维吉尼亚密码

姓名：罗杰 学号：20131003139 班号：121131 指导老师：左博新

摘要：维吉利亚密码是人们在单一恺撒密码的基础上扩展出多表密码，也是世

界上运用最多的，最经典的加密方法。

关键词：维吉利亚密码，密码学。 一：维吉尼亚密码介绍：

1. 什么是维吉利亚密码：

维吉尼亚密码是人们在单一恺撒密码的基础上扩展出多表密码。该方法最早记录在吉奥万·巴蒂斯塔·贝拉索（ Giovan Battista Bellaso）于1553年所著的书《吉奥万·巴蒂斯塔·贝拉索先生的密码》。

2. 维吉尼亚密码的体制：

为讨论维吉利亚密码，我们需要首先建立26个英文字母和0-25这26个数字的对应关系，如表1.

m 是一个正整数。定义p = e = k ={0,1, 2…25},是元素个数为m 的子集, p 代表明文,e 代表密文, k 代表密钥。

加密函数:(x 1 , x 2 , … , x m)= (x 1 + k 1 , x 2 + k 2 , … ,x m + km) 解密函数:(y 1 , y 2 , … , y m)=(y 1 -k 1 , y 2 -k 2 , … , ym- k m) 密钥k =(k 1 , k 2 , … , k m).

二：维吉尼亚密码实例：

通过选取密钥，我们将所给明文翻译为以下密文 密钥：（a,s,y）

所以得到的密文为：

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三：维吉尼亚密码破译理论分析

虽然维吉尼亚密码在凯撒密码的基础上有了很大的提升，但仍旧被证明是可以破译的。维吉尼亚密码的优势在于这种密码被假定为它将不同位置的字母进行不同的加密。一段文字里的同一个单词可能由于对应的密钥的不同而呈现不同的密文，为破译增加了难度，但终究还是会有同样的单词背翻译成同样的密文的时候，通过求取两个相同字母的间隔得出密钥的倍数。最后通过多次求取能得出密钥长度，再通过日常概率分析，将字母出现的频率与表二对比，找出密钥。

表二：频率表

四：维吉尼亚密码的改进

1. 改进方案：

维吉尼亚密码是针对一维的凯撒密码，通过增加维数，使得每一个字母所对应的密码表存在一定的差异，但由于密钥的长度有限，使得存

在同一字母对应同一密钥表的情况，从而使翻译成文了有可能事件，倘若我们将密钥变为无限长的一组数，那么破译的难度就明显增加了。

我们可以选取π的小数点位的数作为密钥，即0.314159……..作为密码的密钥k=（1.4.1.5.9.2.6………）

这样一来密钥的长度就是无限的，破译人就没办法通过确定密钥的长度来试图破解密码了。 2. 改进分析

通过运用π的无线不循环的数字对原文进行加密可以有效的避免被计算出密钥长度，但与此同时的，运用这类数字极大的加大了运算和加密的过程，无限小数的运用，极大的增大的整个程序的计算量。

五：总结

维吉尼亚密码表使人类密码学上的一次进步，也是密码学的基础。随着现代科学的发展，计算机的广泛应用，使得密码学得到了进一步的发展，在维吉尼亚密码的基础上，人们研究出了更具备安全性的密码——MD5、RSA、DES等。密码的存在是为了保证信息的安全，现代社会对于互联网的重视使得密码学有着广阔的发展空间。

参考文献

1. Douglas R.Stinsio n.密码学原理与实践[ M] .第二版.冯登国, 译.北京:电子

工业出版设, 2003 .9 .

2. 马晓荣，吴小雷 西安航空技术高等专科学校学报[M]。2007.3