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Public Immunization Against Complete Subversion Without Random Oracles

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Applied Cryptography and Network Security (ACNS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11464))

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Abstract

We seek constructions of general-purpose immunizers that take arbitrary cryptographic primitives, and transform them into ones that withstand a powerful “malicious but proud” adversary, who attempts to break security by possibly subverting the implementation of all algorithms (including the immunizer itself!), while trying not to be detected. This question is motivated by the recent evidence of cryptographic schemes being intentionally weakened, or designed together with hidden backdoors, e.g., with the scope of mass surveillance.

Our main result is a subversion-secure immunizer in the plain model (assuming collision-resistant hashing), that works for a fairly large class of deterministic primitives, i.e., cryptoschemes where a secret (but tamperable) random source is used to generate the keys and the public parameters, whereas all other algorithms are deterministic. The immunizer relies on an additional independent source of public randomness, which is used to sample a public seed. While the public source is untamperable, the subversion of all other algorithms is allowed to depend on it.

Previous work in the area only obtained subversion-secure immunization for very restricted classes of primitives, often in weaker models of subversion and relying on random oracles, or by leveraging a higher number of independent random sources.

B. Magri—The author was supported by the Concordium Blockchain Research Center, Aarhus University, Denmark.

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Notes

  1. 1.

    The PRG was standardized by NIST in 2006, and later withdrawn in 2014 as it was including a potential backdoor allowing to predict future outputs of the PRG algorithm.

  2. 2.

    One can imagine even more powerful watchdogs monitoring public transcripts while being given the user’s secret keys; these are known as omniscent watchdogs, but will not be considered in this paper.

  3. 3.

    The string \(\textit{pk}\) might be empty for secret-key primitives.

  4. 4.

    The case of stateful subversion can be reduced to that of stateless subversion if we assume that watchdogs are allowed to reset the state of a tested implementation, a trick due to [23].

  5. 5.

    In particular, the result of [15] applies to all unpredictability primitives, and all indistinguishability primitives meeting so-called square security.

  6. 6.

    Hence, our results do not cover, e.g., multi-instance games where several public parameters and keys might be generated.

  7. 7.

    We assume the amount of randomness to generate the public parameters and the keys is the same; a generalization is straightforward.

  8. 8.

    For instance, if \(\varPi \) is a signature scheme, correctness demands that honestly computed signatures (w.r.t. a valid secret key) always verify correctly (w.r.t. the corresponding public key).

  9. 9.

    Of course, we could also treat the detection game as an indistinguishability game \(\mathbf {G}= (\mathsf {C},\gamma )\), and thus define the detection advantage as a function of \(\gamma = 1/2\). However, we prefer the above formulation in order to be consistent with previous work [23, 24].

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Author information

Authors and Affiliations

  1. Stevens Institute of Technology, Hoboken, NJ, USA

    Giuseppe Ateniese & Danilo Francati

  2. Department of Computer Science, Aarhus University, Aarhus, Denmark

    Bernardo Magri

  3. Department of Computer Science, Sapienza University of Rome, Rome, Italy

    Daniele Venturi

Authors
  1. Giuseppe Ateniese
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  2. Danilo Francati
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  3. Bernardo Magri
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  4. Daniele Venturi
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Corresponding author

Correspondence to Danilo Francati .

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Editors and Affiliations

  1. Singapore Management University, Singapore, Singapore

    Robert H. Deng

  2. Universidad del Rosario, Bogota, Colombia

    Valérie Gauthier-Umaña

  3. Cyxtera Technologies, Bogota, Colombia

    Martín Ochoa

  4. Columbia University, New York, NY, USA

    Moti Yung

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Ateniese, G., Francati, D., Magri, B., Venturi, D. (2019). Public Immunization Against Complete Subversion Without Random Oracles. In: Deng, R., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2019. Lecture Notes in Computer Science(), vol 11464. Springer, Cham. https://doi.org/10.1007/978-3-030-21568-2_23

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  • DOI: https://doi.org/10.1007/978-3-030-21568-2_23

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