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How to Obfuscate Programs Directly

  • Joe ZimmermanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9057)

Abstract

We propose a new way to obfuscate programs, via composite-order multilinear maps. Our construction operates directly on straight-line programs (arithmetic circuits), rather than converting them to matrix branching programs as in other known approaches. This yields considerable efficiency improvements. For an NC\(^1\) circuit of size \(s\) and depth \(d\), with \(n\) inputs, we require only \(O(d^2s^2 + n^2)\) multilinear map operations to evaluate the obfuscated circuit—as compared with other known approaches, for which the number of operations is exponential in \(d\). We prove virtual black-box (VBB) security for our construction in a generic model of multilinear maps of hidden composite order, extending previous models for the prime-order setting.

Our scheme works either with “noisy” multilinear maps, which can only evaluate expressions of degree \(\lambda ^c\) for pre-specified constant \(c\); or with “clean” multilinear maps, which can evaluate arbitrary expressions. With “noisy” maps, our new obfuscator applies only to NC\(^1\) circuits, requiring the additional assumption of FHE in order to bootstrap to P/poly (as in other obfuscation constructions). From “clean” multilinear maps, on the other hand (whose existence is still open), we present the first approach that would achieve obfuscation for P/poly directly, without FHE.

Our construction is efficient enough that if “clean” multilinear maps were known, then general-purpose program obfuscation could become implementable in practice. Our results demonstrate that the question of “clean” multilinear maps is not a technicality, but a central open problem.

Keywords

Full Version Chinese Remainder Theorem Arithmetic Circuit Boolean Circuit Ring Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA

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