uses the Hash Function to achieve multi-use property and verifiability. Analysis shows that each participant can recover multiple secrets by keeping only one secret share, and shares do not need to be changed when the multi-secrets are renewed. Furthermore, the distribution of secret shares in the scheme does not require a secure channel, which effectively reduces the computational cost of the system. Compared with the (t, n) threshold secret sharing, the scheme has more vivid access structures.