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Strongly Unforgeable Signature Resilient to Polynomially Hard-to-Invert Leakage Under Standard Assumptions

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Information Security (ISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11060))

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Abstract

A signature scheme is said to be weakly unforgeable, if it is hard to forge a signature on a message not signed before. A signature scheme is said to be strongly unforgeable, if it is hard to forge a signature on any message. In some applications, the weak unforgeability is not enough and the strong unforgeability is required, e.g., the Canetti, Halevi and Katz transformation.

Leakage-resilience is a property which guarantees that even if secret information such as the secret-key is partially leaked, the security is maintained. Some security models with leakage-resilience have been proposed. The auxiliary (input) leakage model, or hard-to-invert leakage model, proposed by Dodis et al. in STOC’09 is especially meaningful one, since the leakage caused by a function which information-theoretically reveals the secret-key, e.g., one-way permutation, is considered.

In this work, we propose a generic construction of a signature scheme strongly unforgeable and resilient to polynomially hard-to-invert leakage which can be instantiated under standard assumptions such as the decisional linear assumption. We emphasize that our signature scheme is not only the first one resilient to polynomially hard-to-invert leakage under standard assumptions, but also the first one which is strongly unforgeable and has hard-to-invert leakage-resilience.

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Notes

  1. 1.

    Secret denotes the secret information. |Secret| denotes the bit-length of Secret.

  2. 2.

    k denotes the minimum entropy of the secret key \(sk\). If the secret-key is generated uniformly at random, k is equivalent to the bit-length of the secret-key \(|sk|\).

  3. 3.

    By the transformation in [18], some new elements are added to the public-key and secret-key.

  4. 4.

    Although \(\mathsf {Dec}\) needs the encryption-key ek as an input since ek includes information such as the prime p , the group \(\mathbb {G}\), and etc., we often omit ek as the input.

  5. 5.

    In this paper, the function class \(\mathcal {F}_{\varSigma _{\mathrm{SIG}}}(\lambda )\) can be simply written as \(\mathcal {F}(\lambda )\), if it is obvious that the function class is for the signature scheme \(\varSigma _{\mathrm{SIG}}\).

  6. 6.

    IND-LCCA is stronger security notion than IND-wLCCA. For the details, refer to [15].

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Acknowledgements

This work was supported by JSPS KAKENHI (Grant Number JP17KT0081). This work was also supported by JSPS and DST under the Japan-India Science Cooperative Program.

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Authors and Affiliations

  1. Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

    Masahito Ishizaka & Kanta Matsuura

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  1. Masahito Ishizaka
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  2. Kanta Matsuura
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Correspondence to Masahito Ishizaka .

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Editors and Affiliations

  1. University of Surrey, Guildford, United Kingdom

    Liqun Chen

  2. University of Surrey, Guildford, United Kingdom

    Mark Manulis

  3. University of Surrey, Guildford, United Kingdom

    Steve Schneider

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Ishizaka, M., Matsuura, K. (2018). Strongly Unforgeable Signature Resilient to Polynomially Hard-to-Invert Leakage Under Standard Assumptions. In: Chen, L., Manulis, M., Schneider, S. (eds) Information Security. ISC 2018. Lecture Notes in Computer Science(), vol 11060. Springer, Cham. https://doi.org/10.1007/978-3-319-99136-8_23

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  • DOI: https://doi.org/10.1007/978-3-319-99136-8_23

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