An algebraic key-exposure attack on the digital signature HAWK

Hawk is a post-quantum signature scheme. The security and efficiency of its most recent version are primarily based on the structured variant of a problem known as the lattice isomorphism problem (the module variant Module-LIP). We propose an attack on Hawk when one of the four coefficients of the signing key is leaked. This attack combines algebraic methods with side-channel exploitations. The proposed attack running time is a polynomial in the degree of the cyclotomic number field.