The purpose of this paper is to realize an authentication system which satisfies four requirements for security, privacy protection, and usability, that is, impersonation resistance against insiders, personalization, unlinkability in multi-service environment, and memory efficiency. The proposed system is the first system which satisfies all the properties. In the proposed system, transactions of a user within a single service can be linked (personalization), while transactions of a user among distinct services can not be linked (unlinkability in multi-service environment). The proposed system can be used with smart cards since the amount of memory required by the system does not depend on the number of services. First, this paper formalizes the property of unlinkability in multi-service environment, which has not been formalized in the literatures. Next, this paper extends an identification scheme with a pseudorandom function in order to realize an authentication system which satisfies all the requirements. This extension can be done with any identification scheme and any pseudorandom function. Finally, this paper shows an implementation with the Schnorr identification scheme and a collision-free hash function as an example of the proposed systems.