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Abstract: Blind signature and ring signature are two signature schemes with privacy concern. Zhang [Jianhong Zhang, Linkability analysis of some blind signature schemes, In International Conference on Computational Intelligence and Security 2006, IEEE, vol. 2, 2006, pp. 1367–1370, (Available at http://dx.doi.org/10.1109/ICCIAS.2006.295283.)] analyzed the unlinkability of Zhang and Kim [Fangguo Zhang, Kwangjo Kim, ID-based blind signature and ring signature from pairings, in: Yuliang Zheng (Ed.), Advances in Cryptology — ASIACRYPT 2002, 8th International Conference on the Theory and Application of Cryptology and Information Security, Queenstown, New Zealand, December 1–5, 2002, Proceedings, Lecture Notes in Computer Science, vol. 2501, Springer, 2002, pp. 533–547], Huang et al. [Zhenjie Huang, Kefei Chen, Yumin Wang, Efficient identity-based signatures and blind signatures, in: Yvo Desmedt, Huaxiong Wang, Yi Mu, Yongqing Li (Eds.), Cryptology and Network Security, 4th International Conference, CANS 2005, Xiamen, China, December 14–16, 2005, Proceedings, Lecture Notes in Computer Science, vol. 3810, Springer, 2005, pp. 120–133] and Wu et al. [Qianhong Wu, Willy Susilo, Yi Mu, Fangguo Zhang, Efficient partially blind signatures with provable security, in: Osvaldo Gervasi, Marina L. Gavrilova, (Eds.), Computational Science and Its Applications — ICCSA 2007, International Conference, Kuala Lumpur, Malaysia, August 26–29, 2007. Proceedings. Part III, Lecture Notes in Computer Science, vol. 4707, Springer, 2007, pp. 1096–1105] and claimed that they are indeed linkable. On the other hand, Gamage et al. [Chandana Gamage, Ben Gras, Bruno Crispo, Andrew S. Tanenbaum, An identity-based ring signature scheme with enhanced privacy, Securecomm and Workshops 2006, IEEE, 2006, pp. 1–5, (Available at http://dx.doi.org/10.1109/SECCOMW.2006.359554)] claimed that the scheme of Chow et al. [Sherman S.M. Chow, Siu-Ming Yiu, Lucas Chi Kwong Hui, Efficient identity based ring signature, in: John Ioannidis, Angelos D. Keromytis, Moti Yung (Eds.), Applied Cryptography and Network Security, Third International Conference, ACNS 2005, New York, NY, USA, June 7–10, 2005, Proceedings, Lecture Notes in Computer Science, vol. 3531, 2005, pp. 499–512] is vulnerable to key exposure attack. This paper shows that all these claims are incorrect. Furthermore, we show that the scheme proposed by Gamage et al. [Chandana Gamage, Ben Gras, Bruno Crispo, Andrew S. Tanenbaum, An identity-based ring signature scheme with enhanced privacy, Securecomm and Workshops 2006, IEEE, 2006, pp. 1–5, (Available at http://dx.doi.org/10.1109/SECCOMW.2006.359554)] which aimed to provide enhanced privacy actually has privacy level reduced. We hope this work can pinpoint the standard one should use when analyzing the unlinkability of blind signatures and the anonymity of ring signatures. [Copyright &y& Elsevier]