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Quantum Cryptanalysis in the RAM Model: Claw-Finding Attacks on SIKE

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Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11692))

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Abstract

We introduce models of computation that enable direct comparisons between classical and quantum algorithms. Incorporating previous work on quantum computation and error correction, we justify the use of the gate-count and depth-times-width cost metrics for quantum circuits. We demonstrate the relevance of these models to cryptanalysis by revisiting, and increasing, the security estimates for the Supersingular Isogeny Diffie–Hellman (SIDH) and Supersingular Isogeny Key Encapsulation (SIKE) schemes. Our models, analyses, and physical justifications have applications to a number of memory intensive quantum algorithms.

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Notes

  1. 1.

    Here we are taking Planck’s constant equal to \(2\pi \), i.e. \(\hbar = 1\).

  2. 2.

    Actually, here and elsewhere, we use a gate set that includes Toffoli gates and controlled-swap gates. These can be built from O(1) Clifford+T gates.

  3. 3.

    One can handle a range of capacities using controlled operations, but the size of the resulting circuit grows linearly with the number of capacities it must handle.

  4. 4.

    We are being slightly imprecise, as the \(\ell \)-isogeny graph is actually directed. However, if there is an edge from u to v corresponding to an isogeny \(\phi \), then there is an edge from v to u corresponding to the dual isogeny \(\hat{\phi }\).

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Acknowledgements

We thank Alfred Menezes for helpful comments on this paper. Samuel Jaques acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). This work was supported by Canada’s NSERC CREATE program. IQC is supported in part by the Government of Canada and the Province of Ontario.

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Authors and Affiliations

  1. Institute for Quantum Computing, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Samuel Jaques & John M. Schanck

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  1. Samuel Jaques
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Correspondence to Samuel Jaques or John M. Schanck .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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© 2019 International Association for Cryptologic Research

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Jaques, S., Schanck, J.M. (2019). Quantum Cryptanalysis in the RAM Model: Claw-Finding Attacks on SIKE. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11692. Springer, Cham. https://doi.org/10.1007/978-3-030-26948-7_2

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  • DOI: https://doi.org/10.1007/978-3-030-26948-7_2

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