The Matsumoto-Imai Cryptosystem

This chapter describes the Matsumoto-Imai cryptosystem, which is one of the oldest multivariate public key cryptosystems. After introducing the plain scheme, we discuss its cryptanalysis by the linearization equations attack of Patarin. We then consider variants of the basic scheme which are immune against this attack. In the area of encryption schemes, these are the PMI and PMI+ schemes, which are obtained by a concept named internal perturbation and the plus modifier. In the area of signature schemes based on MI, we present the MI-Minus or SFlash scheme and its extension PFlash.