破譯維吉尼亞加密法

思路

2種方法：
1.字典攻擊：把字典文件裏的每個單詞作爲維吉尼亞密鑰來嘗試，這種方式只適用密鑰不是隨機密鑰。
2.利用卡西斯基實驗來破解，即使是隨機密鑰也能工作。

建議

永遠不要使用英語單詞作爲維吉尼亞加密密鑰，這樣容易受到字典攻擊。

卡西斯基實驗

1.在密文裏找出每個至少3個字母長的重複字母集
因爲他們是使用密鑰裏的相同子密鑰來加密的相同明文字母
2.獲取間距的因數
次數最高的因數很可能就是維吉尼亞密鑰的長度
3.從字符串獲取每隔N個字母(N爲第二部獲得的因數)
4.利用頻率分析來破譯每個子密鑰
5.暴力破譯(分析出來的字母進行組合)的密鑰

頻率分析

匹配字母頻率。
英語中字母使用頻率爲下面排序(從高到低)
ETAOINSHRDLCUMWFGYPBVKJXQZ
計算字母在明文和密文裏出現的頻率的做法叫做頻率分析。

破解失敗可能原因

1.加密的維吉尼亞密鑰長度大於設定的最大長度
2.明文並不符合正常的字母頻率
3.明文包含太多單詞不在字典文件裏

字典攻擊實例

import detectEnglish, vigenereCipher
# 字典攻擊 
def hackVigenere_D(ciphertext):
    fo = open('dictionary.txt')
    words = fo.readlines()
    fo.close()

    for word in words:
        word = word.strip() # 刪除換行符
        decryptedText = vigenereCipher.decryptMessage(word, ciphertext) # 調用解密方法進行暴力破解
        if detectEnglish.isEnglish(decryptedText, wordPercentage=40):
            # 輸出可能已解情況，讓用戶自行判斷是否破譯成功
            print()
            print('Possible encryption break:')
            print('Key ' + str(word) + ': ' + decryptedText[:100])
            print()
            print('Enter D for done, or just press Enter to continue breaking:')
            response = input('> ')
            if response.upper().startswith('D'):
                return decryptedText
def main_D():
    ciphertext = """Tzx isnz eccjxkg nfq lol mys bbqq I lxcz."""
    hackedMessage = hackVigenere_D(ciphertext)

    if hackedMessage != None:
        print('Hacked message to clipboard:')
        print(hackedMessage)
    else:
        print('Failed to hack encryption.')
if __name__ == '__main__':
    main_D()

頻率分析（freqAnalusis.py）實例

englishLetterFreq = {'E': 12.70, 'T': 9.06, 'A': 8.17, 'O': 7.51, 'I': 6.97, 'N': 6.75, 'S': 6.33, 'H': 6.09, 'R': 5.99, 'D': 4.25, 'L': 4.03, 'C': 2.78, 'U': 2.76, 'M': 2.41, 'W': 2.36, 'F': 2.23, 'G': 2.02, 'Y': 1.97, 'P': 1.93, 'B': 1.29, 'V': 0.98, 'K': 0.77, 'J': 0.15, 'X': 0.15, 'Q': 0.10, 'Z': 0.07}
ETAOIN = 'ETAOINSHRDLCUMWFGYPBVKJXQZ'
LETTERS = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'



def getLetterCount(message):
    # 分析字母出現的次數，並返回頻率字典
    letterCount = {'A': 0, 'B': 0, 'C': 0, 'D': 0, 'E': 0, 'F': 0, 'G': 0, 'H': 0, 'I': 0, 'J': 0, 'K': 0, 'L': 0, 'M': 0, 'N': 0, 'O': 0, 'P': 0, 'Q': 0, 'R': 0, 'S': 0, 'T': 0, 'U': 0, 'V': 0, 'W': 0, 'X': 0, 'Y': 0, 'Z': 0}

    for letter in message.upper():
        if letter in LETTERS:
            letterCount[letter] += 1

    return letterCount


def getItemAtIndexZero(x):
    return x[0]


def getFrequencyOrder(message):
    # 返回一串按字母出現次數多到少的順序排列的字符串

    # 第一步，獲取每個字母及其頻率計數的字典
    letterToFreq = getLetterCount(message)

    # 第二步，製作 以鍵爲頻率計數，值爲出現的字母 的字典
    freqToLetter = {}
    for letter in LETTERS:
        if letterToFreq[letter] not in freqToLetter:
            freqToLetter[letterToFreq[letter]] = [letter]
        else:
            freqToLetter[letterToFreq[letter]].append(letter)

