New differential-algebraic attacks and reparametrization of rainbow

Authors:
Jintai Ding;Bo-Yin Yang;Chia-Hsin Owen Chen;Ming-Shing Chen;Chen-Mou Cheng
Affiliations:
Dept. of Mathematical Sciences, University of Cincinnati;IIS, Academia Sinica, Taiwan;IIS, Academia Sinica, Taiwan;IIS, Academia Sinica, Taiwan;Dept. of Elec. Eng., Nat'l Taiwan University, Taiwan
Venue:
ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
Year:
2008

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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 efficient 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 differential attack. In this paper, we exhibit similar algebraic and diffential 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.