Paper 2026/722 Original: eprint.iacr.org/2026/722 ↗
(Mis)using the Lattice Isomorphism Problem. Cryptanalysis of the double-LIP and Construction of LIP-Based Blind Signatures
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.
- History
- 2026-04-20: last updated
- 2026-04-13: published
- Short URL
- https://ia.cr/2026/722
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}