    # 第三步，把 字典裏的同一個鍵裏的值從列表整理成一個字符串
    for freq in freqToLetter:
        freqToLetter[freq].sort(key=ETAOIN.find, reverse=True)
        freqToLetter[freq] = ''.join(freqToLetter[freq])

    # 第四步，將freqtoLetter字典轉換爲元組對列表（鍵、值），然後對它們進行排序
    freqPairs = list(freqToLetter.items())
    freqPairs.sort(key=getItemAtIndexZero, reverse=True)

    # 第五步，既然字母是按頻率排序的，就提取元組的第二個數據，接合
    freqOrder = []
    for freqPair in freqPairs:
        freqOrder.append(freqPair[1])
    return ''.join(freqOrder)


def englishFreqMatchScore(message):
    # 返回 頻率分析後 前六個字母和後六個字母 與 預先設定的字母排序 中出現的次數
    freqOrder = getFrequencyOrder(message)

    matchScore = 0
    # 尋找前六個字母出現的次數
    for commonLetter in ETAOIN[:6]:
        if commonLetter in freqOrder[:6]:
            matchScore += 1
    # 尋找後六個字母出現的次數
    for uncommonLetter in ETAOIN[-6:]:
        if uncommonLetter in freqOrder[-6:]:
            matchScore += 1
    return matchScore



if __name__ == "__main__":
    b = englishFreqMatchScore('sdhaioffnfwefknfiuefhncali')
    print(b)

卡西斯基實驗破解實例

import itertools, re
import vigenereCipher, freqAnalysis, detectEnglish

LETTERS = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
SILENT_MODE = False # 如果設置爲True，則不顯示嘗試破譯信息
NUM_MOST_FREQ_LETTERS = 4 # attempts this many letters per subkey
MAX_KEY_LENGTH = 16 # 密鑰最長長度
NONLETTERS_PATTERN = re.compile('[^A-Z]')

def findRepeatSequencesSpacings(message):
    # Goes through the message and finds any 3 to 5 letter sequences
    # that are repeated. Returns a dict with the keys of the sequence and
    # values of a list of spacings (num of letters between the repeats).

    # Use a regular expression to remove non-letters from the message.
    message = NONLETTERS_PATTERN.sub('', message.upper())

    # Compile a list of seqLen-letter sequences found in the message.
    seqSpacings = {} # keys are sequences, values are list of int spacings
    for seqLen in range(3, 6):
        for seqStart in range(len(message) - seqLen):
            # Determine what the sequence is, and store it in seq
            seq = message[seqStart:seqStart + seqLen]

            # Look for this sequence in the rest of the message
            for i in range(seqStart + seqLen, len(message) - seqLen):
                if message[i:i + seqLen] == seq:
                    # Found a repeated sequence.
                    if seq not in seqSpacings:
                        seqSpacings[seq] = [] # initialize blank list

                    # Append the spacing distance between the repeated
                    # sequence and the original sequence.
                    seqSpacings[seq].append(i - seqStart)
    return seqSpacings


def getUsefulFactors(num):
    # Returns a list of useful factors of num. By "useful" we mean factors
    # less than MAX_KEY_LENGTH + 1. For example, getUsefulFactors(144)
    # returns [2, 72, 3, 48, 4, 36, 6, 24, 8, 18, 9, 16, 12]

    if num < 2:
        return [] # numbers less than 2 have no useful factors

    factors = [] # the list of factors found

    # When finding factors, you only need to check the integers up to
    # MAX_KEY_LENGTH.
    for i in range(2, MAX_KEY_LENGTH + 1): # don't test 1
        if num % i == 0:
            factors.append(i)
            factors.append(int(num / i))
    if 1 in factors:
        factors.remove(1)
    return list(set(factors))


def getItemAtIndexOne(x):
    return x[1]


def getMostCommonFactors(seqFactors):
    # First, get a count of how many times a factor occurs in seqFactors.
    factorCounts = {} # key is a factor, value is how often if occurs

