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Top1. Introduction
Recently, cloud storage has been paid wide attention for its mass storage capability and low cost (Li, Qiu, Qiu, Qiu & Zhao, 2016). However, the open application mode makes the security of cloud storage face severe challenges (Feng, Zhang, Zhang & Xu, 2011). How to protect the security of cloud storage has become an urgent problem to be resolved. Integrity verification is an important part of the data security. Multiple data copies are often used in the cloud storage to keep the reliability and availability. Dynamic operations are used to support data updating on the cloud platform. Thus, data integrity verification to support multiple data copies and dynamic operation is desirable. Currently, according to the implementation of fault-tolerance preprocessing or not, the existing data integrity verification mechanisms are classified into proof of retrievability (PoR) (Juels & Kaliski, 2007; Yan, 2013; Zhou, Li, Guo & Jia, 2014) and provable data possession (PDP) (Ateniese, Burns, Curtmola, Herring & Kissner, 2007; Erway, Küpçü, Papamanthou & Tamassia, 2009; Gritti, Susilo & Plantard, 2015; Curtmola, Khan, Burns & Ateniese, 2008; Barsoum & Hasan, 2010).
The remote data integrity verification is firstly realized by using HMAC hash function (Deswarte, Quisquater & Saïdane,2004). The MAC value of data is stored in local, and all the data is needed to retrieve from the root node to compute the MAC value during the validation. This mechanism needs a large computation cost and communication overhead; thus, it is cannot be applied to the integrity verification of mass data in cloud storage. After that, the conception of PDP is proposed (Ateniese, Burns, Curtmola, Herring & Kissner, 2007). Homomorphic veritable tags are used to inspect the sampled data in the cloud. It allows verifying data possession without having access to the actual data file, and it achieves a low overhead, but it does not support dynamic operation to the data. Thereafter, they proposed an improved scheme (Ateniese, Pietro, Mancini & Tsudik, 2008), but only modification and deletion can be performed, and it cannot support insertion. Erway et al. (Erway, Küpçü, Papamanthou & Tamassia, 2009) used the rank value of the authentication jump table to support the dynamic operation. Gritti et al. (Gritti, Susilo & Plantard, 2015) proposed a highly efficient scheme that supports dynamic authentication and protects user privacy. These schemes are only designed for the verification of a single copy of data.
In order to solve the problem of data integrity authentication for multiple copies, a MR-PDP (Multiple-Replica PDP) scheme is proposed by Curtmola et al. (Curtmola, Khan, Burns & Ateniese, 2008). It can quickly generate multiple copies and restore the damaged copies. Barsoum & Hasan (Barsoum & Hasan, 2010) put forward a multiple copies PDP scheme for static file, but this scheme only applies single copy PDP scheme to different copies, and the efficiency is low. Homomorphic linear authenticator was used to identify the multiple copies data (Ateniese, Kamara & Katz, 2009). Fu et al. (Fu, Zhang, Chen & Feng, 2014) proposed a proof of data possession scheme of multiple copies by taking the advantages of distributed computing ability of the multiple servers, and it can verify whether the servers hold the correct number of copies or not. However, full dynamic operations are not always supported in these schemes.