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引言密码学中的古典维吉尼亚加密体制是大家所熟知的,并己被密码分析者们用诸如可能字、重复模式、及率频分析等工具所破。然而,从数学观点来研究维吉尼亚体制之间的等价关系是很有趣的,本文的目的就是进行这方面的研究,其结果虽然不难,但也并非像作者原先猜想那么容易。在相当长一段时间大家已经知道,等价于某给定维吉尼亚的另一维吉尼亚体制均可用抽取其字母的方法得到。本文的实际意义在于,在某些情况下,确实存在一些等价体制,不能用抽取的方法得到。本文是在有限域GF(q)上来讨论维吉尼亚体制,稍后的一篇文章将在整数模r环上来考察这类体制,这里r是大于1的任意正整数、可以予料,进一步考察的结果对以后我们计划要研究的更复杂的体制一例如希尔(Hill)体制和基于海波(Hebern)打字机的体制之间的等价关系将是很有价值的。
Introduction Classical Virginia cryptography in cryptography is well-known and has been broken by cryptanalysts using tools such as probable words, repetitive patterns, and rate-frequency analysis. However, it is interesting to study the equivalence between Virginia’s institutions from a mathematical point of view. The purpose of this article is to conduct research in this area. Although the results are not difficult, it is not as easy as the author originally conjectured. It has been known for quite some time that another Virginia equivalent to a given Virginia can be obtained by extracting its alphabets. The practical significance of this paper is that in some cases, some equivalence systems do exist and can not be obtained by decimation. This article discusses the Virginia system in the finite field GF (q), and a later article examines this type of system on an integer modular r-ring, where r is any positive integer greater than one and can be expected The results of the survey will be valuable for the later, more complicated regimes that we plan to study, such as the equivalence between the Hill regime and the Hebern typewriter-based regime.