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Watermarking Public-Key Cryptographic Functionalities and Implementations

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Book cover Information Security (ISC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10599))

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Abstract

A watermarking scheme for a public-key cryptographic functionality enables the embedding of a mark in the instance of the secret-key algorithm such that the functionality of the original scheme is maintained, while it is infeasible for an adversary to remove the mark (unremovability) or mark a fresh object without the marking key (unforgeability). Cohen et al. [STOC’16] has provided constructions for watermarking arbitrary cryptographic functionalities; the resulting schemes rely on indistinguishability obfuscation (iO) and leave two important open questions: (i) the realization of both unremovability and unforgeability, and (ii) schemes the security of which reduces to simpler hardness assumptions than iO.

In this paper we provide a new definitional framework that distinguishes between watermarking cryptographic functionalities and implementations (think of ElGamal encryption being an implementation of the encryption functionality), while at the same time provides a meaningful relaxation of the watermarking model that enables both unremovability and unforgeability under minimal hardness assumptions. In this way we can answer questions regarding the ability to watermark a given implementation of a cryptographic functionality which is more refined compared to the question of whether a watermarked implementation functionality exists. Taking advantage of our new formulation we present the first constructions for watermarking public key encryption that achieve both unremovability and unforgeability under minimal hardness assumptions. Our first construction enables the watermarking of any public-key encryption implementation assuming only the existence of one-way functions for private key detection. Our second construction is at the functionality level and uses a stronger assumption (existence of identity-based encryption (IBE)) but supports public detection of the watermark.

F. Baldimtsi—Part of the work performed while at the National and Kapodistrian University of Athens.

A. Kiayias—Work partly performed at the National and Kapodistrian University of Athens, supported by ERC project CODAMODA #259152. Work partly supported by H2020 Project #653497, PANORAMIX.

K. Samari—Research supported by ERC project CODAMODA, # 259152..

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Notes

  1. 1.

    In [6] a similar relaxation of the marking algorithm is given, in the sense that the algorithm does not receive as input a specific circuit to be marked, but instead samples a key to be marked and returns it together with the marked circuit. However, their watermarking model is restricted to watermarking PRFs only.

  2. 2.

    This partition of the space to marked and unmarked programs is the reason why the impossibility result of [4] does not apply in our setting – applying iO to a marked program in our model would not remove the marking.

  3. 3.

    We consider protocols to also be described as a set of algorithms.

  4. 4.

    The marking algorithm, \(\mathsf {Mark}\), can output the distribution \(\mathcal {D}\) in the form of an algorithm that samples inputs for the circuit \(\widetilde{C}_1\).

  5. 5.

    Our proofs could also be extended for implementations which have a negligible decryption error.

  6. 6.

    In standard IBE the id of the user (i.e. email address or other unique identifier) serves as pk. Here, since id’s are just a short counter value one might want to extend them in some deterministic way - else f could also the identity function.

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Authors and Affiliations

  1. George Mason University, Fairfax, USA

    Foteini Baldimtsi

  2. University of Edinburgh and IOHK, Edinburgh, UK

    Aggelos Kiayias

  3. National and Kapodistrian University of Athens, Athens, Greece

    Katerina Samari

Authors
  1. Foteini Baldimtsi
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  2. Aggelos Kiayias
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  3. Katerina Samari
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Correspondence to Katerina Samari .

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Editors and Affiliations

  1. Inria, Tokyo, Japan

    Phong Q. Nguyen

  2. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

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Baldimtsi, F., Kiayias, A., Samari, K. (2017). Watermarking Public-Key Cryptographic Functionalities and Implementations. In: Nguyen, P., Zhou, J. (eds) Information Security. ISC 2017. Lecture Notes in Computer Science(), vol 10599. Springer, Cham. https://doi.org/10.1007/978-3-319-69659-1_10

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  • DOI: https://doi.org/10.1007/978-3-319-69659-1_10

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