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Tracing Quantum State Distinguishers via Backtracking

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14085))

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Abstract

We show the following results:

  • The post-quantum equivalence of indistinguishability obfuscation and differing inputs obfuscation in the restricted setting where the outputs differ on at most a polynomial number of points. Our result handles the case where the auxiliary input may contain a quantum state; previous results could only handle classical auxiliary input.

  • Bounded collusion traitor tracing from general public key encryption, where the decoder is allowed to contain a quantum state. The parameters of the scheme grow polynomially in the collusion bound.

  • Collusion-resistant traitor tracing with constant-size ciphertexts from general public key encryption, again for quantum state decoders. The public key and secret keys grow polynomially in the number of users.

  • Traitor tracing with embedded identities in the keys, again for quantum state decoders, under a variety of different assumptions with different parameter size trade-offs.

Traitor tracing and differing inputs obfuscation with quantum decoders/auxiliary input arises naturally when considering the post-quantum security of these primitives. We obtain our results by abstracting out a core algorithmic model, which we call the Back One Step (BOS) model. We prove a general theorem, reducing many quantum results including ours to designing classical algorithms in the BOS model. We then provide simple algorithms for the particular instances studied in this work.

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Notes

  1. 1.

    A different example is the quantum random oracle model [BDF+11], though this model is conceptually closer to the superposition attacks mentioned above.

  2. 2.

    Another limitation of Zhandry’s work is that the PLBE must support public encryption for all distributions used during tracing, which is not true of the known succinct LWE-based scheme [GKW18].

  3. 3.

    The usual terminology is that the decoder is “stateless”.

  4. 4.

    Recall that N is the total identity space, and c is the collusion bound.

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Acknowledgements

We thank Fermi Ma for helpful discussions.

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Authors and Affiliations

  1. NTT Research, Sunnyvale, USA

    Mark Zhandry

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  1. Mark Zhandry
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Correspondence to Mark Zhandry .

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  1. Rambus Inc., San Jose, CA, USA

    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Zhandry, M. (2023). Tracing Quantum State Distinguishers via Backtracking. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14085. Springer, Cham. https://doi.org/10.1007/978-3-031-38554-4_1

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  • DOI: https://doi.org/10.1007/978-3-031-38554-4_1

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