Functional Encryption for Turing Machines

Abstract

In this work, we construct an adaptively secure functional encryption for Turing machines scheme, based on indistinguishability obfuscation for circuits. Our work places no restrictions on the types of Turing machines that can be associated with each secret key, in the sense that the Turing machines can accept inputs of unbounded length, and there is no limit to the description size or the space complexity of the Turing machines. Prior to our work, only special cases of this result were known, or stronger assumptions were required. More specifically, previous work implicitly achieved selectively secure FE for Turing machines with a-priori bounded input based on indistinguishability obfuscation STOC 2015, or achieved FE for general Turing machines only based on knowledge-type assumptions such as public-coin differing-inputs obfuscation TCC 2015. A consequence of our result is the first constructions of succinct adaptively secure garbling schemes even for circuits in the standard model. Prior succinct garbling schemes even for circuits were only known to be adaptively secure in the random oracle model.