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.
Category / Keywords: foundations / Functional encryption, security amplification Original Publication (with major differences): IACR-CRYPTO-2020 Date: received 4 Aug 2020, last revised 4 Aug 2020 Contact author: aayushjain at cs ucla edu,alexiskorb@cs ucla edu,nmanohar@cs ucla edu,sahai@cs ucla edu Available format(s): PDF | BibTeX Citation Version: 20200811:113321 (All versions of this report) Short URL: ia.cr/2020/951