G-GG — Generic group, global observable variant; bilinear types 1–3

G-GG (Generic group, global observable variant; bilinear types 1–3) is part of Idealized Setup and Resources in the UC functionality encyclopedia. Status: an idealized setup assumption or shared resource.

This functionality had no reference at all until a 2024 paper on the global, restricted-observable generic group model — it stands to the plain generic group exactly as G-RO stands to F-RO, and establishes UC security of a deployed zero-knowledge proof system without asymptotic overhead. Bilinear-group models are treated as folding into this functionality, since a bilinear group is a generic group with a pairing and the observable global functionality generalizes both.

References:

• Bobolz et al. The brave new world of global generic groups and UC-secure zero-overhead SNARKs. In 22nd Theory of Cryptography Conference (TCC), Part I, volume 15364 of LNCS, pages 90–124, 2024.