Résumé
Multi-input functional encryption is a primitive that allows for the evaluation of an & ell;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-ary function over multiple ciphertexts, without learning any information about the underlying plaintexts. This type of computation is useful in many cases where one has to compute over encrypted data, such as privacy-preserving cloud services, federated learning, or more generally delegation of computation from multiple clients. It has recently been shown by Alborch et al. in PETS '24 to be useful to construct a randomized functional encryption scheme for obtaining differentially private data analysis over an encrypted database supporting linear queries. In this work we propose the first secret-key multi-input quadratic functional encryption scheme satisfying simulation security. Current constructions supporting quadratic functionalities, proposed by Agrawal et al. in CRYPTO '21 and TCC '22, only reach indistinguishibility-based security. Our proposed construction is generic, and for a concrete instantiation, we propose a new function-hiding inner-product functional encryption scheme proven simulation secure against one challenge ciphertext in the standard model, which is of independent interest. We then use these two results to construct an efficient randomized quadratic functional encryption scheme, from which we obtain differentially private data analysis over an encrypted database supporting quadratic queries. Finally, we give and fully benchmark an implementation of the randomized scheme. This work is an extended version of the paper "Simulation Secure Multi-Input Quadratic Functional Encryption" at SAC '24, where the multi-input quadratic functional encryption scheme and function-hiding inner-product functional encryption schemes were first presented (Section 3 and Section 4).