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Individual Cryptography

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14082))

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Abstract

We initiate a formal study of individual cryptography. Informally speaking, an algorithm \(\textsf{Alg}\) is individual if, in every implementation of \(\textsf{Alg}\), there always exists an individual user with full knowledge of the cryptographic data S used by \(\textsf{Alg}\). In particular, it should be infeasible to design implementations of this algorithm that would hide S by distributing it between a group of parties using an MPC protocol or outsourcing it to a trusted execution environment.

We define and construct two primitives in this model. The first one, called proofs of individual knowledge, is a tool for proving that a given message is fully known to a single (“individual”) machine on the Internet, i.e., it cannot be shared between a group of parties. The second one, dubbed individual secret sharing, is a scheme for sharing a secret S between a group of parties so that the parties have no knowledge of S as long as they do not reconstruct it. The reconstruction ensures that if the shareholders attempt to collude, one of them will learn the secret entirely. Individual secret sharing has applications for preventing collusion in secret sharing. A central technique for constructing individual cryptographic primitives is the concept of MPC hardness. MPC hardness precludes an adversary from completing a cryptographic task in a distributed fashion within a specific time frame.

This result is part of a project that received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 and Horizon Europe research and innovation programs (grants PROCONTRA-885666 and CRYPTOLAYER-101044770). This work was also partly supported by the National Science Centre, Poland, under research project No. 463393, by the German Research Foundation (DFG) via the DFG CRC 1119 CROSSING (project S7), by the German Federal Ministry of Education and Research and the Hessen State Ministry for Higher Education, Research and the Arts within their joint support of the National Research Center for Applied Cybersecurity ATHENE.

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Notes

  1. 1.

    We note that a similar (but more involved) idea has been used in a recent work of Mangipudi et al. to construct a collusion-deterrent threshold information escrow [27].

  2. 2.

    Recall that in this case, the sub-adversary \(\mathcal{A}_j\) can take full control over the account of the user, which was something that a malicious user tries to avoid.

  3. 3.

    It is easy to see that in case of our protocol \(\pi ^{\rho ,\sigma }_\textsf{PIK}\) (see Fig. 1) the only message that may contain sensitive information about S is \((W^1,\ldots ,W^\kappa )\) sent by the prover to the verifier in Step 3. Hence, it is enough if only this message is encrypted.

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Acknowledgments

We would like to thank the anonymous Crypto reviewers for their helpful comments, especially for pointing out to use the fact the need to model the pre-processing attacks.

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Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski & Tomasz Lizurej

  2. IDEAS NCBR, Warsaw, Poland

    Stefan Dziembowski & Tomasz Lizurej

  3. TU Darmstadt, Darmstadt, Germany

    Sebastian Faust

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  1. Stefan Dziembowski
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Correspondence to Stefan Dziembowski .

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  1. Rambus Inc., San Jose, CA, USA

    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Dziembowski, S., Faust, S., Lizurej, T. (2023). Individual Cryptography. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14082. Springer, Cham. https://doi.org/10.1007/978-3-031-38545-2_18

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  • DOI: https://doi.org/10.1007/978-3-031-38545-2_18

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