Σ-private private information retrieval protocols

We pose the definition ofΣ-private private information retrieval(PIR)protocol,and then construct a Σ-private PIR protocol based on verifiable secret sharing(VSS)scheme on general access structure.We also construct an efficient robustΣ-private PIR protocol based on robust multiplication protocol and the database is also secure.The corresponding communication complexity is dependent on the size of the access structure and is efficient for minority of servers.