New Classes of Public Key Cryptosystem Constructed on the Basis of Multivariate Polynomials and Random Coding: Another class of K(Ⅲ)RSE(g)PKC

摘要

多次多変数型公開鍵暗号について従来数多くの提案がなされている。しかしその多くはグレブナ一基底攻撃，パタリン攻撃等々に耐性がないことが示されている。本稿では1次→多次変換の部分をメッセージに依存して変化させるという新しい着想に基づいて多次多変数型公開鍵暗号を構成している。グレブナー攻撃に如し強い耐性を有することが期待される。さらに付垂剥こおいて新しい多次多変数型公開鍵暗号を提案している．%The present author proposed a new class of Public-Key Cryptosystem (PKC) based on Random Simultaneous Equation of degree g(RSE(g)PKC) reffered to as K(Ⅲ)RSE(g)PKC [1]. The proposed schemes use a new class of trap-doors based on two classes of transformation, i.e. random transformation and message-dependent random transformation. For constructing the proposed scheme, two random transformations φ and χ are used. The transformation φ would yield a breakthrough to a field of multivaliate cryptosystem in a sense that φ is dependent on a message. Namely it is a time variant transformation on the basis of random coding. In this paper, we present a new class of RSE(g)PKC based on K(Ⅲ)RSE(g)PKC. We present several examples and show that the proposed PKC's, can be secure against the various excellent attacks such as Grobner basis attack, Patarin's attack and Braeken-Wolf-Preneel attacks, due to the random transformations using new trap-doors. We present several examples of K(Ⅲ)RSE(g)PKC whose public key takes on a smaller value compared with the conventional SE(g)PKC(Examples 3 and 4).