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CASE: A New Frontier in Public-Key Authenticated Encryption

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14370))

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Abstract

We introduce a new cryptographic primitive, called Completely Anonymous Signed Encryption (CASE). CASE is a public-key authenticated encryption primitive, that offers anonymity for senders as well as receivers. A “case-packet” should appear, without a (decryption) key for opening it, to be a blackbox that reveals no information at all about its contents. To decase a case-packet fully–so that the message is retrieved and authenticated–a verification key is also required.

Defining security for this primitive is subtle. We present a relatively simple Chosen Objects Attack (COA) security definition. Validating this definition, we show that it implies a comprehensive indistinguishability-preservation definition in the real-ideal paradigm. To obtain the latter definition, we extend the Cryptographic Agents framework of [2, 3] to allow maliciously created objects.

We also provide a novel and practical construction for COA-secure CASE under standard assumptions in public-key cryptography, and in the standard model.

We believe CASE can be a staple in future cryptographic libraries, thanks to its robust security guarantees and efficient instantiations based on standard assumptions.

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Notes

  1. 1.

    For simplicity, we consider a finite message space. If messages of arbitrary length are to be allowed, we will let a case-packet reveal the length of the message (possibly after padding). All our definitions and results can be readily generalized to this setting.

  2. 2.

    These distinct experiments can be combined to give an equivalent unified experiment in which the adversary is allowed to adaptively attack any of the above security properties over a collection of keys and case-packets. Such a definition is presented as an intermediate step to showing the comprehensiveness of this definition (see below).

  3. 3.

    We note that, CCA-QD security is not implied by CCA security and the QD structure alone. E.g., one can modify a CCA-QD secure PKE scheme such that, if the encoding of the randomness (the pre-computed component of the ciphertext) happens to equal the message, it simply sets the second component to \(\bot \), thereby revealing the message; while this remains CCA secure, an adversary in the CCA-QD game can set one of the challenge messages to be equal to the encoding of the randomness and break CCA-QD security.

  4. 4.

    So that, it is statistical indistinguishability in the ideal model that is required to be preserved as computational indistinguishability in the real model.

  5. 5.

    To facilitate keeping track of the arguments being made, we describe the corresponding hybrids from Sect. 6. The goal is to show \(\textsf{H}_{0} \approx \textsf{H}_{7} \), for hybrids corresponding to real executions with \(b=0\) and \(b=1\) respectively.

  6. 6.

    This corresponds to \(\textsf{H}_{0} \approx \textsf{H}_{1} \) (with \(b=0\)) and \(\textsf{H}_{6} \approx \textsf{H}_{7} \) (with \(b=1\)).

  7. 7.

    This corresponds to showing that if \(\textsf{H}_{2} \approx \textsf{H}_{5} \), then \(\textsf{H}_{1} \approx \textsf{H}_{2} \) and \(\textsf{H}_{5} \approx \textsf{H}_{6} \).

  8. 8.

    This shows \(\textsf{H}_{2} \approx \textsf{H}_{3} \) and \(\textsf{H}_{4} \approx \textsf{H}_{5} \).

  9. 9.

    That is, \(\textsf{H}_{3} \approx \textsf{H}_{4} \).

  10. 10.

    If a handle appears more than once among \( {h} _1,\ldots , {h} _t\), it is interpreted as separate agents with the same configuration (but possibly different inputs). In our use-case of CASE, this scenario is not relevant.

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Authors and Affiliations

  1. Coinbase, San Francisco, USA

    Shashank Agrawal

  2. IIT Madras, Chennai, India

    Shweta Agrawal

  3. IIT Bombay, Mumbai, India

    Manoj Prabhakaran, Rajeev Raghunath & Jayesh Singla

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  1. Shashank Agrawal
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  4. Rajeev Raghunath
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Correspondence to Shashank Agrawal .

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Editors and Affiliations

  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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Agrawal, S., Agrawal, S., Prabhakaran, M., Raghunath, R., Singla, J. (2023). CASE: A New Frontier in Public-Key Authenticated Encryption. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14370. Springer, Cham. https://doi.org/10.1007/978-3-031-48618-0_7

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