Abstract-In cloud computing, data owners host their data on cloud servers and users (data consumers) can access the data from cloud servers. Due to the data outsourcing, however, this new paradigm of data hosting service also introduces new security challenges, which requires an independent auditing service to check the data integrity in the cloud. Some existing remote integrity checking methods can only serve for static archive data and thus cannot be applied to the auditing service since the data in the cloud can be dynamically updated. Thus, an efficient and secure dynamic auditing protocol is desired to convince data owners that the data are correctly stored in the cloud. In this paper, we first design an auditing framework for cloud storage systems and propose an efficient and privacy-preserving auditing protocol. Then, we extend our auditing protocol to support the data dynamic operations, which is efficient and provably secure in the random oracle model. We further extend our auditing protocol to support batch auditing for both multiple owners and multiple clouds, without using any trusted organizer. The analysis and simulation results show that our proposed auditing protocols are secure and efficient, especially it reduce the computation cost of the auditor.

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Garnet peridotites occur as lenses, blocks or layers within granulite–amphibolite facies gneiss in the Dabie‐Sulu ultra‐high‐pressure (UHP) terrane and contain coesite‐bearing eclogite. Two distinct types of garnet peridotite were identified based on mode of occurrence and petrochemical characteristics. Type A mantle‐derived peridotites originated from either: (1) the mantle wedge above a subduction zone, (2) the footwall mantle of the subducted slab, or (3) were ancient mantle fragments emplaced at crustal depths prior to UHP metamorphism, whereas type B crustal peridotite and pyroxenite are a portion of mafic–ultramafic complexes that were intruded into the continental crust as magmas prior to subduction. Most type A peridotites were derived from a depleted mantle and exhibit petrochemical characteristics of mantle rocks; however, Sr and Nd isotope compositions of some peridotites have been modified by crustal contamination during subduction and/or exhumation. Type B peridotite and pyroxenite show cumulate structure, and some have experienced crustal metasomatism and contamination documented by high 87Sr/86Sr ratios (0.707–0.708), low εNd(t) values (−6 to −9) and low δ18O values of minerals (+2.92 to +4.52). Garnet peridotites of both types experienced multi‐stage recrystallization; some of them record prograde histories. High‐P–T  estimates (760–970 °C and 4.0–6.5±0.2 GPa) of peak metamorphism indicate that both mantle‐derived and crustal ultramafic rocks were subducted to profound depths >100 km (the deepest may be ≥180–200 km) and experienced UHP metamorphism in a subduction zone with an extremely low geothermal gradient of <5 °C km−1.