Hybrid Group Signcryption Scheme Based on Heterogeneous Cryptosystem
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摘要:
群组签密既能实现群组签名，又能实现群组加密，但是现有的群组签密方案的发送者和接收者基本上在同一个密码系统中，不能满足现实环境的需求，而且基本上采用的是公钥加密技术，公钥加密技术在加密长消息时效率较低。因此该文提出由基于身份的密码体制(IBC)到无证书密码体制(CLC)的异构密码系统的混合群组签密方案。在该方案中，私钥生成器(PKG)和密钥生成中心(KGC)能够分别在IBC密码体制和CLC密码体制中产生自己的系统主密钥；而且群组成员只有协作才能解签密，提高了方案的安全性；同时在无需更换群组公钥和其他成员私钥的情况下，用户可以动态地加入该群组。所提方案采用了混合签密，具有可加密任意长消息的能力。在随机预言模型下，证明了该文方案在计算Diffie-hellman困难问题下具有保密性和不可伪造性。通过理论和数值实验分析表明该方案具有更高的效率和可行性。
Abstract:Group signcryption is a cryptosystem which can realize group signature and group encryption. However, the message sender and receiver of existing group signcryption schemes are basically in the same cryptosystem, which does not meet the needs of the real environment and the public key encryption technology is basically used, public key encryption technology in encrypted long message efficiency is too low. Therefore, this paper proposes a hybrid group signcryption scheme based on heterogeneous cryptosystem from Identity-Based Cryptosystem (IBC) to CertificateLess Cryptosystem (CLC). In the scheme, The Private Key Generator (PKG) in the IBC cryptosystem and Key Generation Center (KGC) in the CLC cryptosystem generate their own system master keys, and group members can only solve signcryption through collaboration, which improves the security of the scheme. Meanwhile, the user can dynamically join the group without changing the group public key and other members’ private key. The scheme uses hybrid signcryption and has the ability to encrypt any long message. It is proved that the scheme satisfies confidentiality and unforgeability in computing the Diffie-hellman hard problem in the random oracle model. Theoretical and numerical analysis shows that the scheme is more efficient and feasible.
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表 1 效率分析
方案 签密阶段运算量 解签密阶段运算量 签密密文长度 文献[13] $(2{n^2} + 7n + 3){P_M} + 3{P_H}$ $({n^2} + n + 3){P_M} + 3{P_H}$ $2|{G_1}| + 3|{{Z}}_q^*|$ 文献[15] $(2{n^2} + 3n + 2){P_M} + 3{P_H}$ $({n^2} + n + 2){P_M} + 3{P_H}$ $|{G_1}| + 3|{{Z}}_q^*|$ 本文 $(2n + 7){P_M} + 4{P_H}$ $(2n + 5){P_M} + 3{P_H}$ $|{G_1}| + 4|{{Z}}_q^*|$ 
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表 2 本文方案计算时间(s)
n 100 200 300 400 500 600 700 800 900 1000 签密时间 1.1861 2.3375 3.6016 4.7899 5.9708 7.1283 8.1671 9.5163 10.7285 11.8963 解签密时间 1.4792 1.5774 1.7442 1.8645 1.8991 1.9001 2.1469 2.3773 2.4658 2.5549
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