    # seqFactors keys are sequences, values are lists of factors of the
    # spacings. seqFactors has a value like: {'GFD': [2, 3, 4, 6, 9, 12,
    # 18, 23, 36, 46, 69, 92, 138, 207], 'ALW': [2, 3, 4, 6, ...], ...}
    for seq in seqFactors:
        factorList = seqFactors[seq]
        for factor in factorList:
            if factor not in factorCounts:
                factorCounts[factor] = 0
            factorCounts[factor] += 1

    # Second, put the factor and its count into a tuple, and make a list
    # of these tuples so we can sort them.
    factorsByCount = []
    for factor in factorCounts:
        # exclude factors larger than MAX_KEY_LENGTH
        if factor <= MAX_KEY_LENGTH:
            # factorsByCount is a list of tuples: (factor, factorCount)
            # factorsByCount has a value like: [(3, 497), (2, 487), ...]
            factorsByCount.append( (factor, factorCounts[factor]) )

    # Sort the list by the factor count.
    factorsByCount.sort(key=getItemAtIndexOne, reverse=True)

    return factorsByCount


def kasiskiExamination(ciphertext):
    # Find out the sequences of 3 to 5 letters that occur multiple times
    # in the ciphertext. repeatedSeqSpacings has a value like:
    # {'EXG': [192], 'NAF': [339, 972, 633], ... }
    repeatedSeqSpacings = findRepeatSequencesSpacings(ciphertext)

    # See getMostCommonFactors() for a description of seqFactors.
    seqFactors = {}
    for seq in repeatedSeqSpacings:
        seqFactors[seq] = []
        for spacing in repeatedSeqSpacings[seq]:
            seqFactors[seq].extend(getUsefulFactors(spacing))

    # See getMostCommonFactors() for a description of factorsByCount.
    factorsByCount = getMostCommonFactors(seqFactors)

    # Now we extract the factor counts from factorsByCount and
    # put them in allLikelyKeyLengths so that they are easier to
    # use later.
    allLikelyKeyLengths = []
    for twoIntTuple in factorsByCount:
        allLikelyKeyLengths.append(twoIntTuple[0])

    return allLikelyKeyLengths


def getNthSubkeysLetters(n, keyLength, message):
    # Returns every Nth letter for each keyLength set of letters in text.
    # E.g. getNthSubkeysLetters(1, 3, 'ABCABCABC') returns 'AAA'
    #      getNthSubkeysLetters(2, 3, 'ABCABCABC') returns 'BBB'
    #      getNthSubkeysLetters(3, 3, 'ABCABCABC') returns 'CCC'
    #      getNthSubkeysLetters(1, 5, 'ABCDEFGHI') returns 'AF'

    # Use a regular expression to remove non-letters from the message.
    message = NONLETTERS_PATTERN.sub('', message)

    i = n - 1
    letters = []
    while i < len(message):
        letters.append(message[i])
        i += keyLength
    return ''.join(letters)


def attemptHackWithKeyLength(ciphertext, mostLikelyKeyLength):
    # Determine the most likely letters for each letter in the key.
    ciphertextUp = ciphertext.upper()
    # allFreqScores is a list of mostLikelyKeyLength number of lists.
    # These inner lists are the freqScores lists.
    allFreqScores = []
    for nth in range(1, mostLikelyKeyLength + 1):
        nthLetters = getNthSubkeysLetters(nth, mostLikelyKeyLength, ciphertextUp)

