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Publicly Verifiable Deletion from Minimal Assumptions

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14372))

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Abstract

We present a general compiler to add the publicly verifiable deletion property for various cryptographic primitives including public key encryption, attribute-based encryption, and quantum fully homomorphic encryption. Our compiler only uses one-way functions, or more generally hard quantum planted problems for \(\textsf{NP}\), which are implied by one-way functions. It relies on minimal assumptions and enables us to add the publicly verifiable deletion property with no additional assumption for the above primitives. Previously, such a compiler needs additional assumptions such as injective trapdoor one-way functions or pseudorandom group actions [Bartusek-Khurana-Poremba, CRYPTO 2023]. Technically, we upgrade an existing compiler for privately verifiable deletion [Bartusek-Khurana, CRYPTO 2023] to achieve publicly verifiable deletion by using digital signatures.

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Notes

  1. 1.

    SKE, COM, ABE, TRE, and WE stand for secret key encryption, commitment, attribute-based encryption, time-release encryption, and witness encryption, respectively. Although Bartusek et al. [7] did not mention, we can apply their transformation to SKE and COM as the results by Bartusek and Khurana [8].

  2. 2.

    We do not abbreviate when we refer to this type to avoid confusion.

  3. 3.

    Although Bartusek and Khurana [8] did not mention, we can apply their transformation to SKE.

  4. 4.

    SKE, PKE, ABE, (Q)FHE, TRE, and WE fall into this category.

  5. 5.

    WE does not seem to imply one-way functions.

  6. 6.

    The compilers of [8, 9] are also applicable to schemes that have quantum encryption and decryption (or committing) algorithms though they do not explicitly mention it.

  7. 7.

    For simplicity, we state a simplified version of the lemma that is sufficient for the conversion for PKE, FHE, TRE, and WE, but not for ABE. See Lemma 4.1 for the general version.

  8. 8.

    We write \(\textsf{Enc}(\theta ,b \oplus \bigoplus _{j: \theta _j = 1} x_j)\) to mean an encryption of the message \((\theta ,b \oplus \bigoplus _{j: \theta _j = 1} x_j)\) where we omit the encryption key.

  9. 9.

    We assume that the verification algorithm of Z with \(\text {PVD}\) is a classical deterministic algorithm. If we allow it to be a quantum algorithm, we have to consider hard quantum planted problems for \(\textsf{QCMA}\), which are also sufficient to instantiate our compiler.

  10. 10.

    The definitions in [8] only consider privately verifiable deletion, but it is straightforward to extend them to ones with publicly verifiable deletion.

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Authors and Affiliations

  1. NTT Social Informatics Laboratories, Tokyo, Japan

    Fuyuki Kitagawa, Ryo Nishimaki & Takashi Yamakawa

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  1. Fuyuki Kitagawa
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  2. Ryo Nishimaki
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Correspondence to Takashi Yamakawa .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Kitagawa, F., Nishimaki, R., Yamakawa, T. (2023). Publicly Verifiable Deletion from Minimal Assumptions. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14372. Springer, Cham. https://doi.org/10.1007/978-3-031-48624-1_9

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