ABBA: Lattice-based Commitments from Commutators

Alberto Centelles; Andrew Mendelsohn

Paper 2026/148

ABBA: Lattice-based Commitments from Commutators

Alberto Centelles, Imperial College London, ICME Labs

Andrew Mendelsohn

, Imperial College London

Abstract

We study the cryptographic properties of sums of commutators of quaternions modulo $q$. We show that for certain parameters, the distribution of the sum of commutators of uniformly random elements with elements sampled from a discrete Gaussian is statistically close to uniform. We also give reductions from worst-case lattice problems such as SIVP to SIS-style problems defined using commutators on structured quaternionic lattices. Together these results indicate one-wayness and collision resistance of the sum-of-commutators function, under worst-case assumptions on lattices. We use this to develop a linearly homomorphic commitment scheme, dubbed `ABBA', which in many cases can be substituted for the widely-used Ajtai commitment scheme. We demonstrate the utility of the properties of commutation by replacing the Ajtai commitments used in Neo (a state-of-the-art folding scheme from lattices) with ABBA commitments, obtaining a 25% commitment size reduction and an almost equally efficient scheme.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. PQCrypto 2026
Keywords: SIS commutator quaternions commitments lattices
Contact author(s): alberto centelles22 @ imperial ac uk
am3518 @ ic ac uk
History: 2026-01-31: approved; 2026-01-30: received; See all versions
Short URL: https://ia.cr/2026/148
License: CC BY

BibTeX

@misc{cryptoeprint:2026/148,
      author = {Alberto Centelles and Andrew Mendelsohn},
      title = {{ABBA}: Lattice-based Commitments from Commutators},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/148},
      year = {2026},
      url = {https://eprint.iacr.org/2026/148}
}