如何在找到密钥时终止凯撒密码暴力破解程序

我写了一个能根据输入偏移量完成凯撒密码加解密的程序，核心功能已经实现，但暴力破解模块遇到了麻烦——没法找到通用的最优终止条件。目前只能针对已知密钥为17的测试用例写临时判断逻辑，想实现一个适用于所有输入的方案，让程序在破解出有效英文语句或正确密钥时自动终止。

以下是我的C++代码：

char decrypt(char letter, int key);

int main(){
  // Part 3 Brute-Force Attack
  std::string ciphertext;
  
  std::cout << "Enter in the ciphertext: ";
  std::getline(std::cin, ciphertext);

  std::cout << "\nBrute-Force Decryptions:" << std::endl;

  int i = 0;
  int keyCode = 0;
  std::string gang = "";
  int alphaArray[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24};
  
  // The algorithm has nested for each loops, the first one keeps track of the key initialized to           0
  // and the second loop goes through the string given and converts it to the proper value based
  // on the shift key. The reason we want to find 't', 'h' or 'e' is because this signifies the 
  // begginning of an actual English sentence, and most likely our cracked message. I was able to 
  // determine this would begin the correct string we are looking for by bruteforcing the first      // few letters using pencil and paper 
  
  for(auto key : alphaArray){
    std::cout << "\nkey = " << key << ":\t";
    for(auto letter : ciphertext){
      letter = decrypt(letter, i);
      gang += letter;
    }
    std::cout << gang << std::endl;
    if (tolower(ciphertext[0]) - key + 26 == 't' && tolower(ciphertext[1]) - key == 'h' && tolower(ciphertext[2]) - key == 'e'){
      keyCode = key;
      break;
    }
    i++;
    gang = "";
  }

  // Output results

  std::cout << "\nPart 3 KeyCode: " << keyCode << std::endl;
  std::cout << "\n\n";

  return 0;
}

//////////////////////////////////////////////////////////////////////////////////////
// Function: Attempts to decrypt letter by shifting it up the alphabet 'key' times   /
// Params: Letter as a char and key as an int value                                  /
// Return: Letter shifted 'key' times                                                /
//////////////////////////////////////////////////////////////////////////////////////
char decrypt(char letter, int key){
  int position = (letter - key - 'A') % 26;
  if(position < 0)
      position += 26;
  return (char)position + 'a';
}

程序运行输出：

Brute-Force Decryptions:

key = 0:    kyvtjyzwkttzgyvitzjtrcjftbefnetrjtkyvttrvjrittzgyviftrwkvitalczljttrvjriftnyftivglkvucptljvutkyvttzgyvitkftgrjjtdvjjrxvjtkftyzjtkiffgjtulizextyzjtdzczkripttrdgrzxejtzetxrlchtefkvtkyrktkyvttrvjrittzgyvitzjtvrjzcpttirtbvutsptkyvtsilkvgwfitvtrkkrtbh

key = 1:    jxusixyvjssyfxuhsyisqbiesademdsqisjxussquiqhssyfxuhesqvjuhszkbykissquiqhesmxeshufkjutboskiutsjxussyfxuhsjesfqiiscuiiqwuisjesxyisjheefistkhydwsxyiscybyjqhossqcfqywdisydswqkbgsdejusjxqjsjxussquiqhssyfxuhsyisuqiybosshqsautsrosjxusrhkjufvehsusqjjqsag

key = 2:    iwtrhwxuirrxewtgrxhrpahdrzcdlcrphriwtrrpthpgrrxewtgdrpuitgryjaxjhrrpthpgdrlwdrgtejitsanrjhtsriwtrrxewtgridrephhrbthhpvthridrwxhrigddehrsjgxcvrwxhrbxaxipgnrrpbepxvchrxcrvpjafrcditriwpiriwtrrpthpgrrxewtgrxhrtphxanrrgprztsrqnriwtrqgjiteudgrtrpiiprzf

key = 3:    hvsqgvwthqqwdvsfqwgqozgcqybckbqogqhvsqqosgofqqwdvsfcqothsfqxizwigqqosgofcqkvcqfsdihsrzmqigsrqhvsqqwdvsfqhcqdoggqasggousgqhcqvwgqhfccdgqrifwbuqvwgqawzwhofmqqoadowubgqwbquoizeqbchsqhvohqhvsqqosgofqqwdvsfqwgqsogwzmqqfoqysrqpmqhvsqpfihsdtcfqsqohhoqye

key = 4:    gurpfuvsgppvcurepvfpnyfbpxabjapnfpgurppnrfneppvcurebpnsgrepwhyvhfppnrfnebpjubperchgrqylphfrqpgurppvcurepgbpcnffpzrffntrfpgbpuvfpgebbcfpqhevatpuvfpzvyvgnelppnzcnvtafpvaptnhydpabgrpgungpgurppnrfneppvcurepvfprnfvylppenpxrqpolpgurpoehgrcsbeprpnggnpxd

