An Online Verifiable and Detectable (t, n) Multi-secret Sharing Scheme Based on a Hyperelliptic Function

摘要

In 1979, secret sharing schemes was proposed by Blakley and Shamir to distribute a secret among n participants in such a way that only qualified subsets of participants can recover the secret. In 1905. Wu and He proposed a (t, n,)-threshold scheme for sharing a secret based on a hyperspherical function (HS-TS). HS-TS gives a practical algorithm to solve the problem of dividing the secret into n shadows efficiently. However, in HS-TS, the dealer must send new shares to each participant when the dealer shares a new secret. In addition, participants cannot verify the shares and detect the cheater. Hance. Juan, Chuang and Li propose a new online verifiable and detectable (t. n) multi-secret sharing scheme based on HS-TS (OVDHS-TS) in 2007. In OVDHS-TS, The dealer need not redistribute fresh secret shares to every participant for- next secret sharing session. However, participants can verify the shares and detect the cheater. In order- to reduce the computation cost of the each participant to enhance OVDHS-TS, a new online verifiable1 and detectable (t.n) multi-secret sharing scheme based on a hypeielliptic function (called OVDHE-TS) is proposed in this paper. Further, OVDHE-TS are more practical and efficient than OVDHS-TS.