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

ASIACRYPT 2019: Advances in Cryptology – ASIACRYPT 2019 pp 112–141Cite as

Towards Attribute-Based Encryption for RAMs from LWE: Sub-linear Decryption, and More

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11921))

Abstract

Attribute based encryption (ABE) is an advanced encryption system with a built-in mechanism to generate keys associated with functions which in turn provide restricted access to encrypted data. Most of the known candidates of attribute based encryption model the functions as circuits. This results in significant efficiency bottlenecks, especially in the setting where the function associated with the ABE key is represented by a random access machine (RAM) and a database, with the runtime of the RAM program being sublinear in the database size. In this work we study the notion of attribute based encryption for random access machines (RAMs), introduced in the work of Goldwasser, Kalai, Popa, Vaikuntanathan and Zeldovich (Crypto 2013). We present a construction of attribute based encryption for RAMs satisfying sublinear decryption complexity assuming learning with errors; this is the first construction based on standard assumptions. Previously, Goldwasser et al. achieved this result based on non-falsifiable knowledge assumptions. We also consider a dual notion of ABE for RAMs, where the database is in the ciphertext and we show how to achieve this dual notion, albeit with large attribute keys, also based on learning with errors.

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Notes

  1. 1.

    All known lattice-based ABE for circuits [13] are based on the same assumption.

  2. 2.

    The works [6, 11] show implication of ABE for Turing machines (as defined in [6]) to succinct randomized encodings (Appendix A.5 in [11]).

  3. 3.

    All known lattice-based ABE for circuits [13] are based on the same assumption.

  4. 4.

    The formal definition of a RAM program can be found in the preliminaries.

  5. 5.

    An exception is the reusable garbling scheme of Goldwasser et al. [35], however their scheme only offers one-sided reusability: that is, their scheme only allows the adversary to get a single garbled circuit which can be reused across multiple input encodings. This is not useful in our setting since the adversary gets to query multiple keys. Moreover, just like any garbling scheme, even reusable garbled circuits require secret-key to perform the encoding operations.

  6. 6.

    \(\mathbf{A}_i^* + D[i] \mathbf{G}\) will be denoted by \(\mathbf{E_i}\) in the technical sections.

  7. 7.

    This would tantamount to obtaining two approximate encodings of the form \(\mathbf {s} (\mathbf {A}_i + b_i \cdot \mathbf {G})\) and \(\mathbf {s} (\mathbf {A}_i + b'_i \cdot \mathbf {G})\), where \(b_i\) is the old value and \(b'_i \) is the newly written value; assuming \(b'_i \ne b_i\), having these two encodings is sufficient to break LWE.

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Acknowledgements

We would like to thank the anonymous reviewers of Asiacrypt 2019 and Jiaxin Pan for helpful suggestions to improve the presentation of the paper. Xiong Fan is supported in part by IBM under Agreement 4915013672 and NSF Award CNS-1561209. Elaine Shi is supported by NSF Award CNS-1617676.

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  1. MIT CASIL, Boston, MA, USA

    Prabhanjan Ananth

  2. Cornell University, Ithaca, NY, USA

    Xiong Fan & Elaine Shi

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  1. University of Auckland, Auckland, New Zealand

    Steven D. Galbraith

  2. Security Fundamentals Lab, NICT, Tokyo, Japan

    Shiho Moriai

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Ananth, P., Fan, X., Shi, E. (2019). Towards Attribute-Based Encryption for RAMs from LWE: Sub-linear Decryption, and More. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11921. Springer, Cham. https://doi.org/10.1007/978-3-030-34578-5_5

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