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

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.

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