中文摘要：

在基于身份的公钥密码体制中PKG负责生成用户密钥，对PKG的信任级别过高，存在密钥托管问题．人们为解决此问题提出了很多方案但均有一定缺陷．Goyal提出了一种解决这类问题的新思路．基于该思路，提出了两种降低对私钥生成中心的信任级别的门限密码体制．在这两个体制中，利用了Goyal提出的基于身份的可追踪公钥加密体制的思想与公开可验证加密技术，有效解决了在基于身份的门限加密体制中，PKG对同一用户恶意生成多个私钥的追踪问题．对降低PKG信任级的基于身份的门限密码体制进行了形式化定义，并在所定义的形式化安全模型下证明了这两个方案可以对抗门限自适应选择密文攻击、密钥寻找攻击以及计算新密钥攻击．

英文摘要：

In the traditional identity based cryptosystems, since private key generator （PKG） is able to compute the private key corresponding to any identity, the malicious activities of PKG would be hard to find, which restricts the use of identity based cryptosystems. People have employed multiple PKGs to solve this problem. However it brings other problems. In this paper, two identity based threshold cryptosystems are proposed, which reduce the trust in PKG. The traceable identity based encryption technique suggested by Goyal is used, which successfully restricts the potential misbehaviors of PKG, and the idea of public verifiable encryption which is widely used in the threshold cryptosystems to achieve distributed decryption. These two schemes solve the malicious PKG tracing problem effectively, and if PKG generates more than one private key to a single user, the misbehavior could be detected with evidence. We define the formal model of identity based threshold cryptosystem with reduced trust in PKG. We also prove the two schemes＇ security against the adaptive chosen ciphertext attack, the find key attack and the compute new key attack under the formal security model. The result shows that their security is based on the truncated augmented bilinear Diffie-Hellman exponent assumption.