CAJ | 학술논문

探讨频率测度论在保密通信中的应用，研究单钥密码系统中加密变换非线性性质的相关问题。针对目前常见分组密码算法在非线性性质方面缺乏理论规范描述和严格证明的现状，探讨一般单钥密码系统中非线性加密变换严格的数学描述和实现方法。利用频率测度论中的不相关概念，引入不相关单钥密码系统这一新概念，指出这类不相关基本单钥密码系统的存在性，并在理论上严格证明了强大数定律，即在利用不相关基本单钥密码系统进行所有可能的保密通信过程中，当明文单元序列服从离散无记忆均匀分布且密钥周期性更换时，明文序列与密文序列将必然不相关。
탐토빈솔측도론재보밀통신중적응용，연구단약밀마계통중가밀변환비선성성질적상관문제。침대목전상견분조밀마산법재비선성성질방면결핍이론규범묘술화엄격증명적현상，탐토일반단약밀마계통중비선성가밀변환엄격적수학묘술화실현방법。이용빈솔측도론중적불상관개념，인입불상관단약밀마계통저일신개념，지출저류불상관기본단약밀마계통적존재성，병재이론상엄격증명료강대수정률，즉재이용불상관기본단약밀마계통진행소유가능적보밀통신과정중，당명문단원서렬복종리산무기억균균분포차밀약주기성경환시，명문서렬여밀문서렬장필연불상관。
This paper explores applications of frequency measure theory in secrecy communication systems and studies the nonlinearity of encryption transformation in one-key cryptosystems. Aiming at the lack of normative description and strict demonstration in the theory for the nonlinearity of familiar block cipher systems, we introduce a strict mathematical definition and its implementation on nonlinear encryption transformation in general one-key cryptosystems. Based on the notion of irrelevance in the frequency measure theory, we propose a new definition called “irrelevant one-key cryptosystem” and testify to the existence of irrelevant basic one-key cryptosystems. In addition, we prove the following strong law of large numbers theoretically: sequences of message units and their corresponding cryptograph units are certainly irrelevant in probability 1 for any periodic sequence of secret keys on condition that the sequence of message units has a discrete memoryless uniform distribution during the secrecy communication process when an irrelevant basic one-key cryptosystem is used to transmit all possible messages secretly.