中文摘要：

基于拉格朗日插值多项式并利用超椭圆曲线离散对数问题的难解性,提出一个新的基于HECC的门限秘密共享方案。该方案通过共享者对子秘密的验证可以防止子秘密分发中心对共享者的欺诈行为和共享者之间的欺诈行为,又由于超椭圆曲线离散对数问题的难解性确保攻击者无法从公开信息中获取子秘密。相比现有的基于椭圆曲线密码体制的门限秘密共享方案,该方案具有较小的通信代价和较高的安全性。

英文摘要：

Based on the Lagrange interpolation polynomial and Hyperel iptic Curve Discrete Logarithm Problem（HECDLP）, a new secret sharing threshold scheme is present. In the scheme, the sharer verify the sub-secrets to prevent fraudulent conduct by the Distribution Center to sharer, and prevent the fraud behavior between the sharers. Because of the intractability of Hyperel iptic Curve Discrete Logarithm Problem ensures that the attacker can＇t obtain sub-secret from the public information. Compared with the existing secret sharing threshold scheme based on the Ellipse Curve Discrete Logarithm Problem, this scheme has lower communication cost and higher security.