Bootstrapping Homomorphic Encryption via Functional Encryption

Nir Bitansky, Tomer Solomon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Homomorphic encryption is a central object in modern cryptography, with far-reaching applications. Constructions supporting homomorphic evaluation of arbitrary Boolean circuits have been known for over a decade, based on standard lattice assumptions. However, these constructions are leveled, meaning that they only support circuits up to some a-priori bounded depth. These leveled constructions can be bootstrapped into fully homomorphic ones, but this requires additional circular security assumptions, which are construction-dependent, and where reductions to standard lattice assumptions are no longer known. Alternative constructions are known based on indistinguishability obfuscation, which has been recently constructed under standard assumptions. However, this alternative requires subexponential hardness of the underlying primitives. We prove a new bootstrapping theorem based on functional encryption, which is known based on standard polynomial hardness assumptions. As a result we obtain the first fully homomorphic encryption scheme that avoids both circular security assumptions and super-polynomial hardness assumptions. The construction is secure against uniform adversaries, and can be made non-uniformly secure assuming a generalization of the time-hierarchy theorem, which follows for example from non-uniform ETH. At the heart of the construction is a new proof technique based on cryptographic puzzles and decomposable obfuscation. Unlike most cryptographic reductions, our security reduction does not fully treat the adversary as a black box, but rather makes explicit use of its running time (or circuit size).

Original languageEnglish
Title of host publication14th Innovations in Theoretical Computer Science Conference, ITCS 2023
EditorsYael Tauman Kalai
ISBN (Electronic)9783959772631
DOIs
StatePublished - 1 Jan 2023
Event14th Innovations in Theoretical Computer Science Conference, ITCS 2023 - Cambridge, United States
Duration: 10 Jan 202313 Jan 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume251

Conference

Conference14th Innovations in Theoretical Computer Science Conference, ITCS 2023
Country/TerritoryUnited States
CityCambridge
Period10/01/2313/01/23

Keywords

  • Cryptographic Puzzles
  • Fully Homomorphic Encryption
  • Polynomial Assumptions

All Science Journal Classification (ASJC) codes

  • Software

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