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Revisiting TESLA in the Quantum Random Oracle Model

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Post-Quantum Cryptography (PQCrypto 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10346))

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Abstract

We study a scheme of Bai and Galbraith (CT-RSA’14), also known as TESLA. TESLA was thought to have a tight security reduction from the learning with errors problem (LWE) in the random oracle model (ROM). Moreover, a variant using chameleon hash functions was lifted to the quantum random oracle model (QROM). However, both reductions were later found to be flawed and hence it remained unresolved until now whether TESLA can be proven to be tightly secure in the (Q)ROM.

In the present paper we provide an entirely new, tight security reduction for TESLA from LWE in the QROM (and thus in the ROM). Our security reduction involves the adaptive re-programming of a quantum oracle. Furthermore, we propose parameter sets targeting 128 bits of security against both classical and quantum adversaries and compare TESLA’s performance with state-of-the-art signature schemes.

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Notes

  1. 1.

    It is not necessary that TESLA parameters be convenient in order to derive negligibly small upper bounds on \(\varepsilon '\); the definition of convenience merely facilitates a simplified statement of those bounds.

  2. 2.

    We make an exception for BLISS. The authors of the software obviously did not spend any effort on reducing the size of signatures and keys; we report sizes with “trivial” compression through choosing native data types of appropriate sizes.

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Acknowledgments

We are especially grateful to Peter Schwabe for contributions to our software implementation and to the presentation of the paper. We thank Chris Peikert for pointing out a flaw in previous security reductions for TESLA in the random oracle model. We thank Steven Galbraith and anonymous reviewers for valuable feedback on an earlier version of this manuscript.

This work has been supported by the German Research Foundation (DFG) as part of project P1 within the CRC 1119 CROSSING, by TÜBITAK under 2214-A Doctoral Research Program Grant and 2211-C PhD Scholarship, by Ege University under project 2014-FEN-065, and by CryptoWorks21.

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Authors and Affiliations

  1. Ege University, İzmir, Turkey

    Erdem Alkim

  2. Technische Universität Darmstadt, Darmstadt, Germany

    Nina Bindel, Johannes Buchmann & Juliane Krämer

  3. BridgingIT GmbH, Mannheim, Germany

    Özgür Dagdelen

  4. ISARA Corporation, Waterloo, Canada

    Edward Eaton, Gus Gutoski & Filip Pawlega

  5. University of Waterloo, Waterloo, Canada

    Edward Eaton & Filip Pawlega

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  1. Erdem Alkim
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  2. Nina Bindel
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  4. Özgür Dagdelen
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Correspondence to Nina Bindel or Gus Gutoski .

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Editors and Affiliations

  1. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Tanja Lange

  2. Kyushu University , Fukuoka, Japan

    Tsuyoshi Takagi

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Alkim, E. et al. (2017). Revisiting TESLA in the Quantum Random Oracle Model. In: Lange, T., Takagi, T. (eds) Post-Quantum Cryptography . PQCrypto 2017. Lecture Notes in Computer Science(), vol 10346. Springer, Cham. https://doi.org/10.1007/978-3-319-59879-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-59879-6_9

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