New Differential-Algebraic Attacks and Reparametrization of Rainbow

1 Dept. of Mathematical Sciences, University of Cincinnati, USA, [email protected] 2 IIS, Academia Sinica, Taiwan, [byyang,owenhsin,mschen]@iis.sinica.edu.tw 3 Dept. of Elec. Eng., Nat'l Taiwan University, Taiwan, [email protected] Abstract. A recently proposed class of multivariate Public-Key Cryptosystems, the Rainbow-Like Digital Signature Schemes, in which successive sets of central variables are obtained from previous ones by solving linear equations, seem to lead to e cient schemes (TTS, TRMS, and Rainbow) that perform well on systems of low computational resources. Recently SFLASH (C∗−) was broken by Dubois, Fouque, Shamir, and Stern via a di erential attack. In this paper, we exhibit similar algebraic and di ential attacks, that will reduce published Rainbow-like schemes below their security levels. We will also discuss how parameters for Rainbow and TTS schemes should be chosen for practical applications.