International Association for Cryptologic Research

International Association
for Cryptologic Research


Owen Chen


New Differential-Algebraic Attacks and Reparametrization of Rainbow
A recently proposed class of multivariate quadratic schemes, the Rainbow-Like signature Schemes, in which successive sets of central variables are obtained from previous ones by solving linear equations, seem to lead to efficient schemes (TTS, TRMS, and Rainbow) that perform well on systems of low computational resources. Recently SFLASH ($C^{\ast-}$) was broken by Dubois, Fouque, Shamir, and Stern via a differential attack. In this paper, we exhibit similar attacks based on differentials, that will reduce published Rainbow-like schemes below their security levels. We will present a new type of construction of Rainbow-Like schemes and design signature schemes with new parameters for practical applications.
Breaking the Symmetry: a Way to Resist the New Differential Attack
Sflash had recently been broken by Dubois, Stern, Shamir, etc., using a differential attack on the public key. The $C^{\ast-}$ signature schemes are hence no longer practical. In this paper, we will study the new attack from the point view of symmetry, then (1) present a simple concept (projection) to modify several multivariate schemes to resist the new attacks; (2) demonstrate with practical examples that this simple method could work well; and (3) show that the same discussion of attack-and-defence applies to other big-field multivariates. The speed of encryption schemes is not affected, and we can still have a big-field multivariate signatures resisting the new differential attacks with speeds comparable to Sflash.