Lower Bounds on Transparent Vector Commitments

Master’s thesis, ETH Zürich, Fall 2025
Supervised by Prof. Dr. Dennis Hofheinz and Dr. Emanuele Giunta

Abstract

We prove a lower bound on the size of commitments and openings of algebraic vector commitment (VC) schemes with transparent public parameters (i.e. only uniformly random group elements) in Maurer’s Generic Group Model with pairings. We also provide a VC scheme with pairings that beats the lower bound for schemes without pairings, although a gap remains between the construction and the lower bound with pairings.