New Classes of Public Key Cryptosystems Constructed on the Basis of Low-Density Multivariate Polynomials: Along with K(Ⅰ)-Knapsack Scheme

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ー基底攻撃、パタリン攻撃等々に耐性がないことが知られている。本稿では低密度、すなわち項数を削減した多次多変数多項式に基づく多次多変数公開鍵暗号を構成している。公開鍵サイズを比較的小さくしたまま、変数の総数を大とすることが可能となり、グレブナー攻撃に対し強い耐性を有することが期待される。付録にK（Ⅰ）ナップザックスキームを与える。%Extensive studies have been made of the public key cryptosystems based on multivariate polynomials over F_2 and also F_2m. However most of the proposed public key cryptosystems based on multivariate polynomials, are proved not secure. In this paper, we construct random multivariate polynomials with relatively small number of terms which will be referred to as low-density multivariate polynomials. We show that the proposed scheme referred to as K(V)·RSE(g)PKC can be secure against the possible attacks, particularly Groebner basis attack. In Appendix, we present a new cryptographic scheme, referred to as K (Ⅰ)·Knapsack Scheme that can be applied to a wide class of knapsack PKCs.