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Incompressible Cryptography

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Advances in Cryptology – EUROCRYPT 2022 (EUROCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13275))

Abstract

Incompressible encryption allows us to make the ciphertext size flexibly large and ensures that an adversary learns nothing about the encrypted data, even if the decryption key later leaks, unless she stores essentially the entire ciphertext. Incompressible signatures can be made arbitrarily large and ensure that an adversary cannot produce a signature on any message, even one she has seen signed before, unless she stores one of the signatures essentially in its entirety.

In this work, we give simple constructions of both incompressible public-key encryption and signatures under minimal assumptions. Furthermore, large incompressible ciphertexts (resp. signatures) can be decrypted (resp. verified) in a streaming manner with low storage. In particular, these notions strengthen the related concepts of disappearing encryption and signatures, recently introduced by Guan and Zhandry (TCC 2021), whose previous constructions relied on sophisticated techniques and strong, non-standard assumptions. We extend our constructions to achieve an optimal “rate”, meaning the large ciphertexts (resp. signatures) can contain almost equally large messages, at the cost of stronger assumptions.

J. Guan—Part of this research was conducted while this author was a research intern at NTT Research, Inc.

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Notes

  1. 1.

    The symmetric-key scheme of [Dzi06b] also only offers one-time security. However, a simple hybrid argument shows that this implies many-time security, where the adversary can compress each of many ciphertexts separately and later sees the secret key. However, it inherently does not offer any security if the adversary can jointly compress many ciphertexts, even if the compressed value is much smaller than a single ciphertext! In contrast, public-key incompressible encryption automatically ensures security in such setting via a simple hybrid argument.

  2. 2.

    It’s not hard to see that one-way functions, and therefore symmetric key cryptography, are implied by disappearing ciphertexts, since the secret key can be information-theoretically recovered from the public key.

  3. 3.

    This is equivalent to the \(\alpha \)-expansion property as defined in [MW20] for \(\alpha =L_c/L_m\).

  4. 4.

    This is equivalent to \(\beta \)-incompressibility as defined in [MW20] for \(\beta =S\).

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Author information

Authors and Affiliations

  1. Princeton University, Princeton, NJ, 08544, USA

    Jiaxin Guan & Mark Zhandry

  2. Northeastern University, Boston, MA, 02115, USA

    Daniel Wichs

  3. NTT Research, Inc., Sunnyvale, CA, 94085, USA

    Daniel Wichs & Mark Zhandry

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  1. Jiaxin Guan
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Correspondence to Jiaxin Guan .

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Editors and Affiliations

  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Guan, J., Wichs, D., Zhandry, M. (2022). Incompressible Cryptography. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_24

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