CWI Cryptology Group

Abstract: This summer, the signature scheme HAWK, which is based on the Lattice Isomorphism Problem (LIP), suffered from multiple new attacks. One attack by Anthropic reduced HAWK's security by almost 50% [SW26], and HAWK withdrew from NIST's on-ramp standardization process. In this presentation, I will explain the last part of this attack, which is a specific case of a general theorem around lattice automorphisms [vGP25]. Namely, we show if an adversary has any nontrivial automorphism of the underlying integer lattice, that they can reduce search rank-2 module-LIP, over a cyclotomic ring of degree a power of two to a LIP instance of at most half the rank. Hence, knowledge of such a nontrivial automorphism speeds up the key recovery attack on HAWK at least quadratically. Additionally, we also show which specific automorphism is constructed in Anthropic's attack. [SW26] Z. Straznickas and S.A. Weis. HAWK-n Key Recovery Reduces to SVP in Dimension n/2+1. https://eprint.iacr.org/2026/1593 [vGP25] D.M.H. van Gent and L.N. Pulles. HAWK: Having Automorphisms Weakens Key. https://doi.org/10.62056/a3qjp2w9p

Abstract: Lattice-based cryptography plays a central role in the migration to post-quantum cryptography, highlighting the importance of understanding the hardness of the underlying lattice problems. In this talk, I will present joint work from my PhD research that focuses on the Short Integer Solution problem (SIS), which is a foundational lattice problem underlying the NIST standard ML-DSA. I will describe a classical algorithm for solving nontrivial instances of SIS in subexponential time, using a strategy inspired by Wagner’s algorithm combined with discrete-Gaussian techniques. Time permitting, I will discuss ongoing work extending this approach to LWE.

Abstract: We study the spinor genus, a classification of quadratic forms in the context of cryptography based on the lattice isomorphism problem (LIP). The spinor genus lies between the genus and the equivalence class, thereby refining the concept of genus. For the special case of binary forms over certain number fields, we offer an efficient quantum algorithm to test if two forms lie in the same spinor genus. Finally, we present a quantum polynomial-time attack on a digital signature scheme DEFI based on indefinite quadratic forms.