        # freqScores is a list of tuples like:
        # [(<letter>, <Eng. Freq. match score>), ... ]
        # List is sorted by match score. Higher score means better match.
        # See the englishFreqMatchScore() comments in freqAnalysis.py.
        freqScores = []
        for possibleKey in LETTERS:
            decryptedText = vigenereCipher.decryptMessage(possibleKey, nthLetters)
            keyAndFreqMatchTuple = (possibleKey, freqAnalysis.englishFreqMatchScore(decryptedText))
            freqScores.append(keyAndFreqMatchTuple)
        # Sort by match score
        freqScores.sort(key=getItemAtIndexOne, reverse=True)

        allFreqScores.append(freqScores[:NUM_MOST_FREQ_LETTERS])

    if not SILENT_MODE:
        for i in range(len(allFreqScores)):
            # use i + 1 so the first letter is not called the "0th" letter
            print('Possible letters for letter %s of the key: ' % (i + 1), end='')
            for freqScore in allFreqScores[i]:
                print('%s ' % freqScore[0], end='')
            print() # print a newline

    # Try every combination of the most likely letters for each position
    # in the key.
    for indexes in itertools.product(range(NUM_MOST_FREQ_LETTERS), repeat=mostLikelyKeyLength):
        # Create a possible key from the letters in allFreqScores
        possibleKey = ''
        for i in range(mostLikelyKeyLength):
            possibleKey += allFreqScores[i][indexes[i]][0]

        if not SILENT_MODE:
            print('Attempting with key: %s' % (possibleKey))

        decryptedText = vigenereCipher.decryptMessage(possibleKey, ciphertextUp)

        if detectEnglish.isEnglish(decryptedText):
            # Set the hacked ciphertext to the original casing.
            origCase = []
            for i in range(len(ciphertext)):
                if ciphertext[i].isupper():
                    origCase.append(decryptedText[i].upper())
                else:
                    origCase.append(decryptedText[i].lower())
            decryptedText = ''.join(origCase)

            # Check with user to see if the key has been found.
            print('Possible encryption hack with key %s:' % (possibleKey))
            print(decryptedText[:200]) # only show first 200 characters
            print()
            print('Enter D for done, or just press Enter to continue hacking:')
            response = input('> ')

            if response.strip().upper().startswith('D'):
                return decryptedText

    # No English-looking decryption found, so return None.
    return None


def hackVigenere(ciphertext):
    # First, we need to do Kasiski Examination to figure out what the
    # length of the ciphertext's encryption key is.
    allLikelyKeyLengths = kasiskiExamination(ciphertext)
    if not SILENT_MODE:
        keyLengthStr = ''
        for keyLength in allLikelyKeyLengths:
            keyLengthStr += '%s ' % (keyLength)
        print('Kasiski Examination results say the most likely key lengths are: ' + keyLengthStr + '\n')

    for keyLength in allLikelyKeyLengths:
        if not SILENT_MODE:
            print('Attempting hack with key length %s (%s possible keys)...' % (keyLength, NUM_MOST_FREQ_LETTERS ** keyLength))
        hackedMessage = attemptHackWithKeyLength(ciphertext, keyLength)
        if hackedMessage != None:
            break

    # If none of the key lengths we found using Kasiski Examination
    # worked, start brute-forcing through key lengths.
    if hackedMessage == None:
        if not SILENT_MODE:
            print('Unable to hack message with likely key length(s). Brute forcing key length...')
        for keyLength in range(1, MAX_KEY_LENGTH + 1):
            # don't re-check key lengths already tried from Kasiski
            if keyLength not in allLikelyKeyLengths:
                if not SILENT_MODE:
                    print('Attempting hack with key length %s (%s possible keys)...' % (keyLength, NUM_MOST_FREQ_LETTERS ** keyLength))
                hackedMessage = attemptHackWithKeyLength(ciphertext, keyLength)
                if hackedMessage != None:
                    break
    return hackedMessage

