Paper 2026/2872

On the Security of the Cubic UOV Variant CML

Abstract

CML is a cubic multivariate signature scheme proposed over $\mathbb{F}_q$ with $q = 2^8$. Earlier cubic Oil--Vinegar variants such as CUOV and CSSv were broken by differential and high-rank attacks. CML adds an $\ell$-invertible cycle system and a secret position-hiding map to hide the cubic positions. We show that the cubic homogeneous parts of the public key span a space of dimension at most two, so a publicly derived output combination has degree at most two. After restriction to the oil-direction space, the polar matrices of the publicly derived quadratic components span rank-two matrices associated with the edges of a path. This structure yields a procedure for recovering an equivalent key. Our implementation recovered an equivalent key in under 5~minutes for each tested parameter set, including the set targeting 256-bit security.