Public Parameters as a First-Class Cost: A Three-Dimensional View of Updatable Vector Commitments, and a Group/Lattice Separation

Kefan Liu

Paper 2026/1280

Public Parameters as a First-Class Cost: A Three-Dimensional View of Updatable Vector Commitments, and a Group/Lattice Separation

Kefan Liu

, Nanyang Technological University

Abstract

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 empirical group/lattice gap into a theorem, and we show the new axis is orthogonal to known lower bounds.

Note: Initial version

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: vector commitments updatable commitments public parameters generic group model lower bounds
Contact author(s): KEFAN001 @ e ntu edu sg
History: 2026-06-20: approved; 2026-06-18: received; See all versions
Short URL: https://ia.cr/2026/1280
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1280,
      author = {Kefan Liu},
      title = {Public Parameters as a First-Class Cost: A Three-Dimensional View of Updatable Vector Commitments, and a Group/Lattice Separation},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1280},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1280}
}