1970-01-01

(2026-02) Investigating the Wedge Map on SNOVA

• [[Po-En Tseng]]
• [[Lih-Chung Wang]]
• [[Peigen Li]]
• [[Yen-Liang Kuan]]

2026-02-14

• #cryptography
• #paper

Abstract

This paper investigates the algebraic structure of SNOVA, a NIST PQC Round 2 candidate, with a specific focus on the kernel dimension of the wedge map. We employ lifting techniques to transform the public key from the matrix ring $\mathbb{F}_q^{l \times l}$ to an equivalent representation over the extension field $\mathbb{F}_{q^l}$, establishing that the rank of the wedge map is a structural invariant. A key contribution of this work is the derivation of a generating function that explicitly characterizes the wedge map's kernel dimension. This algebraic analysis provides a rigorous understanding of SNOVA's geometry, verifying the safety of specific parameter sets and enabling future refined adjustments to guarantee structural security.