Privacy-Preserving Public Auditing Scheme for Shared Data with Supporting Multi-function

most common concerns for users in cloud storage are data integrity, confidentiality and availability, so various data integrity auditing schemes for cloud storage have been proposed in the past few years, some of which achieve privacy-preserving public auditing, data sharing and group dynamic, or support data dynamic. However, as far as we know, until now yet there doesn't exist a practical auditing scheme which can simultaneously realize all the functions above; In addition, in all the existing schemes, Block Authentication Tag (BAT) is adopted by data owner to achieve data integrity auditing; nevertheless, it's a arduous task to compute BATs for the resource-constrained data owner. In this paper, we propose a novel privacy-preserving public auditing scheme for shared data in the cloud, which can also support data dynamic operations and group dynamic. Our scheme has the following advantages:(1) we introduce proxy signature into the existing auditing scheme to reduce the cloud user's computation burden; (2) by introducing a Lagrange interpolating polynomial, our scheme realizes the identity's privacy-preserving without increasing computation cost and communication overhead, moreover it makes group dynamic simple;(3) it can realize the practical and secure dynamic operations of shared data bycombining the Merkle Hash Tree and index-switch table which is built by us; (4) to protect the data privacy and resist the active attack, the cloud storage server hides the actual proof information by inserting its private key in producing proof information process. Theoretical analysis demonstrates our scheme's security.