(Mis)using the Lattice Isomorphism Problem. Cryptanalysis of the double-LIP and Construction of LIP-Based Blind Signatures

Veronika Kuchta; Francesco Sica

Paper 2026/722

(Mis)using the Lattice Isomorphism Problem. Cryptanalysis of the double-LIP and Construction of LIP-Based Blind Signatures

Veronika Kuchta

, Florida Atlantic University

Francesco Sica

, Florida Atlantic University

Abstract

We explore the design of blind schemes based on the Lattice Isomorphism Problem (LIP), a recently proposed group-action-based assumption for post-quantum cryptography. Our work highlights both the potential and the limitations of LIP-based constructions. In particular, we analyze the Abe–Okamoto framework and demonstrate that it does not yield a secure instantiation under LIP. We further present an attack on the double LIP problem, allowing from two generic distinct instances of a LIP problem to recover the secret unimodular matrix. Finally, we propose a new blind signature scheme that combines LIP with the Closest Vector Problem (CVP) and a modular version of the Short Integer Solution (SIS) problem, offering a fresh direction for lattice-based blind constructions.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: cryptanalysis lattice-isomorphism problem blind signatures
Contact author(s): vkuchta @ fau edu
sicaf @ fau edu
History: 2026-04-20: revised; 2026-04-13: received; See all versions
Short URL: https://ia.cr/2026/722
License: CC BY

BibTeX

@misc{cryptoeprint:2026/722,
      author = {Veronika Kuchta and Francesco Sica},
      title = {(Mis)using the Lattice Isomorphism Problem. Cryptanalysis of the double-{LIP} and Construction of {LIP}-Based Blind Signatures},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/722},
      year = {2026},
      url = {https://eprint.iacr.org/2026/722}
}