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International Conference on Information Security and Cryptology

Inscrypt 2014: Information Security and Cryptology pp 170–190Cite as

Optimal Proximity Proofs

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8957))

Abstract

Provably secure distance-bounding is a rising subject, yet an unsettled one; indeed, very few distance-bounding protocols, with formal security proofs, have been proposed. In fact, so far only two protocols, namely SKI (by Boureanu et al.) and FO (by Fischlin and Onete), offer all-encompassing security guaranties, i.e., resistance to distance-fraud, mafia-fraud, and terrorist-fraud. Matters like security, alongside with soundness, or added tolerance to noise do not always coexist in the (new) distance-bounding designs. Moreover, as we will show in this paper, efficiency and simultaneous protection against all frauds seem to be rather conflicting matters, leading to proposed solutions which were/are sub-optimal. In fact, in this recent quest for provable security, efficiency has been left in the shadow. Notably, the tradeoffs between the security and efficiency have not been studied. In this paper, we will address these limitations, setting the “security vs. efficiency” record straight.

Concretely, by combining ideas from SKI and FO, we propose symmetric protocols that are efficient, noise-tolerant and—at the same time—provably secure against all known frauds. Indeed, our new distance-bounding solutions outperform the two aforementioned provably secure distance-bounding protocols. For instance, with a noise level of \(5\,\%\), we obtain the same level of security as those of the pre-existent protocols, but we reduce the number of rounds needed from 181 to 54.

The full version of this paper is available on [10].

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Notes

  1. 1.

    As discussed herein, FO has an incomparable approach for TF-resistance in which the number of rounds is not relevant.

  2. 2.

    Our model was recently extended to cover public-key distance-bounding [31, 32].

  3. 3.

    The verification phase can be interactive or not.

  4. 4.

    Provers have no clock. They are in a waiting state to receive the challenge and loose the notion of time while waiting.

  5. 5.

    A “malicious verifier” running an algorithm \(V^*(x)\) can be seen as a malicious prover running \(V^*(x)\).

  6. 6.

    we stress that this is a local definition of independence which is unrelated to statistical independence.

  7. 7.

    “Seen” means either received as being the destinator or by eavesdropping.

  8. 8.

    In [33], a protocol with two bits of challenges and one bit of response achieving \(\alpha =\mathsf {Tail}(n,\tau ,\frac{1}{3})\) is proposed. But it actually works with \(\mathsf {num}_r=3\) as it allows response 0, response 1, and no response.

  9. 9.

    Same remark about [33] as in Theorem 7.

  10. 10.

    Since provers loose the notion of time in the challenge phase, pre-ask and post-ask attacks cannot be detected.

  11. 11.

    Note that cases where there is a close-by prover or a close-by verifier are trivial since they hold the secret \(x\) in their view.

  12. 12.

    this is actually confirmed by experiment for the data we use.

  13. 13.

    We take the FO protocol as described in [30] since the original one from [18] introduces two counters and has an incorrect parameter \(p_e\). The one from [30] has been shown to provide an optimal expression for \(p_e\).

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Author information

Authors and Affiliations

  1. Akamai Technologies Limited, EMEA HQ, London, UK

    Ioana Boureanu

  2. EPFL, Lausanne, Switzerland

    Serge Vaudenay

Authors
  1. Ioana Boureanu
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  2. Serge Vaudenay
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Correspondence to Ioana Boureanu .

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Editors and Affiliations

  1. SKLOIS, Institute of Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  2. Computer Science Department, Columbia University, New York, New York, USA

    Moti Yung

  3. Infocomm Security Department, Institute for Infocomm Research, Singapore, Singapore

    Jianying Zhou

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Boureanu, I., Vaudenay, S. (2015). Optimal Proximity Proofs. In: Lin, D., Yung, M., Zhou, J. (eds) Information Security and Cryptology. Inscrypt 2014. Lecture Notes in Computer Science(), vol 8957. Springer, Cham. https://doi.org/10.1007/978-3-319-16745-9_10

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  • DOI: https://doi.org/10.1007/978-3-319-16745-9_10

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