一、Vigenere密码简介

信息代码:X=(x1,x2,…,xd)∈(Z/26)d
密钥:K=(k1,k2,…,kd) ∈(Z/26)d
加密函数:E(x)=X+K=( x1+k1,x2+k2,…,xd+kd);
解密函数: D(x)=X-K=( x1-k1,x2-k2,…,xd-kd);
其实，vigenere密码本身也是一种凯撒挪移密码，但是比起凯撒密码，这个密码存在比较难确定的两个因素:区域长度d的选定和密钥K向量;但是，这种密码并非不可破解，而且破解思路也比较简单(如果不深究其中深刻的数学原理)，接下来给出破解思路和代码实现:

**

二、一些公用代码:

**
求模函数:

public class OperationUtil {
       /** * @param start * @param end exclude * @param result * @return */
       public static int mod(int start,int end,int result) {
             int res;
             int difference=end-start;
             int resultFromStart=result-start;
             res=start+resultFromStart%difference;
             while(res<start) {
                    res+=difference;
             }
             return res;
       }

}

       //把文本text分成""+text[0]+text[0+keyLength]...+,""+text[1]+text[1+keyLength]+...,..如
       //此分组    
       public static ArrayList<String> groupText(String text, int keyLength) {
             ArrayList<String> groups = new ArrayList<String>();
             for (int i = 0; i < keyLength; ++i) {
                    StringBuilder tempGroup = new StringBuilder();
                    for (int j = 0; i + j * keyLength < text.length(); ++j) {
                           tempGroup.append(text.charAt(i + j * keyLength));
                    }
                    groups.add(tempGroup.toString());
             }
             return groups;
       }

    /** * 计算密文字母频率向量和统计字母使用频率向量左旋g的内积 * @param frequencies * 密文字母频率 * @param w * 统计字母使用频率 * @param g * 左旋步长 * @param subTextLength * 区域段密文长度 * @return 拟重合指数 */
       public static double transvection(Map<Character, Integer> frequencies, double[] w, int g, int subTextLength) {
             double MG = 0.0D;
             for (char ch = 'A'; ch <= 'Z'; ++ch) {
                    // int的除法
                    double fi = frequencies.get(ch) * 1.0 / subTextLength;
                    int index = OperationUtil.mod(0, 26, ch - 'A' - g);
                    MG += fi * w[index];
             }
             return MG;
       }

吻合指数计算方法[图片来源《密码学–加密演算法》]

       /** * 计算吻合指数 * @param wordMap 字符频率映射表 * @param textLength groupText产生每个分组的长度 * @return */
       public static double calculateCoincidence(Map<Character, Integer> wordMap, int textLength) {
             double IC = 0.0D;
             double denominator = Math.pow((double) textLength, 2);
             for (int k = 0; k < 26; ++k) {
                    double frequency = (double) wordMap.get((char) (k + 65));
                    IC += frequency * (frequency - 1);
             }
             IC /= denominator;
             return IC;
       }

    /** * 统计每个字符出现次数 * @param text groupText分组文本 * @return */
       public static Map<Character, Integer> countEveryWord(String text) {
             Map<Character, Integer> map = new HashMap<>();
             for (int i = 0; i < 26; ++i) {
                    map.put((char) (i + 65), 0);
             }

             for (int i = 0; i < text.length(); ++i) {
                    char current = text.charAt(i);
                    int frenquency = map.get(current) + 1;
                    map.put(current, frenquency);
             }
             return map;
       }

三、求出密钥长度

大致思路:在猜测最大密钥长度范围内找出平均重合指数最大的密钥长度

      /** * Friedman解密 * @param text 密文 * @param guess 猜测密钥最大长度 * @return 密钥长度 */
       public static int Friedman(String text,int guess) {
             // 重合指数
             double[] Ic = null;
             // 平均重合指数
             double avgIc = 0;
             // 密文分组
             ArrayList<String> groups=null;
             double max=0;
             int keyLength=0;
             // 可能密钥长度
             int possibleLength = 1;

             while (possibleLength<=guess) {
                    Ic = new double[possibleLength];
                    avgIc = 0;

                    // 1 先根据密钥长度分组
                    groups = groupText(text, possibleLength);
                    // 2 再计算每一组的重合指数
                    for (int i = 0; i < possibleLength; ++i) {
                           String subCipher = groups.get(i); // 子串
                           Map<Character, Integer> frequencies = countEveryWord(subCipher);
                           Ic[i] = calculateCoincidence(frequencies, subCipher.length());
                    }

                    for (int i = 0; i < possibleLength; ++i) {
                           avgIc += Ic[i];
                    }
                    avgIc /= (double) possibleLength;
                    //求最大重合指数
                    if (avgIc >= max) {
                           max=avgIc;
                           keyLength=possibleLength;
                    }
                    possibleLength++;
             }
             return keyLength;
       }

四、确定密钥

大致思路:因为字母移位周期为26，所以就相当于在26中寻找密文频率比例和字母统计频率内积值最大的就是密钥

      /** * 重合指数获取密钥 * @param keyLength 密钥长度 * @param text 密文 * @return 密钥 */
       public static int[] decryptCipher(int keyLength, String text) {
             int[] key = new int[keyLength];
             //字母常用频率分布表
             double[] probability = new double[] { 0.082, 0.015, 0.028, 0.043, 0.127, 0.022, 0.02, 0.061, 0.07, 0.002, 0.008,
                           0.04, 0.024, 0.067, 0.075, 0.019, 0.001, 0.06, 0.063, 0.091, 0.028, 0.01, 0.023, 0.001, 0.02, 0.001 };
             ArrayList<String> groups = groupText(text, keyLength);
             for (int i = 0; i < keyLength; ++i) {
                    double MG;
                    double maxMG=0;
                    for (int g=0;g<26;++g) {
                           MG = 0;
                           String subCipher = groups.get(i);
                           Map<Character, Integer> frequencies = countEveryWord(subCipher);
                           MG = transvection(frequencies, probability, g, subCipher.length());
                           if (MG >= maxMG) {
                                 maxMG=MG;
                                 key[i] = g;
                           }
                    }
             }

             return key;
       }

五、根据密钥得出明文

    public static String decrypt(String text,int[]keys) {
             StringBuilder plainText=new StringBuilder();
             for (int i=0;i<text.length();++i) {
                    plainText.append((char)OperationUtil.mod(65, 91, text.charAt(i)-keys[i%keys.length]));
             }## 标题 ##
             return plainText.toString();
       }

六、测试文本

OCWYIKOOONIWUGPMXWKTZDWG
TSSAYJZWYEMDLBNQAAAVSUWD
VBRFLAUPLOOUBFGQHGCSCMGZ
LATOEDCSDEIDPBHTMUOVPIEK
IFPIMFNOAMVLPQFXEJSMXMPG
KCCAYKWFZPYUAVTELWHRHMWK
BBVGTGUVTEFJLODFEFKVPXSG
RSORVGTAJBSAUHZRZALKWUOW
HGEDEFNSWMRCIWCPAAAVOGPD
NFPKTDBALSISURLNPSJYEATC
UCEESOHHDARKHWOTIKBROQRD
FMZGHGUCEBVGWCDQXGPBGQWL
PBDAYLOOQDMUHBDQGMYWEUIK

密钥:7,14,11,12,4,18
真实密钥:7,14,11,12,4,10
最后一个误差可以通过考虑单词特征纠错
本文参考《密码学-加密演算法》，如有错误，欢迎指正