基于保形迭代深度问题的公钥密码体制

Public Key Cryptosystem Based on the Conformal Iterative Depth Problem

提出了一种新的公钥密码体制,其安全性主要在于多变元非线性保形迭代函数A(x)的迭代深度问题,可进行密钥分配、加密和数字签名.第一类A(x)为有限域上的有理分式组,其分子和分母均为线性多项式;第二类A(x)为有限域上的有理分式组,其分子或分母有非线性多项式;第三类A(x)为有限环上的非线性多项式组.构造第二、三类A(x)的方法是:先运用二层迭代建立关于系数变量的不定方程组T,再用T的一组特解建立A(x).其独特的编码风格表现为代数意义上的分形(fractal):每个未知元的局部都具有与函数整体相似的结构,而把函数展开、化简后,其函数爆炸方式的规律性就会消失.

In this paper, a new public key cryptosystem is developed. Its security is based on the problem of finding the depth of multivariate nonlinear conformal iterative function A（x）. The scheme can be used for key distributing, encryption and digital signature. In the first class A（x） is the rational fraction function over finite field in which the denominator and numerator are linear polynomials. In the secondclass A（x） is the rational fraction function over finite field in which the denominator and/or numerator are nonlinear polynomials. In the third class A（x） is the nonlinear polynomials over finite ring. The method of constructing A（x） in the latter two classes is： first, to construct indeterminate equations T about coefficient by exercising two-level iterative, then to construct A（x） by using a set of particular solutions of T. Its distinctive encoding style is known as a fractal construction from the view point of algebraic： the local structure of each variable is similar to the structure of global function. However, after expansion and reduction of the function, the traces left after explosion of the function will disappear.