Public Parameters as a First-Class Cost: A Three-Dimensional View of Updatable Vector Commitments, and a Group/Lattice Separation (opens in new tab)

Updatable vector commitments are judged by how a k-position update affects the broadcast update information S and the per-proof update time T. We promote the public-parameter size P to a first-class metric, systematize known schemes in the resulting three-dimensional (S,T,P) space, and prove that every linear group-model vector commitment with position-binding requires P at least N, while the lattice homomorphic Merkle tree is simultaneously sublinear-update and pp-succinct. This turns the em...