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Paper: 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 $$\ell $$ clients to encrypt ciphertexts $$(\mathbf {C}_{t,1},\mathbf {C}_{t,2},\ldots ,\mathbf {C}_{t,\ell })$$ under some label. Each client can encrypt his own data $$X_i$$ for a label t using a private encryption key $$\mathsf {ek}_i$$ issued by a trusted authority in such a way that, as long as all $$\mathbf {C}_{t,i}$$ share the same label t, an evaluator endowed with a functional key $$\mathsf {dk}_f$$ can evaluate $$f(X_1,X_2,\ldots ,X_\ell )$$ without learning anything else on the underlying plaintexts $$X_i$$. 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 ($$\mathsf {LWE}$$) 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 $$\mathsf {LWE}$$ 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
}