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Title:
The Brave New World of Global Generic Groups and UC-Secure Zero-Overhead SNARKs
Authors: Jan Bobolz, Pooya Farshim, Markulf Kohlweiss, Akira Takahashi
Abstract:The universal composability (UC) model provides strong security guarantees for protocols used in arbitrary contexts. While these guarantees are highly desirable, in practice, schemes with a standalone proof of security, such as the Groth16 proof system, are preferred. This is because UC security typically comes with undesirable overhead, sometimes making UC-secure schemes significantly less efficient than their standalone counterparts. We establish the UC security of Groth16 without any significant overhead. In the spirit of global random oracles, we design a global (restricted) observable generic group functionality that models a natural notion of observability: computations that trace back to group elements derived from generators of other sessions are observable. This notion turns out to be surprisingly subtle to formalize. We provide a general framework for proving protocols secure in the presence of global generic groups, which we then apply to Groth16.
ePrint: https://eprint.iacr.org/2024/818
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