Adaptive Security in SNARGs via iO and Lossy Functions

We construct an adaptively sound SNARGs in the plain model with CRS relying on the assumptions of (subexponential) indistinguishability obfuscation (iO), subexponential one-way functions and a notion of lossy functions we call length parameterized lossy functions. Length parameterized lossy functions take in separate security and input length parameters and have the property that the function image size in lossy mode depends only on the security parameter. We then show a novel way of constructing such functions from the Learning with Errors (LWE) assumption.

Our work provides an alternative path towards achieving adaptively secure SNARGs from the recent work of Waters and Wu. Their work required the use of (essentially) perfectly re-randomizable one way functions (in addition to obfuscation). Such functions are only currently known to be realizable from assumptions such as discrete log or factoring that are known to not hold in a quantum setting.