[Resource Topic] 2020/951: Amplifying the Security of Functional Encryption, Unconditionally

Welcome to the resource topic for 2020/951

Title:
Amplifying the Security of Functional Encryption, Unconditionally

Authors: Aayush Jain, Alexis Korb, Nathan Manohar, 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.

ePrint: https://eprint.iacr.org/2020/951

Talk: https://www.youtube.com/watch?v=SUtkFHIbZiw

Slides: https://iacr.org/submit/files/slides/2020/crypto/crypto2020/131/slides.pdf

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