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A Variant of BLS Signature Scheme with Tight Security Reduction

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Mobile Networks and Management (MONAMI 2017)

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Abstract

In 2001, Boneh, Lynn and Shacham designed a signature scheme using the properties of bilinear pairing from elliptic curve, and based its security under the Computational Diffie-Hellman (CDH) assumption. However, the security reduction is not tight as there is a loss of roughly \(q_s\), the number of sign queries. In this paper, we propose a variant of the BLS signature with tight security reduction based on the co-CDH assumption. Besides upgraded to the notion of strong existential unforgeability under chosen message attack, the variant is backward-compatible with the original BLS signature.

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Notes

  1. 1.

    The co-CDH assumption was first proposed by Boneh et al. in [4]. Our scheme lean towards the modified co-CDH (co-CDH\(^*\)) assumption proposed by Chatterjee et al. in [10]. However, we use the co-CDH assumption throughout this paper for simplicity, as the co-CDH and co-CDH\(^*\) assumptions are equivalent [10].

  2. 2.

    We propose the usage of a single bit similar to Katz-Wang’s technique in [21] to optimize the signature length. However, the security proof for an integer instead of a bit r works just as well as the RSA-PFDH [11]. The security of PRBG to randomize the signature is not an issue, as proposed and used by Katz-Wang [21] and Koblitz-Menezes [19].

  3. 3.

    To avoid having a state where two signatures for a message exist at once where the value of the bit r may be either 0 or 1, the signer may enclose the bit r alongside \(\sigma \) to avoid further confusion during verification.

  4. 4.

    The value of r cannot be changed as once the signature is generated, the value of \(\delta \) in the signature would be corrupted if the value of r is of a different value.

  5. 5.

    Different from Katz-Wang’s work in [21], \(\mathcal {A}\) is not allowed to query the value of r, since it is not part of the hash inputs.

  6. 6.

    In this case, \(\mathcal {A}\) falls under the category of an euf-cma Adversary, whose \(m^*\) in the forgery must not be signed before.

  7. 7.

    In this case, \(\mathcal {A}\) falls under the category of a seuf-cma Adversary, whose \(m^*\) in the forgery must be signed before.

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Acknowledgment

The authors would like to thank the Malaysia government’s Fundamental Research Grant Scheme (FRGS/2/2014/ICT04/MMU/03/1) for supporting this work.

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Authors and Affiliations

  1. Faculty of Information Science and Technology, Multimedia University, Melaka, Malaysia

    Tiong-Sik Ng & Syh-Yuan Tan

  2. Faculty of Engineering, Multimedia University, Cyberjaya, Malaysia

    Ji-Jian Chin

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  1. Tiong-Sik Ng
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Correspondence to Tiong-Sik Ng .

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Editors and Affiliations

  1. SEIT, UNSW Canberra, Canberra, Australia

    Jiankun Hu

  2. RMIT University, Melbourne, Victoria, Australia

    Ibrahim Khalil

  3. RMIT University, Melbourne, Victoria, Australia

    Zahir Tari

  4. Swinburne University of Technology, Hawthorne, Melbourne, Victoria, Australia

    Sheng Wen

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Ng, TS., Tan, SY., Chin, JJ. (2018). A Variant of BLS Signature Scheme with Tight Security Reduction. In: Hu, J., Khalil, I., Tari, Z., Wen, S. (eds) Mobile Networks and Management. MONAMI 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 235. Springer, Cham. https://doi.org/10.1007/978-3-319-90775-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-90775-8_13

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