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 (FE). We show two main results:

1. For any constant epsilon in (0,1), we can amplify any FE scheme for P/poly which is epsilon-secure against all polynomial sized adversaries to a fully secure FE scheme for P/poly, unconditionally.

2. For any constant epsilon in (0,1), we can amplify any FE scheme for P/poly which is epsilon-secure against subexponential sized adversaries to a fully 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.