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Cryptography with Certified Deletion

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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 propose a unifying framework that yields an array of cryptographic primitives with certified deletion. These primitives enable a party in possession of a quantum ciphertext to generate a classical certificate that the encrypted plaintext has been information-theoretically deleted, and cannot be recovered even given unbounded computational resources.

  • For \(X \in \{\textsf{public}\text {-}\textsf{key},\mathsf {attribute\text {-}based},\mathsf {fully\text {-}homomorphic},\textsf{witness},\textsf{timed}\text {-}\textsf{release}\}\), our compiler converts any (post-quantum) X encryption to X encryption with certified deletion. In addition, we compile statistically-binding commitments to statistically-binding commitments with certified everlasting hiding. As a corollary, we also obtain statistically-sound zero-knowledge proofs for QMA with certified everlasting zero-knowledge assuming statistically-binding commitments.

  • We also obtain a strong form of everlasting security for two-party and multi-party computation in the dishonest majority setting. While simultaneously achieving everlasting security against all parties in this setting is known to be impossible, we introduce everlasting security transfer (EST). This enables any one party (or a subset of parties) to dynamically and certifiably information-theoretically delete other participants’ data after protocol execution. We construct general-purpose secure computation with EST assuming statistically-binding commitments, which can be based on one-way functions or pseudorandom quantum states.

We obtain our results by developing a novel proof technique to argue that a bit b has been information-theoretically deleted from an adversary’s view once they output a valid deletion certificate, despite having been previously information-theoretically determined by the ciphertext they held in their view. This technique may be of independent interest.

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Notes

  1. 1.

    In contrast, in the one-time pad encryption setting as considered by [11], the original encrypted message is already information-theoretically hidden from the adversary, so to obtain any interesting notion of certified deletion, one must explicitly consider leaking the secret key.

  2. 2.

    Subsequent to the original posting of our paper on arXiv, an update to [39] was posted with somewhat different results. We provide a comparison between our work and the updated version of [39] in Sect. 1.3.

  3. 3.

    In order to fully capture all of our applications, we actually allow \(\mathcal{Z}_\lambda \) to operate on all inputs, including the BB84 states. See Sect. 3 for the precise details.

  4. 4.

    It may seem counter-intuitive that the certified deletion guarantees provided by our theorem hold even when instantiating \(\mathcal{Z}_\lambda \) with general semantically secure schemes, such as a fully-homomorphic encryption scheme. In particular, what if an adversary evaluated the FHE to recover a classical encryption of b, and then reversed their computation and finally produced a valid deletion certificate? This may seem to contradict everlasting security, since a classical ciphertext could be used to recover b given unbounded time. However, this attack is actually not feasible. After performing FHE evaluation coherently, the adversary would obtain a register holding a superposition over classical ciphertexts encrypting b, but with different random coins. Measuring this superposition to obtain a single classical ciphertext would collapse the state, and prevent the adversary from reversing their computation to eventually produce a valid deletion certificate. Indeed, our Theorem rules out this (and all other) efficient attacks.

  5. 5.

    We discuss comparisons with a recently updated version of [39] in Sect. 1.3.

  6. 6.

    One might be concerned that extending this argument to multi-bit messages may eventually reduce the advantage by too much, since the entire message must be guessed. However, it actually suffices to prove Theorem 1 for single bit messages and then use a bit-by-bit hybrid argument to obtain security for any polynomial-length message.

  7. 7.

    It suffices to require that the relative Hamming weight of each u is \(< 1/2\).

  8. 8.

    This proof strategy is inspired by the techniques of [8], who show a similar claim using a seeded extractor.

  9. 9.

    If we had tried to rely on generic properties of a seeded randomness extractor, as done in [11], we would still have had to deal with the fact the adversary’s view includes an encryption of the seed, which is required to be uniform and independent of the source of entropy. Even if the challenger’s state can be shown to produce a sufficient amount of min-entropy when measured in the standard basis, we cannot immediately claim that this source of entropy is perfectly independent of the seed of the extractor. Similar issues with using seeded randomness extraction in a related context are discussed by [41] in their work on revocable timed-release encryption.

  10. 10.

    In this notion, the adversary is an eavesdropper who sits between a ciphertext generator Alice and a ciphertext receiver Bob (using a symmetric-key encryption scheme), who attempts to learn some information about the ciphertext. The guarantee is that, either the eavesdropper gains information-theoretically no information about the underlying plaintext, or Bob can detect that the ciphertext was tampered with. While this is peripherally related to our setting, [22] does not consider public-key encryption, and moreover Bob’s detection procedure is quantum.

  11. 11.

    The term “ideal committment” can sometimes refer to the commitment ideal funtionality, but in this work we use the term ideal commitment to refer to a real-world protocol that can be shown to securely implement the commitment ideal functionality.

  12. 12.

    Technically, we require that for any \(\{\mathcal{A}_\lambda \}_{\lambda \in {\mathbb N}} \in \mathscr {A}\), every adversary \(\mathcal{B}\) with time and space complexity that is linear in \(\lambda \) more than that of \(\mathcal{A}_\lambda \), is also in \(\mathscr {A}\).

  13. 13.

    One might expect that the everlasting security definition described above already captures this property, since whether the certificate accepts or rejects is included in the output of the experiment. However, this experiment does not include the output of the adversary in the case that the certificate is rejected. So we still need to capture the fact that the joint distribution of the final adversarial state and the bit indicating whether the verification passes semantically hides b.

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Acknowledgments

We thank Bhaskar Roberts and Alex Poremba for comments on an earlier draft, and for noting that quantum fully-homomorphic encryption is not necessary for our FHE with certified deletion scheme, classical fully-homomorphic encryption suffices.

D.K. was supported in part by DARPA, NSF 2112890 and NSF 2247727. This material is based on work supported by DARPA under Contract No. HR001120C0024. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government or DARPA.

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Authors and Affiliations

  1. UC Berkeley, Berkeley, USA

    James Bartusek

  2. UIUC, Champaign, USA

    Dakshita Khurana

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Correspondence to Dakshita Khurana .

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    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Bartusek, J., Khurana, D. (2023). Cryptography with Certified Deletion. 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_7

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