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The Lattice-Based Digital Signature Scheme qTESLA

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Applied Cryptography and Network Security (ACNS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12146))

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Abstract

We present qTESLA, a post-quantum provably-secure digital signature scheme that exhibits several attractive features such as simplicity, strong security guarantees against quantum adversaries, and built-in protection against certain side-channel and fault attacks. qTESLA—selected for round 2 of NIST’s post-quantum cryptography standardization project—consolidates a series of recent schemes originating in works by Lyubashevsky, and Bai and Galbraith. We provide full-fledged, constant-time portable C implementations consisting of only about 300 lines of C code, which showcases the code compactness of the scheme. Our results also demonstrate that a conservative, provably-secure signature scheme can be efficient and practical, even with a compact and portable implementation. For instance, our C-only implementation executes signing and verification in approximately 0.9 ms on an x64 Intel processor using the proposed level 1 parameter set. Finally, we also provide AVX2-optimized assembly implementations that achieve an additional factor-1.5 speedup.

The work of EA was partially supported by the German Federal Ministry of Education and Research and the Hessen State Ministry for Higher Education, Research and the Arts within their joint support of the National Research Center for Applied Cybersecurity ATHENE, and was partially carried out during his tenure of the ERCIM ‘Alain Bensoussan’ Fellowship Programme. NB is supported by the NSERC Discovery Accelerator Supplement grant RGPIN-2016-05146. JK is co-funded by the Deutsche Forschungsgemeinschaft (DFG) – SFB 1119 – 236615297. JR is partially supported by the joint São Paulo Research Foundation (FAPESP)/Intel Research grant 2015/50520-6 “Efficient Post-Quantum Cryptography for Building Advanced Security Applications”.

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Notes

  1. 1.

    It is important to note that the security reduction requires a conjecture, see Sect. 4.

  2. 2.

    This count excludes the parameter-specific packing functions, header files, NTT constants, and (c)SHAKE functions.

  3. 3.

    Recently, a variant of Dilithium that produces probabilistic signatures was included as a modification for round 2 of the NIST post-quantum project  [34]. However,  [34] suggests the deterministic version as the default option.

  4. 4.

    In an earlier version of this document we needed to distinguish \(L_S\)/\(L_E\) and S/E. Although this is not necessary in this version, we keep all four values \(L_S,S,L_E,E\) for consistency reasons.

  5. 5.

    To be precise, we assume that the time to simulate the (quantum) random oracle is smaller than the time to forge a signature. This assumption is commonly made in “provably secure” cryptography.

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Acknowledgments

We are grateful to the anonymous reviewers for their valuable comments on earlier versions of this paper. We thank Vadim Lyubashevsky for pointing out that the heuristic parameters proposed in a previous paper version were lacking security estimates with respect to the SIS problem. We also thank Greg Zaverucha for bringing up the vulnerability of some signature schemes, including a previous version of qTESLA, to KS attacks, and for several fruitful discussions. We are thankful to Edward Eaton for his advice concerning the conjecture used in Theorem 1 and carrying out the supporting experiments, and to Joo Woo for pointing out an incorrectness in the conjecture. Finally, we thank Fernando Virdia, Martin Albrecht and Shi Bai for fruitful discussions and helpful advice on the hardness estimation of SIS for an earlier version of this paper.

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Authors and Affiliations

  1. Ondokuz Mayis University, Atakum, Turkey

    Erdem Alkim

  2. Fraunhofer SIT, Darmstadt, Germany

    Erdem Alkim

  3. University of Washington Tacoma, Tacoma, USA

    Paulo S. L. M. Barreto

  4. University of Waterloo, Waterloo, Canada

    Nina Bindel

  5. Technische Universität Darmstadt, Darmstadt, Germany

    Juliane Krämer

  6. Microsoft Research, Redmond, USA

    Patrick Longa

  7. LG Electronics, Englewood Cliffs, USA

    Jefferson E. Ricardini

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  1. Erdem Alkim
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  2. Paulo S. L. M. Barreto
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  3. Nina Bindel
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  4. Juliane Krämer
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Correspondence to Nina Bindel .

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Editors and Affiliations

  1. Department of Mathematics, University of Padua, Padua, Italy

    Mauro Conti

  2. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  3. Dipt di Informatica Sistemi e Produ, Università di Roma “Tor Vergata”, Rome, Roma, Italy

    Emiliano Casalicchio

  4. Sapienza University of Rome, Rome, Italy

    Angelo Spognardi

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Alkim, E., Barreto, P.S.L.M., Bindel, N., Krämer, J., Longa, P., Ricardini, J.E. (2020). The Lattice-Based Digital Signature Scheme qTESLA. In: Conti, M., Zhou, J., Casalicchio, E., Spognardi, A. (eds) Applied Cryptography and Network Security. ACNS 2020. Lecture Notes in Computer Science(), vol 12146. Springer, Cham. https://doi.org/10.1007/978-3-030-57808-4_22

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