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Multi-Client Functional Encryption for Linear Functions in the Standard Model from LWE

Authors:
Benoît Libert
Radu Ţiţiu
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DOI: 10.1007/978-3-030-34618-8_18
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Abstract: Multi-client functional encryption (MCFE) allows ℓ clients to encrypt ciphertexts (Ct,1,Ct,2,…,Ct,ℓ) under some label. Each client can encrypt his own data Xi for a label t using a private encryption key eki issued by a trusted authority in such a way that, as long as all Ct,i share the same label t, an evaluator endowed with a functional key dkf can evaluate f(X1,X2,…,Xℓ) without learning anything else on the underlying plaintexts Xi. Functional decryption keys can be derived by the central authority using the master secret key. Under the Decision Diffie-Hellman assumption, Chotard et al. (Asiacrypt 2018) recently described an adaptively secure MCFE scheme for the evaluation of linear functions over the integers. They also gave a decentralized variant (DMCFE) of their scheme which does not rely on a centralized authority, but rather allows encryptors to issue functional secret keys in a distributed manner. While efficient, their constructions both rely on random oracles in their security analysis. In this paper, we build a standard-model MCFE scheme for the same functionality and prove it fully secure under adaptive corruptions. Our proof relies on the Learning-With-Errors (LWE) assumption and does not require the random oracle model. We also provide a decentralized variant of our scheme, which we prove secure in the static corruption setting (but for adaptively chosen messages) under the LWE assumption.
BibTeX
@article{asiacrypt-2019-30072,
  title={Multi-Client Functional Encryption for Linear Functions in the Standard Model from LWE},
  booktitle={Advances in Cryptology – ASIACRYPT 2019},
  series={Advances in Cryptology – ASIACRYPT 2019},
  publisher={Springer},
  volume={11923},
  pages={520-551},
  doi={10.1007/978-3-030-34618-8_18},
  author={Benoît Libert and Radu Ţiţiu},
  year=2019
}