Paper 2020/1042

Candidate Obfuscation via Oblivious LWE Sampling

Hoeteck Wee and Daniel Wichs

Abstract

We present a new, simple candidate construction of indistinguishability obfuscation (iO). Our scheme is inspired by lattices and learning-with-errors (LWE) techniques, but we are unable to prove security under a standard assumption. Instead, we formulate a new falsifiable assumption under which the scheme is secure. Furthermore, the scheme plausibly achieves post-quantum security. Our construction is based on the recent "split FHE" framework of Brakerski, Döttling, Garg, and Malavolta (EUROCRYPT '20), and we provide a new instantiation of this framework. As a first step, we construct an iO scheme that is provably secure assuming that LWE holds \emph{and} that it is possible to obliviously generate LWE samples without knowing the corresponding secrets. We define a precise notion of oblivious LWE sampling that suffices for the construction. It is known how to obliviously sample from any distribution (in a very strong sense) using iO, and our result provides a converse, showing that the ability to obliviously sample from the specific LWE distribution (in a much weaker sense) already also implies iO. As a second step, we give a heuristic contraction of oblivious LWE sampling. On a very high level, we do this by homomorphically generating pseudoradnom LWE samples using an encrypted pseudorandom function.