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International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2022: Advances in Cryptology – ASIACRYPT 2022 pp 160–194Cite as

Collusion-Resistant Functional Encryption for RAMs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13791))

Abstract

In recent years, functional encryption (FE) has established itself as one of the fundamental primitives in cryptography. The choice of model of computation to represent the functions associated with the functional keys plays a critical role in the complexity of the algorithms of an FE scheme. Historically, the functions are represented as circuits. However, this results in the decryption time of the FE scheme growing proportional to not only the worst case running time of the function but also the size of the input, which in many applications can be quite large.

In this work, we present the first construction of a public-key collusion-resistant FE scheme, where the functions, associated with the keys, are represented as random access machines (RAMs). We base the security of our construction on the existence of: (i) public-key collusion-resistant FE for circuits and, (ii) public-key doubly-efficient private-information retrieval [Boyle et al., Canetti et al., TCC 2017]. Our scheme enjoys many nice efficiency properties, including input-specific decryption time.

We also show how to achieve FE for RAMs in the bounded-key setting with weaker efficiency guarantees from laconic oblivious transfer, which can be based on standard cryptographic assumptions. En route to achieving our result, we present conceptually simpler constructions of succinct garbling for RAMs [Canetti et al., Chen et al., ITCS 2016] from weaker assumptions.

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Notes

  1. 1.

    Note that the work of [36] also construct an FE for RAMs scheme in the bounded-key setting: however, the decryption time of the bounded-key FE scheme grows polynomially in the database size and thus doesn’t enjoy the sublinear decryption runtime property that we desire.

  2. 2.

    The security notion we consider in this work is indistinguishability-based (IND-based) selective security. We delve more on this when we formally define FE for RAMs in the technical sections.

  3. 3.

    In fact, we define a stronger version called succinct reusable garbled RAM; this notion implies succinct garbled RAM.

  4. 4.

    In the technical sections, we use indistinguishability obfuscation for circuits with logarithmic inputs to construct succinct reusable garbled RAMs. However, it has been shown [49] that iO for logarithmic inputs is equivalent to collusion-resistant functional encryption for circuits.

  5. 5.

    We note that the parallel notion we consider here is also different from the notion considered by the works of constructing garbled parallel RAM [13, 23, 25, 50], in particular, we consider the setting where each agent can compute a different program in parallel, while garbled parallel RAMs consider the setting where multiple CPUs/agents jointly compute a single program to speed up the computation.

  6. 6.

    To be precise, [42] shows that traditional ORAM schemes are insecure in the parallel reusability setting. This correspondingly means that the garbled RAMs schemes building upon these ORAM schemes would correspondingly be insecure in the parallel setting.

  7. 7.

    A program obfuscation is a compiler that transforms a program P into a functionally equivalent program that hides all the implementation details of the original program. In the technical sections, we use a specific definition of obfuscation, called indistinguishability obfuscation.

  8. 8.

    The terminology of local simulation is only introduced for the benefit of describing our techniques and will be implicit in our security proof.

  9. 9.

    In general these two notions are not equivalent: in our setting, they are equivalent since we only consider programs with boolean outputs.

  10. 10.

    \([\tau _k,\tau _{k+1})\) denotes the contents of the random tape starting from \(\tau _k^{th}\) position to \((\tau _{k+1}-1)^{th}\) position.

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Acknowledgement

We than Shota Yamada and anonymous ASIACRYPT 2022 reviewers for improving our work. Luowen Qian is supported by DARPA under Agreement No. HR00112020023.

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Authors and Affiliations

  1. UC Santa Barbara, Santa Barbara, CA, USA

    Prabhanjan Ananth

  2. Academia Sinica, Taipei, Taiwan

    Kai-Min Chung

  3. Rutgers University, Piscataway, NJ, USA

    Xiong Fan

  4. Boston University, Boston, MA, USA

    Luowen Qian

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  1. Prabhanjan Ananth
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  2. Kai-Min Chung
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  4. Luowen Qian
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Correspondence to Prabhanjan Ananth .

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Editors and Affiliations

  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Ananth, P., Chung, KM., Fan, X., Qian, L. (2022). Collusion-Resistant Functional Encryption for RAMs. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_6

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