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Efficient Fully-Leakage Resilient One-More Signature Schemes

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Topics in Cryptology – CT-RSA 2019 (CT-RSA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11405))

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Abstract

In a recent paper Faonio, Nielsen and Venturi (ICALP 2015) gave new constructions of leakage-resilient signature schemes. The signature schemes proposed remain unforgeable against an adversary leaking arbitrary information on the entire state of the signer, including the random coins of the signing algorithm. The main feature of their signature schemes is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible. The notion, put forward by Nielsen, Venturi, and Zottarel (PKC 2014), defines a slack parameter \(\gamma \) which, roughly speaking, describes how gracefully the security degrades. Unfortunately, the standard-model signature scheme of Faonio, Nielsen and Venturi has a slack parameter that depends on the number of signatures queried by the adversary.

In this paper we show two new constructions in the standard model where the above limitation is avoided. Specifically, the first scheme achieves slack parameter \(O(1/\lambda )\) where \(\lambda \) is the security parameter and it is based on standard number theoretic assumptions, the second scheme achieves optimal slack parameter (i.e. \(\gamma =1\)) and it is based on knowledge of the exponent assumptions. Our constructions are efficient and have leakage rate \(1-o(1)\), most notably our second construction has signature size of only 8 group elements which makes it the leakage-resilient signature scheme with the shortest signature size known to the best of our knowledge.

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Notes

  1. 1.

    In [30], the authors show that the notion, even for small value of the slack parameter, allows for interesting applications such as leakage-resilient identification schemes.

  2. 2.

    Intuitively, any trapdoor for equivocation would break the knowledge of the exponent assumption.

  3. 3.

    As the forth scheme is a variation of FNV15\(_1\) and it achieves worse efficiency parameters.

  4. 4.

    Also notice that we quantify the extractor after the sampler, so to avoid pathological situation where the adversary \(\mathsf {A}\) simply forwards the output of the sampler \(\mathcal {S} \).

  5. 5.

    The adversary gets to see the public key \(\mathsf {pk}\) for uniformly sampled keys .

  6. 6.

    We reverse the order of the quantifiers in the usual definition of knowledge soundness. Namely, for each adversary \(\mathsf {A}\) there exists an extractor \(\mathsf {Ext}\).

  7. 7.

    Namely, the set of assignment for the randomness \(z_i\) for which the execution of \(\mathsf {P}\) with randomness \(z_i\) and the appropriate tuple instance and witness does compute exactly the proof \(\pi _i\).

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Acknowledgements

Research leading to these results has been supported by the Spanish Ministry of Economy under the projects Dedetis (ref. TIN2015-70713-R) and Datamantium (ref. RTC-2016-4930-7), and by the Madrid Regional Government under project N-Greens (ref. S2013/ICE-2731).

I would like to thank Dario Fiore for a conversation we had on his paper [16]. Also, I would like to thank Dennis Hofheinz which suggested to me the paper of Fujisaki on ABM Encryption.

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  1. IMDEA Software Institute, Madrid, Spain

    Antonio Faonio

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  1. Antonio Faonio
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  1. Mitsubishi Electric Corporation, Kamakura, Japan

    Mitsuru Matsui

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Faonio, A. (2019). Efficient Fully-Leakage Resilient One-More Signature Schemes. In: Matsui, M. (eds) Topics in Cryptology – CT-RSA 2019. CT-RSA 2019. Lecture Notes in Computer Science(), vol 11405. Springer, Cham. https://doi.org/10.1007/978-3-030-12612-4_18

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