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Fully Secure Attribute-Based Encryption for t-CNF from LWE

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Book cover Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

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Abstract

Attribute-based Encryption (ABE), first introduced by [SW05, GPSW06], is a public key encryption system that can support multiple users with varying decryption permissions. One of the main properties of such schemes is the supported function class of policies. While there are fully secure constructions from bilinear maps for a fairly large class of policies, the situation with lattice-based constructions is less satisfactory and many efforts were made to close this gap. Prior to this work the only known fully secure lattice construction was for the class of point functions (also known as IBE).

In this work we construct for the first time a lattice-based (ciphertext-policy) ABE scheme for the function class t-CNF, which consists of CNF formulas where each clause depends on at most t bits of the input, for any constant t. This class includes NP-verification policies, bit-fixing policies and t-threshold policies. Towards this goal we also construct a fully secure single-key constrained PRF from OWF for the same function class, which might be of independent interest.

Supported by the Israel Science Foundation (Grant No. 468/14), Binational Science Foundation (Grants No. 2016726, 2014276), and by the European Union Horizon 2020 Research and Innovation Program via ERC Project REACT (Grant 756482) and via Project PROMETHEUS (Grant 780701).

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Notes

  1. 1.

    In key-policy ABE the policies are attached to the keys and the attributes are attached to the ciphertexts.

  2. 2.

    For all \(n \in \mathbb {Z}\) and \(v \in \{0,1\}^n\) the term \(v \otimes \mathbf {G}\) denotes a tensor product of the binary row-vector \(v=(v_1,\dots ,v_n)\) and the matrix \(\mathbf {G}\). That is, \(v \otimes \mathbf {G}= [v_1\cdot \mathbf {G}\Vert \dots \Vert v_n \cdot \mathbf {G}]\).

  3. 3.

    Previous works used an ABE definition where the decryption succeeds conditioned on \(f(x)=0\), while we require that \(f(x)=1\). Note that in our scheme the decryption succeeds conditioned on \(f(x) = 1 \wedge r \ne r'\), i.e. \(f(x) = 1 \wedge I_r(r') = 0\).

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Acknowledgements

We thank Sina Shiehian for pointing out that the construction in Sect. 4 can be initialized with a polynomial modulus q whenever the depth of the conforming cPRF is logarithmic, which in turn implies that a low-depth PRF from LWE with a polynomial modulus suffices to derive an ABE construction for t-CNF with similar parameters.

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  1. Weizmann Institute of Science, Rehovot, Israel

    Rotem Tsabary

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  1. Rotem Tsabary
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Correspondence to Rotem Tsabary .

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  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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Tsabary, R. (2019). Fully Secure Attribute-Based Encryption for t-CNF from LWE. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11692. Springer, Cham. https://doi.org/10.1007/978-3-030-26948-7_3

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