Abstract
We present a general framework for constructing attribute-based encryption (ABE) schemes for arbitrary function class based on lattices from two ingredients, i) a noisy linear secret sharing scheme for the class and ii) a new type of inner-product functional encryption (IPFE) scheme, termed evasive IPFE, which we introduce in this work. We propose lattice-based evasive IPFE schemes and establish their security under simple conditions based on variants of evasive learning with errors (LWE) assumption recently proposed by Wee [EUROCRYPT ’22] and Tsabary [CRYPTO ’22].
Our general framework is modular and conceptually simple, reducing the task of constructing ABE to that of constructing noisy linear secret sharing schemes, a more lightweight primitive. The versatility of our framework is demonstrated by three new ABE schemes based on variants of the evasive LWE assumption.
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We obtain two ciphertext-policy ABE schemes for all polynomial-size circuits with a predetermined depth bound. One of these schemes has succinct ciphertexts and secret keys, of size polynomial in the depth bound, rather than the circuit size. This eliminates the need for tensor LWE, another new assumption, from the previous state-of-the-art construction by Wee [EUROCRYPT ’22].
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We develop ciphertext-policy and key-policy ABE schemes for deterministic finite automata (DFA) and logspace Turing machines (\(\textsf{L}\)). They are the first lattice-based public-key ABE schemes supporting uniform models of computation. Previous lattice-based schemes for uniform computation were limited to the secret-key setting or offered only weaker security against bounded collusion.
Lastly, the new primitive of evasive IPFE serves as the lattice-based counterpart of pairing-based IPFE, enabling the application of techniques developed in pairing-based ABE constructions to lattice-based constructions. We believe it is of independent interest and may find other applications.
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Notes
- 1.
The reductions in this work do not “increase non-uniformity”. Samplers, considered in many security definitions in this work, are a part of the adversary.
- 2.
The terminology is changed from “secret sharing” in introduction and technical overview, because the policy function might not be monotone.
- 3.
Precisely speaking, \(r_\textsf{GenF}\) conditioned on the sampled matrices must be efficiently sampleable given those matrices (with negligible statistical error), e.g., when the matrices are just the bits read sequentially from \(r_\textsf{GenF}\). This ensures that no sampled matrix has a known trapdoor, and is important because \(r_\textsf{GenF}\) is incorporated into the sampler’s randomness in a security proof.
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Acknowledgment
The authors were supported by NSF grants CNS-1936825 (CAREER), CNS-2026774, a JP Morgan AI Research Award, a Cisco Research Award, and a Simons Collaboration on the Theory of Algorithmic Fairness. The views expressed are those of the authors and do not reflect the official policy or position of the funding agencies. The authors thank the anonymous reviewers of Eurocrypt 2024 for their valuable comments.
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Hsieh, YC., Lin, H., Luo, J. (2024). A General Framework for Lattice-Based ABE Using Evasive Inner-Product Functional Encryption. In: Joye, M., Leander, G. (eds) Advances in Cryptology – EUROCRYPT 2024. EUROCRYPT 2024. Lecture Notes in Computer Science, vol 14652. Springer, Cham. https://doi.org/10.1007/978-3-031-58723-8_15
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