Obfuscating circuits via composite-order graded encoding

Benny Applebaum, Zvika Brakerski

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

Abstract

We present a candidate obfuscator based on composite-order Graded Encoding Schemes (GES), which are a generalization of multilinear maps. Our obfuscator operates on circuits directly without converting them into formulas or branching programs as was done in previous solutions. As a result, the time and size complexity of the obfuscated program, measured by the number of GES elements, is directly proportional to the circuit complexity of the program being obfuscated. This improves upon previous constructions whose complexity was related to the formula or branching program size. Known instantiations of Graded Encoding Schemes allow us to obfuscate circuit classes of polynomial degree, which include for example families of circuits of logarithmic depth. We prove that our obfuscator is secure against a class of generic algebraic attacks, formulated by a generic graded encoding model. We further consider a more robust model which provides more power to the adversary and extend our results to this setting as well. As a secondary contribution, we define a new simple notion of algebraic security (which was implicit in previous works) and show that it captures standard security relative to an ideal GES oracle.

Original languageEnglish
Title of host publicationTheory of Cryptography - 12th Theory of Cryptography Conference, TCC 2015, Proceedings
EditorsYevgeniy Dodis, Jesper Buus Nielsen
PublisherSpringer Verlag
Pages528-556
Number of pages29
ISBN (Electronic)9783662464960
DOIs
StatePublished - 2015
Event12th Theory of Cryptography Conference, TCC 2015 - Warsaw, Poland
Duration: 23 Mar 201525 Mar 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9015
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th Theory of Cryptography Conference, TCC 2015
Country/TerritoryPoland
CityWarsaw
Period23/03/1525/03/15

Funding

FundersFunder number
Israel Science Foundation468/14

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