key = 5:    ftqoeturfooubtqdoueomxeaowzaizomeoftqoomqemdooubtqdaomrfqdovgxugeoomqemdaoitaodqbgfqpxkogeqpoftqooubtqdofaobmeeoyqeemsqeofaotueofdaabeopgduzsotueoyuxufmdkoomybmuszeouzosmgxcozafqoftmfoftqoomqemdooubtqdoueoqmeuxkoodmowqponkoftqondgfqbradoqomffmowc

key = 6:    espndstqenntaspcntdnlwdznvyzhynldnespnnlpdlcnntaspcznlqepcnufwtfdnnlpdlcznhszncpafepowjnfdponespnntaspcneznalddnxpddlrpdneznstdneczzadnofctyrnstdnxtwtelcjnnlxaltrydntynrlfwbnyzepneslenespnnlpdlcnntaspcntdnpldtwjnnclnvponmjnespnmcfepaqzcnpnleelnvb

key = 7:    dromcrspdmmszrobmscmkvcymuxygxmkcmdrommkockbmmszrobymkpdobmtevsecmmkockbymgrymbozedonvimeconmdrommszrobmdymzkccmwocckqocmdymrscmdbyyzcmnebsxqmrscmwsvsdkbimmkwzksqxcmsxmqkevamxydomdrkdmdrommkockbmmszrobmscmokcsvimmbkmuonmlimdromlbedozpybmomkddkmua

key = 8:    cqnlbqrocllryqnalrbljubxltwxfwljblcqnlljnbjallryqnaxljocnalsdurdblljnbjaxlfqxlanydcnmuhldbnmlcqnllryqnalcxlyjbblvnbbjpnblcxlqrblcaxxyblmdarwplqrblvrurcjahlljvyjrpwblrwlpjduzlwxcnlcqjclcqnlljnbjallryqnalrblnjbruhllajltnmlkhlcqnlkadcnyoxalnljccjltz

key = 9:    bpmkapqnbkkqxpmzkqakitawksvwevkiakbpmkkimaizkkqxpmzwkinbmzkrctqcakkimaizwkepwkzmxcbmltgkcamlkbpmkkqxpmzkbwkxiaakumaaiomakbwkpqakbzwwxaklczqvokpqakuqtqbizgkkiuxiqovakqvkoictykvwbmkbpibkbpmkkimaizkkqxpmzkqakmiaqtgkkziksmlkjgkbpmkjzcbmxnwzkmkibbiksy

key = 10:   aoljzopmajjpwolyjpzjhszvjruvdujhzjaoljjhlzhyjjpwolyvjhmalyjqbspbzjjhlzhyvjdovjylwbalksfjbzlkjaoljjpwolyjavjwhzzjtlzzhnlzjavjopzjayvvwzjkbypunjopzjtpspahyfjjhtwhpnuzjpujnhbsxjuvaljaohajaoljjhlzhyjjpwolyjpzjlhzpsfjjyhjrlkjifjaoljiybalwmvyjljhaahjrx

key = 11:   znkiynolziiovnkxioyigryuiqtuctigyiznkiigkygxiiovnkxuiglzkxiparoayiigkygxuicnuixkvazkjreiaykjiznkiiovnkxizuivgyyiskyygmkyizuinoyizxuuvyijaxotminoyisorozgxeiigsvgomtyiotimgarwituzkizngziznkiigkygxiiovnkxioyikgyoreiixgiqkjiheiznkihxazkvluxikigzzgiqw

key = 12:   ymjhxmnkyhhnumjwhnxhfqxthpstbshfxhymjhhfjxfwhhnumjwthfkyjwhozqnzxhhfjxfwthbmthwjuzyjiqdhzxjihymjhhnumjwhythufxxhrjxxfljxhythmnxhywttuxhizwnslhmnxhrnqnyfwdhhfrufnlsxhnshlfzqvhstyjhymfyhymjhhfjxfwhhnumjwhnxhjfxnqdhhwfhpjihgdhymjhgwzyjuktwhjhfyyfhpv

key = 13:   xligwlmjxggmtlivgmwgepwsgorsargewgxliggeiwevggmtlivsgejxivgnypmywggeiwevsgalsgvityxihpcgywihgxliggmtlivgxsgtewwgqiwwekiwgxsglmwgxvsstwghyvmrkglmwgqmpmxevcggeqtemkrwgmrgkeypugrsxigxlexgxliggeiwevggmtlivgmwgiewmpcggvegoihgfcgxligfvyxitjsvgigexxegou

