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Ring Signatures of Constant Size Without Random Oracles

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Information Security and Cryptology (Inscrypt 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8957))

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Abstract

Ring signatures allow a signer to anonymously sign on behalf of a group of users, the so-called ring; the only condition is that the signer is a member of the ring. At PKC 2007, Shacham and Waters left an open problem, “obtain a ring signature secure without random oracles and its signature size is independent of the number of signers implicated in the ring”, which has not been solved yet. In this paper, by using a powerful tool, indistinguishability obfuscator (\(\mathsf i \mathcal {O}\)), we construct a constant size ring signature scheme without random oracles and thus answer Shacham et al.’s open problem. Furthermore, we construct an identity-based ring signature scheme which also has constant signature size in the standard model. However, we stress that due to the low efficiency of the existing \(\mathsf i \mathcal {O}\) candidates, we mainly focus on the existence of the constant size ring signature schemes without random oracles, but do not care about their practicability. A shortcoming of our approach is that the ring unforgeability merely is selective but not adaptive.

This research is supported by the National Natural Science Foundation of China (Grant No. 60970139) and the Strategic Priority Program of Chinese Academy of Sciences (Grant No. XDA06010702).

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Notes

  1. 1.

    For ease of notation on the reader, we suppress repeated \(\mathbb {PP}\) arguments that are provided to all of the following algorithms. For example, we will write \((SK, VK)\leftarrow \mathsf{KeyGen }()\) instead of \((SK, VK) \leftarrow \mathsf{KeyGen }(\mathbb {PP})\).

  2. 2.

    We consider a weaker version of this notion in which corruptions of honest users are allowed but adversary-chosen public keys are not allowed. This weaker notion has been used in [20, 29].

  3. 3.

    In the beginning, \(\mathcal {A}\) does not given the keys \(S=\{VK_i\}_{i=1}^{n(\lambda )}\). In order to obtain the forgery ring \(R^{*}\), we require that \(\mathcal {A}\) submits a set of index \(I_{R^{*}}=\{i_1, \ldots , i_{|R^{*}|}\}\subseteq [n(\lambda )]\). Then after the keys \(S=\{VK_i\}_{i=1}^{n(\lambda )}\) are generated, the forgery ring \(R^{*}=\{VK_{i_1}, \ldots , VK_{i_{|R^{*}|}}\}\subseteq S\) is also obtained.

  4. 4.

    This idea is from [9] where Boneh and Zhandry constructed a non-interactive key exchange protocol.

  5. 5.

    The idea of our identity-based ring signature scheme is from Boneh and Zhandry’s [9] identity-based non-interactive key exchange scheme.

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Acknowledgement

The authors would like to thank anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering of Chinese Academy of Sciences, Beijing, China

    Fei Tang & Hongda Li

  2. Data Assurance and Communication Security Research Center of Chinese Academy of Sciences, Beijing, China

    Fei Tang & Hongda Li

  3. University of Chinese Academy Sciences, Beijing, China

    Fei Tang

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  1. Fei Tang
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Correspondence to Fei Tang .

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Editors and Affiliations

  1. SKLOIS, Institute of Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  2. Computer Science Department, Columbia University, New York, New York, USA

    Moti Yung

  3. Infocomm Security Department, Institute for Infocomm Research, Singapore, Singapore

    Jianying Zhou

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Tang, F., Li, H. (2015). Ring Signatures of Constant Size Without Random Oracles. In: Lin, D., Yung, M., Zhou, J. (eds) Information Security and Cryptology. Inscrypt 2014. Lecture Notes in Computer Science(), vol 8957. Springer, Cham. https://doi.org/10.1007/978-3-319-16745-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-16745-9_6

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