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有界单向函数是一个新的密码学概念.有界单向函数是为了研究设计更为灵活、更实用的密码系统的基础而提出的.该文的作者在以前的文章中,对有界单向函数与一般单向函数的关系进行了探讨,从而得到一般单向函数的一个刻画.由于单向函数的存在性与计算机科学中一系列重要未决的问题相联系,其本身的存在性是一个未决的问题.有界单向函数的研究对一般单向函数存在性的研究提供了一个新的途径.从它们之间的关系来看,如果对任意正整数c,存在c-单向函数,那么一定存在单向函数.鉴于现代密码学对单向函数的依赖性,对单向函数的存在性的研究具有重要的意义.该文进一步探讨有界单向函数的困难性.由于单向函数的存在性被规约到了有界单向函数的存在性,该文章着眼于固定的有界单向函数的研究.文中的主要结果是:对任意正整数c,存在一个被称为关于所有c-有界单向函数的通用c-有界算法,满足对于充分大的n,这个算法求逆的成功概率是所有c-有界算法求逆的成功概率的上界.从而给出了一个关于c-单向函数的刻画.
The bounded one-way function is a new concept of cryptography. The bounded one-way function is proposed to study the basis for designing a more flexible and practical cryptosystem. In the previous article, The relationship between one-way function and general one-way function is discussed, and a characterization of general one-way function is obtained.As the existence of one-way function is connected with a series of important outstanding problems in computer science, its own existence Is a pending issue.The study of bounded one-way function provides a new way for the study of the existence of general one-way function.From the relationship between them, if for any positive integer c, there exists c- To the function, then there must be a one-way function.Considering the dependence of modern cryptography on the one-way function, the study of the existence of one-way function is of great significance.This paper further discusses the difficulty of the one-way function The existence of a one-way function is formalized to the existence of a bounded one-way function, which focuses on the study of a fixed, bounded one-way function. The main result of this paper is that for any positive integer c, The universal c-bounded algorithm for all c-bounded one-way functions, which satisfies the success probability of inversion of this algorithm for a sufficiently large n, is the upper bound of the success probability of all c-bounded algorithms inversions. A description of the c-one-way function.