# PriSign, A Privacy-Preserving Single Sign-On System for Cloud Environments
## 8 Conclusions  
In this paper, we introduce the notion of PriSign to solve the problem of fine-grained access control, token-hiding, and stability of verification services for cloud environments in an ASSO system. First, we redefine the system model of PriSign and provide formal security definitions, including unforgeability, unlinkability, and token-hiding. Second, we provide a concrete construction using the ABCT scheme from Section 5.2.1, the ABCB scheme from Section 5.2.2, the TIPFE scheme from Section 5.2.3, and the SPS signature scheme in [33]. Finally, we provide formal security definitions and proofs and describe our implementation of the algorithms used in the PriSign scheme on a personal laptop to demonstrate its practicability. Note that there is a relatively higher computing overhead due to our adoption of TIPFE for token-hiding and policy issuing. To further address this problem, we intend to explore new efficient construction schemes for TIPFE in the future along with other approaches for achieving token-hiding. **Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/app13020727/s1](https://www.mdpi.com/article/10.3390/app13020727/s1)]([https://www.mdpi.com/article/10.3390/app13020727/s1](https://www.mdpi.com/article/10.3390/app13020727/s1)). **Author Contributions:** Conceptualization, H.X. and R.S. ; methodology, R.S., Y.Y. and H.X. ; validation, R.S., Y.Y., H.X. and H.F.; formal analysis, H.F., G.S. and J.Z. ; writing--original draft preparation, R.S., Y.Y. and H.X. ; writing--review and editing, H.F. and G.S. ; visualization, G.S. and J.Z. ; project administration, G.S. ; funding acquisition, H.F. and J.Z. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by National Key Research and Development Program of China under Grant 2018 YFB0803600 and the National Natural Science Foundation of China under Grant No.61872091. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no potential conflict of interest with respect to the research, authorship, or publication of this article. * (3) European Union. General data protection regulation. _Off. J. Eur. Union_**2016**, _49_, L119. Available online: [[https://gdpr-info.eu](https://gdpr-info.eu)]([https://gdpr-info.eu](https://gdpr-info.eu)) (accessed on 20 November 2022). * (4) [PERSON]; [PERSON]; [PERSON]; [PERSON] Anonymous authentication for mobile single sign-on to protect user privacy. _Int. J. Mob. Commun._**2008**, \(6\), 760-769. [CrossRef]
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