key = 14:   wkhfvkliwfflskhuflvfdovrfnqrzqfdvfwkhffdhvdufflskhurfdiwhufmxolxvffdhvdurfzkrfuhsxwhgobfxvhgfwkhfflskhufwrfsdvvfphvvdjhvfwrfklvfwurrsvfgxulqjfklvfplolwdubffdpsdljqvflqfjdxotfqrwhfwkdwfwkhffdhvdufflskhuflvfhdvlobffudfnhgfebfwkhfeuxwhsirufhfdwwdfnt

key = 15:   vjgeujkhveekrjgtekuecnuqempqypecuevjgeecgucteekrjgtqechvgtelwnkwueecguctqeyjqetgrwvgfnaewugfevjgeekrjgtevqercuueoguuciguevqejkuevtqqruefwtkpiejkueoknkvctaeecorckipuekpeicwnsepqvgevjcvevjgeecgucteekrjgtekuegcuknaeetcemgfedaevjgedtwvgrhqtegecvvcems

key = 16:   uifdtijguddjqifsdjtdbmtpdlopxodbtduifddbftbsddjqifspdbgufsdkvmjvtddbftbspdxipdsfqvufemzdvtfeduifddjqifsdupdqbttdnfttbhftdupdijtdusppqtdevsjohdijtdnjmjubszddbnqbjhotdjodhbvmrdopufduibuduifddbftbsddjqifsdjtdfbtjmzddsbdlfedczduifdcsvufqgpsdfdbuubdlr

key = 17:   thecshiftccipherciscalsocknowncasctheccaesarccipherocaftercjuliusccaesarocwhocreputedlycusedctheccipherctocpasscmessagesctochisctroopscduringchiscmilitaryccampaignscincgaulqcnotecthatctheccaesarcciphercisceasilyccrackedcbycthecbrutepforcecattackq


Part 3 KeyCode: 17

针对凯撒密码暴力破解的通用终止问题，推荐以下几种可行方案：

1. 基于英文常用词匹配判断 #

英文文本中高频出现的词汇（比如"the"、"and"、"is"、"of"）可作为有效语句的判定依据。破解后的文本只要包含多个这类常用词，就大概率是正确解密结果。

实现思路： #

• 预先定义常用词集合，比如std::unordered_set<std::string> common_words = {"the", "and", "is", "of", "to", "in", "it"};
• 对每个密钥解密后的文本，按空格分割成单词；若密文无空格，可滑动匹配3-5个字符的短词组合
• 统计匹配到的常用词数量，当数量超过阈值（比如至少匹配2个常用词，或匹配数占文本长度的15%以上）时，判定为有效解密，终止程序。

代码修改示例： #

在解密完成后添加判断逻辑：

// 解密完成后处理
std::istringstream iss(gang);
std::string word;
int match_count = 0;
std::unordered_set<std::string> common_words = {"the", "and", "is", "of", "to", "in", "it"};

while (iss >> word) {
    if (common_words.count(word)) {
        match_count++;
    }
}

// 设定阈值判断
if (match_count >= 2 || (gang.size() > 0 && match_count * 100 / gang.size() > 15)) {
    keyCode = key;
    std::cout << "\nFound valid decryption with key: " << key << std::endl;
    break;
}

2. 基于英文词频统计判断 #

英文中字母出现频率相对固定（比如'e'占比约12%，'t'约9%，'a'约8%）。计算解密后文本的字母频率，与标准英文频率对比，相似度最高的即为正确密钥。

实现思路： #

• 预先定义标准英文字母频率数组：double standard_freq[] = {8.167, 1.492, 2.782, 4.253, 12.702, 2.228, 2.015, 6.094, 6.966, 0.153, 0.772, 4.025, 2.406, 6.749, 7.507, 1.929, 0.095, 5.987, 6.327, 9.056, 2.758, 0.978, 2.360, 0.150, 1.974, 0.074};
• 对每个解密后的文本，统计每个字母的出现频率
• 计算当前频率与标准频率的相似度（比如用平方差之和，值越小相似度越高）
• 记录相似度最低的密钥，遍历完所有密钥后输出结果，或当相似度低于阈值时直接终止。

3. 让用户手动确认 #

若担心自动判断误判，可在每个密钥解密后询问用户是否为有效文本，用户确认后立即终止程序。

代码修改示例： #

在输出解密文本后添加：

char confirm;
std::cout << "\nIs this the correct decryption? (y/n): ";
std::cin >> confirm;
if (tolower(confirm) == 'y') {
    keyCode = key;
    break;
}

额外代码优化建议： #

• alphaArray仅到24，凯撒密码偏移量应为0-25，建议补全25
• decrypt函数仅处理大写字母，建议兼容小写字母，可先将输入字母转大写再计算
• 循环中i与key