Abstract: This paper points out that there exists a private key leakage problem in Caifen Wang’s multi-message and multi-receiver hybrid signcryption scheme based on discrete logarithm. To get over this private key leakage problem, an improved ID-based multi-message and multi-receiver hybrid signcryption scheme is proposed by combining with bilinear pairing and identity-based key mechanism. The symmetry of bilinear pairing and identity-based key generation mechanism avoids the problem of key leakage in the original scheme. Finally, the confidentiality and unforgeability of the improved scheme has been proved on the basis of DBDH problem and CDH problem in the random oracle model.

Key words: signcryption, hybrid signcryption, multi-message, multi-receiver

摘要： 指出王彩芬等人的基于离散对数的多消息多接收者混合签密方案存在着密钥泄露问题。为了克服该私钥泄漏问题，结合双线性对和基于身份密钥机制提出了一个改进的多消息多接收者混合签密方案。利用双线性对的对称性和基于身份密钥机制的密钥生成方式避免了原方案中存在的密钥泄露问题。最后，基于DBDH难题和CDH难题，在随机预言机模型下证明了改进方案的机密性和不可伪造性。

关键词: 签密, 混合签密, 多消息, 多接收者