Obfuscation of Probabilistic Circuits and Applications

This paper studies the question of how to define, construct, and use obfuscators for probabilistic programs. Such obfuscators compile a possibly randomized program into a deterministic one, which achieves computationally indistinguishable behavior from the original program as long as it is run on each input at most once. For obfuscation, we propose a notion that extends indistinguishability obfuscation to probabilistic circuits: It should be hard to distinguish between the obfuscations of any two circuits whose output distributions at each input are computationally indistinguishable, possibly in presence of some auxiliary input. We call the resulting notion probabilistic indistinguishability obfuscation (pIO). We define several variants of pIO, using different approaches to formalizing the above security requirement, and study non-trivial relations among them. Moreover, we give a construction of one of our pIO variants from sub-exponentially hard indistinguishability obfuscation (for deterministic circuits) and one-way functions, and conjecture this construction to be a good candidate for other pIO variants. We then move on to show a number of applications of pIO: • We give a general and natural methodology to achieve leveled homomorphic encryptio