(2026-04) (Mis)using the Lattice Isomorphism Problem. Cryptanalysis of the double-LIP and Construction of LIP-Based Blind Signatures
2026-04-13
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.