基于双线性对的可公开验证多秘密共享方案

现有可公开验证多秘密共享方案只能由Lagrange插值多项式构造,且共享的秘密仅限于有限域或加法群。为解决上述问题,提出一个基于双线性对的可公开验证多秘密共享方案。该方案中每个参与者需持有2个秘密份额来重构多个秘密,并且在秘密分发的同时生成验证信息。任何人都可以通过公开的验证信息对秘密份额的有效性进行验证,及时检测分发者和参与者的欺骗行为。在秘密重构阶段采用Hermite插值定理重构秘密多项式,并结合双线性运算重构秘密。分析结果表明,在双线性Diffie-Hellman问题假设下,该方案能抵抗内外部攻击,具有较高的安全性。

Publicly Verifiable Multi-secret Sharing Scheme Based on Bilinear Pairings

In order to solve the problems that the previous publicly verifiable multi-secret sharing schemes can be constructed only by Lagrange interpolation polynomial and the shared secret is limited to the finite field or additive group,a publicly verifiable multi-secret sharing scheme based on bilinear pairings is proposed. In the scheme,each participant has to hold two shares for reconstructing multiple secrets,and the verification information is generated in the process of secret distribution. According to public verification information,anyone can verify the validity of secret shares.Cheating of dealer and participants can be detected in time. In the secret reconstructing process,Hermite interpolation theorem is used to reconstruct the secret polynomial,and bilinear operation is combined to reconstruct the secret. Under the assumptions of Bilinear Diffie-Hellman Problem（BDHP）,the analysis result shows that this scheme can resist internal and external attacks and is a secure and efficient multi-secret sharing scheme.