Multi-Input Functional Encryption.
Shafi Goldwasser, Vipul Goyal, Abhishek Jain, Amit Sahai · 2013
We introduce the problem of Multi-Input Functional Encryption, where a secret key SKf can correspond to an n-ary function f that takes multiple ciphertexts as input. Multi-input functional encryption is a general tool for computing on encrypting data which allows for mining aggregate information from several different data sources (rather than just a single source as in single input functional encryption). We show wide applications of this primitive to running SQL queries over encrypted database, non-interactive differentially private data release, delegation of computation, etc. We formulate both indistinguishability-based and simulation-based definitions of security for this notion, and show close connections with indistinguishability and virtual black-box def-initions of obfuscation. Assuming indistinguishability obfuscation for circuits, we present con-structions achieving indistinguishability security for a large class of settings. We show how to modify this construction to achieve simulation-based security as well, in those settings where simulation security is possible. Assuming differing-inputs obfuscation [Barak et al., FOCS’01], we also provide a construction with similar security guarantees as above, but where the keys and ciphertexts are compact.