Cryptology ePrint Archive: Report 2020/951

Amplifying the Security of Functional Encryption, Unconditionally

Aayush Jain and Alexis Korb and Nathan Manohar and Amit Sahai

Abstract: 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.

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


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