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ABE for Circuits with Constant-Size Secret Keys and Adaptive Security

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13747))

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Abstract

An important theme in the research on attribute-based encryption (ABE) is minimizing the sizes of secret keys and ciphertexts. In this work, we present two new ABE schemes with constant-size secret keys, i.e., the key size is independent of the sizes of policies or attributes and dependent only on the security parameter \(\lambda \).

  • We construct the first key-policy ABE scheme for circuits with constant-size secret keys, \({|{\textsf{sk}}_f| = {\text {poly}}(\lambda )}\), which concretely consist of only three group elements. The previous state-of-the-art scheme by [Boneh et al., Eurocrypt ’14] has key size polynomial in the maximum depth d of the policy circuits, \({|{\textsf{sk}}_f| = {\text {poly}}(d,\lambda )}\). Our new scheme removes this dependency of key size on d while keeping the ciphertext size the same, which grows linearly in the attribute length and polynomially in the maximal depth, \({|{\textsf{ct}}_{{{\textbf{x}}}}| = |{{\textbf{x}}}|{\text {poly}}(d, \lambda )}\).

  • We present the first ciphertext-policy ABE scheme for Boolean formulae that simultaneously has constant-size keys and succinct ciphertexts of size independent of the policy formulae, namely, \({|{\textsf{sk}}_f| = {\text {poly}}(\lambda )}\) and \({|{\textsf{ct}}_{{{\textbf{x}}}}| = {\text {poly}}(|{{\textbf{x}}}|, \lambda )}\). Concretely, each secret key consists of only two group elements. Previous ciphertext-policy ABE schemes either have succinct ciphertexts but non-constant-size keys [Agrawal–Yamada, Eurocrypt ’20, Agrawal–Wichs–Yamada, TCC ’20], or constant-size keys but large ciphertexts that grow with the policy size as well as the attribute length. Our second construction is the first ABE scheme achieving double succinctness, where both keys and ciphertexts are smaller than the corresponding attributes and policies tied to them.

Our constructions feature new ways of combining lattices with pairing groups for building ABE and are proven selectively secure based on LWE and in the generic (pairing) group model. We further show that when replacing the LWE assumption with its adaptive variant introduced in [Quach–Wee–Wichs FOCS ’18], the constructions become adaptively secure.

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Notes

  1. 1.

    We always ignore polynomial factors in the security parameter.

  2. 2.

    When working with lattices, it is more convenient to indicate authorization of decryption by zero, thus the negation of \(C({{\textbf{x}}})\).

  3. 3.

    This truncation only introduces an exponentially small statistical error.

  4. 4.

    It is stronger in that it is adaptive, but weaker in that the shares are not necessarily pseudorandom.

  5. 5.

    We use \(f({{\textbf{x}}})=0\) to express authorization.

  6. 6.

    There are \(2|{{\textbf{x}}}|+2\) shares, so the total share size is linear in the length of \({{\textbf{x}}}\).

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Acknowledgement

The authors were supported by NSF grants CNS-1528178, CNS-1929901, CNS-1936825 (CAREER), CNS-2026774, a Hellman Fellowship, a JP Morgan AI Research Award, the Defense Advanced Research Projects Agency (DARPA) and Army Research Office (ARO) under Contract No. W911NF-15-C-0236, and a subcontract No. 2017-002 through Galois. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government. The authors thank the anonymous reviewers for their valuable comments

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Authors and Affiliations

  1. Paul G. Allen School of Computer Science & Engineering, University of Washington, Seattle, USA

    Hanjun Li, Huijia Lin & Ji Luo

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  1. Hanjun Li
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Correspondence to Hanjun Li , Huijia Lin or Ji Luo .

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  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Li, H., Lin, H., Luo, J. (2022). ABE for Circuits with Constant-Size Secret Keys and Adaptive Security. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13747. Springer, Cham. https://doi.org/10.1007/978-3-031-22318-1_24

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