Amplifying the Security of Functional Encryption, Unconditionally 📺
Security amplification is a fundamental problem in cryptography. In this work, we study security amplification for functional encryption. We show two main results: - For any constant epsilon in (0,1), we can amplify an epsilon-secure FE scheme for P/poly which is secure against all polynomial sized adversaries to a fully secure FE scheme for P/poly, unconditionally. - For any constant epsilon in (0,1), we can amplify an epsilon-secure FE scheme for P/poly which is secure against subexponential sized adversaries to a subexponentially secure FE scheme for P/poly, unconditionally. Furthermore, both of our amplification results preserve compactness of the underlying FE scheme. Previously, amplification results for FE were only known assuming subexponentially secure LWE. Along the way, we introduce a new form of homomorphic secret sharing called set homomorphic secret sharing that may be of independent interest. Additionally, we introduce a new technique, which allows one to argue security amplification of nested primitives, and prove a general theorem that can be used to analyze the security amplification of parallel repetitions.