def main():
    # Instead of typing this ciphertext out, you can copy & paste it
    ciphertext = """Adiz Avtzqeci Tmzubb wsa m Pmilqev halpqavtakuoi, lgouqdaf, kdmktsvmztsl, izr xoexghzr kkusitaaf. Vz wsa twbhdg ubalmmzhdad qz hce vmhsgohuqbo ox kaakulmd gxiwvos, krgdurdny i rcmmstugvtawz ca tzm ocicwxfg jf "stscmilpy" oid "uwydptsbuci" wabt hce Lcdwig eiovdnw. Bgfdny qe kddwtk qjnkqpsmev ba pz tzm roohwz at xoexghzr kkusicw izr vrlqrwxist uboedtuuznum. Pimifo Icmlv Emf DI, Lcdwig owdyzd xwd hce Ywhsmnemzh Xovm mby Cqxtsm Supacg (GUKE) oo Bdmfqclwg Bomk, Tzuhvif'a ocyetzqofifo ositjm. Rcm a lqys ce oie vzav wr Vpt 8, lpq gzclqab mekxabnittq tjr Ymdavn fihog cjgbhvnstkgds. Zm psqikmp o iuejqf jf lmoviiicqg aoj jdsvkavs Uzreiz qdpzmdg, dnutgrdny bts helpar jf lpq pjmtm, mb zlwkffjmwktoiiuix avczqzs ohsb ocplv nuby swbfwigk naf ohw Mzwbms umqcifm. Mtoej bts raj pq kjrcmp oo tzm Zooigvmz Khqauqvl Dincmalwdm, rhwzq vz cjmmhzd gvq ca tzm rwmsl lqgdgfa rcm a kbafzd-hzaumae kaakulmd, hce SKQ. Wi 1948 Tmzubb jgqzsy Msf Zsrmsv'e Qjmhcfwig Dincmalwdm vt Eizqcekbqf Pnadqfnilg, ivzrw pq onsaafsy if bts yenmxckmwvf ca tzm Yoiczmehzr uwydptwze oid tmoohe avfsmekbqr dn eifvzmsbuqvl tqazjgq. Pq kmolm m dvpwz ab ohw ktshiuix pvsaa at hojxtcbefmewn, afl bfzdakfsy okkuzgalqzu xhwuuqvl jmmqoigve gpcz ie hce Tmxcpsgd-Lvvbgbubnkq zqoxtawz, kciup isme xqdgo otaqfqev qz hce 1960k. Bgfdny'a tchokmjivlabk fzsmtfsy if i ofdmavmz krgaqqptawz wi 1952, wzmz vjmgaqlpad iohn wwzq goidt uzgeyix wi tzm Gbdtwl Wwigvwy. Vz aukqdoev bdsvtemzh rilp rshadm tcmmgvqg (xhwuuqvl uiehmalqab) vs sv mzoejvmhdvw ba dmikwz. Hpravs rdev qz 1954, xpsl whsm tow iszkk jqtjrw pug 42id tqdhcdsg, rfjm ugmbddw xawnofqzu. Vn avcizsl lqhzreqzsy tzif vds vmmhc wsa eidcalq; vds ewfvzr svp gjmw wfvzrk jqzdenmp vds vmmhc wsa mqxivmzhvl. Gv 10 Esktwunsm 2009, fgtxcrifo mb Dnlmdbzt uiydviyv, Nfdtaat Dmiem Ywiikbqf Bojlab Wrgez avdw iz cafakuog pmjxwx ahwxcby gv nscadn at ohw Jdwoikp scqejvysit xwd "hce sxboglavs kvy zm ion tjmmhzd." Sa at Haq 2012 i bfdvsbq azmtmd'g widt ion bwnafz tzm Tcpsw wr Zjrva ivdcz eaigd yzmbo Tmzubb a kbmhptgzk dvrvwz wa efiohzd."""
    hackedMessage = hackVigenere(ciphertext)
    if hackedMessage != None:
        print('Hacked message :')
        print(hackedMessage)
    else:
        print('Failed to hack encryption.')
if __name__ == '__main__':
    main()