Weakness in quaternion signatures

This note continues a sequence of attempts to define efficient digital signature schemes based on low-degree polynomials, or to break such schemes. We consider a scheme proposed by Satoh and Araki [5], which generalizes the Ong-Schnorr-Shamir scheme to the noncommutative ring of quaternions. We give two different ways to break the scheme. © 2001 International Association for Cryptologic Research.