Indistinguishability Obfuscation from Compact Functional Encryption

Prabhanjan Ananth, Abhishek Jain

Published Aug 14, 2016• 0 citations

Abstract

The arrival of indistinguishability obfuscation (iO) has transformed the cryptographic land-scape by enabling several security goals that were previously beyond our reach. Consequently, one of the pressing goals currently is to construct iO from well-studied standard cryptographic assumptions. In this work, we make progress in this direction by presenting a reduction from iO to a natural form of public-key functional encryption (FE). Specifically, we construct iO for general functions from any single-key FE scheme for NC1 that achieves selective, indistinguishability security against sub-exponential time adversaries. Further, the FE scheme should be compact, namely, the running time of the encryption algorithm must only be a polynomial in the security parameter and the input message length (and not in the function description size or its output length). We achieve this result by developing a novel arity amplification technique to transform FE for single-ary functions into FE for multi-ary functions (aka multi-input FE). Instantiating our approach with known, non-compact FE schemes, we obtain the first constructions of multi-input FE for constant-ary functions based on standard assumptions. Finally, as a result of independent interest, we construct a compact FE scheme from ran-domized encodings for Turing machines and learning with errors assumption.

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