Paper 2022/659

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

Hanjun Li, University of Washington
Huijia Lin, University of Washington
Ji Luo, University of Washington
Abstract

An important theme in research on attribute-based encryption (ABE) is minimizing the sizes of the secret keys and ciphertexts. In this work, we present two new ABE schemes with *constant-size* secret keys, that is, 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, |sk_f|=poly(lambda), which concretely consist of only three group elements. The previous state-of-the-art construction by [Boneh et al., Eurocrypt '14] has key size polynomial in the maximum depth d of the policy circuits, |sk_f|=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, |ct|=|x|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, in particular, |sk_f|=poly(lambda) and |ct_x|=poly(|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.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint.
Keywords
attribute-based encryptioninner-product functional encryptionlatticespairinggeneric group model
Contact author(s)
hanjul @ cs washington edu
rachel @ cs washington edu
luoji @ cs washington edu
History
2022-05-31: approved
2022-05-27: received
See all versions
Short URL
https://ia.cr/2022/659
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/659,
      author = {Hanjun Li and Huijia Lin and Ji Luo},
      title = {{ABE} for Circuits with Constant-Size Secret Keys and Adaptive Security},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/659},
      year = {2022},
      url = {https://eprint.iacr.org/2022/659}
}
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