In P2P network, the existing researches focus on protecting the security of information transmission, or ensuring users privacy. Security certification is a basic demand of P2P network, including the general authenticity, credibility, integrity and so on. Privacy protection for transactions is the high-level requirement of security, including confidentiality, copyright management, access control. One-sided pursuit of certification will affect the privacy rights of users while one-sided pursuit of anonymous will bring a series of anonymous abuse problems. However, little research has paid attention to urgency of this dilemma, leading to the emergence of a large number of problems in the applications. This study presents an anonymous authentication scheme based on homomorphic encryption, called FHET (Fully homomorphic encryption trust). FHET makes use of trust certificates and can also be combined with existing P2P reputation system which effectively prevents the selfish behavior of peers and ensures scalability, portability and practicality.