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A Light-Weight Group Signature Scheme with Time-Token Dependent Linking

  • Conference paper
Lightweight Cryptography for Security and Privacy (LightSec 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9542))

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Abstract

Group signature is a central topic of cryptography with anonymity, and its several applications have been considered so far, e.g., privacy-preserving vehicle communications. Since anonymity (a.k.a. unlinkability) is quite strong in certain situations and it requires heavy cryptographic costs, group signatures with relaxed anonymity also have been proposed. For example, group signatures with controllable linkability was proposed by Hwang et al., (LightSec 2011) where an authority called Linker can anonymously check whether two group signatures are made by the same signer or not by using a linking key. However, the linking algorithm requires a heavy computation, i.e., bilinear pairings. In this paper, we propose the notion group signatures with time-token dependent Linking (GS-TDL), where a signer is unlinkable unless it generates multiple signatures at the same time period. It is particularly worth noting that our linking algorithm does not require cryptographic computations (i.e., comparisons to determine two elements are the same). Moreover, the signature size is 25 % shorter than that of the Hwang et al. scheme, and is 34 % shorter than that of the Boneh-Boeyn-Shacham short group signature scheme. Our GS-TDL scheme supports verifier-local revocation (VLR), which maintains constant signing and verification costs by using the linkable part of signatures. These appear to be related to independent interests. Finally, we provide our experimental results (using the TEPLA library on a cheap and constrained computational power device, Raspberry Pi).

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Notes

  1. 1.

    We remark that these schemes [14, 28–30] also achieve only CPA-anonymity (i.e., no opening oracle access is allowed in anonymity game) as in ours.

  2. 2.

    Even if a random nonce is included as a part of signed message, no linking algorithm works and this leads to a wag-the-dog situation. Even if a time T is included, e.g., sign M||T by using a message-dependent linking group signature scheme, anyone can manipulate T and such a signer-driven anonymous system must be avoided because vehicles have incentive to hide identity. On the contrary, in GS-TDL, time T is authorized by TGU and no vehicle can manipulate T.

  3. 3.

    As a remark, the case that an adversary generates a valid signature using a revoked user’s signing key cannot be captured by unforgeability since the open algorithm is not defined. Instead, we consider the case that a signature is invalid when the corresponding signer is revoked in correctness, though it might be additionally defined such as revocation soundness.

  4. 4.

    This condition must be required to exclude the trivially-broken case, e.g., \(\mathcal {A}\) honestly generates \(t_{T_0}\) and sets \(t_{T_1}\) as arbitrary value. Then, \(\mathcal {A}\) can check whether \(\sigma ^*\) is valid or not. If yes, then \(b=0\) and \(b=1\) otherwise.

  5. 5.

    That is, the \(\mathsf{TSK}\) oracle returns \(\mathsf {tsk}\) if all identities input in the \(\mathsf{USK}\) oracle were revoked.

  6. 6.

    We can assume that two group signatures input are valid. That is, the signature verification has been done before running the link algorithm. Then our linking algorithm does not require cryptographic computations (i.e., comparisons to determine two elements are the same).

  7. 7.

    https://www.openssl.org.

  8. 8.

    https://wiki.gnome.org/Projects/GLib.

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Acknowledgement

We would like to thank anonymous reviewers of LightSec 2015 and Dr. Ryo Nojima for their helpful comments and suggestions.

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  1. Security Fundamentals Laboratory, Network Security Research Institute, National Institute of Information and Communications Technology (NICT), Tokyo, Japan

    Keita Emura & Takuya Hayashi

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  1. Keita Emura
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Correspondence to Keita Emura .

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  1. University of Bremen and DFKI, Bremen, Germany

    Tim Güneysu

  2. Ruhr-Universität Bochum, Bochum, Germany

    Gregor Leander

  3. Ruhr-Universität Bochum, Bochum, Germany

    Amir Moradi

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Emura, K., Hayashi, T. (2016). A Light-Weight Group Signature Scheme with Time-Token Dependent Linking. In: Güneysu, T., Leander, G., Moradi, A. (eds) Lightweight Cryptography for Security and Privacy. LightSec 2015. Lecture Notes in Computer Science(), vol 9542. Springer, Cham. https://doi.org/10.1007/978-3-319-29078-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-29078-2_3

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