Functional encryption introduces a new paradigm of public key encryption that decryption only reveals the function value of encrypted data. To curb key leakage issues and trace users in FE-IP, a new primitive called traceable functional encryption for inner product (TFE-IP) has been proposed. However, the privacy protection of user's identities has not been considered in the existing TFE-IP schemes. In order to balance privacy and accountability, we propose the concept of privacy-preserving traceable functional encryption for inner product (PPTFE-IP) and give a concrete construction. Our scheme provides the following features: (1) To prevent key sharing, a user's key is bound with both his/her identity and a vector; (2) The key generation center (KGC) and a user execute a two-party secure computing protocol to generate a key without the former knowing anything about the latter's identity; (3) Each user can verify the correctness of his/her key; (4) A user can calculate the inner product of the two vectors embedded in his/her key and in a ciphertext; (5) Only the tracer can trace the identity embedded in a key. The security of our scheme is formally reduced to well-known complexity assumptions, and the implementation is conducted to evaluate its efficiency. The novelty of our scheme is to protect users' privacy and provide traceability if required.

翻译：功能加密引入了一种新的公钥加密范式，解密仅能揭示加密数据的函数值。为遏制FE-IP中的密钥泄露问题并实现用户追踪，研究者提出了可追踪内积功能加密（TFE-IP）这一新原语。然而，现有TFE-IP方案均未考虑用户身份的隐私保护。为平衡隐私与可问责性，我们提出了面向内积的隐私保护可追踪功能加密（PPTFE-IP）概念，并给出具体构造。我们的方案具有以下特性：（1）为防止密钥共享，用户密钥同时绑定其身份与向量；（2）密钥生成中心（KGC）与用户通过两方安全计算协议生成密钥，后者无需获知前者身份信息；（3）每个用户可验证其密钥的正确性；（4）用户可计算其密钥与密文中嵌入的两向量的内积；（5）仅追踪者能解密密钥中嵌入的身份信息。本方案的安全性可归约至公认的复杂性假设，并通过实验评估其效率。本方案的创新性在于保护用户隐私的同时，在需要时提供可追踪性。