Vol.:(0123456789) Wireless Personal Communications https://doi.org/10.1007/s11277-019-06208-1 1 3 Privacy‑Preserving Certifcateless Cloud Auditing with Multiple Users Ge Wu 1  · Yi Mu 2  · Willy Susilo 1  · Fuchun Guo 1  · Futai Zhang 3 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract Cloud auditing is one of the important processes to ensure the security and integrity of data in cloud storage. Implementing cloud auditing requires various cryptographic tools such as identity-based cryptography and its variant: certifcateless cryptography which solves the inherent key escrow problem in identity-based cryptography. Applying certifcateless cryptography to cloud auditing has shown many merits. However, in a multi-user setting, certifcateless cloud auditing (CLCA) schemes require additional security requirements. For instance, the identity privacy becomes an important issue that should be taken into consideration in some applications. In this paper, we concentrate on the identity privacy of CLCA schemes. We defne the security models of privacy-preserving CLCA schemes, namely the uncheatability and anonymity and propose an efcient CLCA scheme, which is secure in the security models. As a feature of our scheme, the tag of a message is compact, which consists of only one group element. The uncheatability is based on variants of bilin- ear Dife–Hellman assumption in the random oracle model. The identity privacy of the user is information-theoretically guaranteed against the third party auditor. Keywords Cloud computing · Cloud auditing · Certifcateless cryptography · Privacy- preserving 1 Introduction Cloud storage is one of the most essential services that the cloud platforms can provide. Data integrity is the primary security concern in cloud storage since the data is uploaded to the cloud servers and is no longer maintained locally by the user. A cryptographic solution * Yi Mu ymu.ieee@gmail.com Ge Wu gw523@uowmail.edu.au 1 Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Wollongong, Australia 2 Fujian Provincial Key Laboratory of Network Security and Cryptography, Fujian Normal University, Fuzhou, China 3 School of Computer Science and Technology, Nanjing Normal University, Nanjing, China