频率不相关性及其在单钥密码系统中的应用

Frequency irrelevance and its applications in one-key cryptosystems

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.

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.