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Improved Security Proof for the Camenisch-Lysyanskaya Signature-Based Synchronized Aggregate Signature Scheme

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Information Security and Privacy (ACISP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12248))

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Abstract

The Camenisch-Lysyanskaya signature scheme in CRYPTO 2004 is a useful building block to construct privacy-preserving schemes such as anonymous credentials, group signatures or ring signatures. However, the security of this signature scheme relies on the interactive assumption called the LRSW assumption. Even if the interactive assumptions are proven in the generic group model or bilinear group model, the concerns about these assumptions arise in a cryptographic community. This fact caused a barrier to the use of cryptographic schemes whose security relies on these assumptions.

Recently, Pointcheval and Sanders proposed the modified Camenisch-Lysyanskaya signature scheme in CT-RSA 2018. This scheme satisfies the EUF-CMA security under the new q-type assumption called the Modified-q-Strong Diffie-Hellman-2 () assumption. However, the size of a q-type assumptions grows dynamically and this fact leads to inefficiency of schemes.

In this work, we revisit the Camenisch-Lysyanskaya signature-based synchronized aggregate signature scheme in FC 2013. This scheme is one of the most efficient synchronized aggregate signature schemes with bilinear groups. However, the security of this synchronized aggregate scheme was proven under the one-time LRSW assumption in the random oracle model. We give the new security proof for this synchronized aggregate scheme under the (static) assumption in the random oracle model with little loss of efficiency.

Supported in part by Input Output Hong Kong, Nomura Research Institute, NTT Secure Platform Laboratories, Mitsubishi Electric, I-System, JST CREST JPMJCR14D6, JST OPERA and JSPS KAKENHI 16H01705, 17H01695.

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Notes

  1. 1.

    Their modification from the \(\mathsf {CL}\) scheme to the \(\mathsf {MCL}\) scheme increases the number of group elements in a signature and an aggregate signature from 2 to 3.

  2. 2.

    In the assumption, an input is changed to \((\mathcal {G}, g, g^{x},\dots , g^{x^{q+1}},g^b, g^{bx},\dots , g^{bx^{q+1}}, g^a, g^{abx})\) and the condition of the order of P(x) is changed to at most q.

  3. 3.

    Fault-tolerant aggregate signature schemes [14] allow us to determine the subset of all messages belonging to an aggregate signature that were signed correctly. However, this scheme has a drawback that the aggregate signature size depends on the number of signatures to be aggregated into it.

  4. 4.

    The \(\mathsf {SAS_{LLY}}\) scheme described here is slightly different from the original ones [19] in that the range of \(H_2\) is changed from \(\mathbb {G}\) to \(\mathbb {G}^*\).

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Acknowledgement

We would like to thank anonymous referees for their constructive comments.

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  1. Tokyo Institute of Technology, Tokyo, Japan

    Masayuki Tezuka & Keisuke Tanaka

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  1. Masayuki Tezuka
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  2. Keisuke Tanaka
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Correspondence to Masayuki Tezuka .

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Editors and Affiliations

  1. Faculty of Information Technology, Monash University, Clayton, VIC, Australia

    Joseph K. Liu

  2. Murdoch University, Perth, WA, Australia

    Hui Cui

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Tezuka, M., Tanaka, K. (2020). Improved Security Proof for the Camenisch-Lysyanskaya Signature-Based Synchronized Aggregate Signature Scheme. In: Liu, J., Cui, H. (eds) Information Security and Privacy. ACISP 2020. Lecture Notes in Computer Science(), vol 12248. Springer, Cham. https://doi.org/10.1007/978-3-030-55304-3_12

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  • DOI: https://doi.org/10.1007/978-3-030-55304-3_12

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