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第四讲 古典替换密码

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第四讲 古典替换密码. 1 。多字母表替换密码 (Polyalphabetic ciphers). 增强密码安全性的方法是使用多字母替换密码 hence the name polyalphabetic ciphers 使得密码分析更困难,因为有较多的密码表去猜测 打乱了字母出现的频率 用一个密钥决定对每个字母使用什么字母变换表 密钥的第 I 个字母指定第 I 个字母表 ith letter of key specifies ith alphabet to use 依次使用每个字母表 use each alphabet in turn

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1 polyalphabetic ciphers
1。多字母表替换密码 (Polyalphabetic ciphers)
  • 增强密码安全性的方法是使用多字母替换密码
  • hence the name polyalphabetic ciphers
  • 使得密码分析更困难,因为有较多的密码表去猜测
  • 打乱了字母出现的频率
  • 用一个密钥决定对每个字母使用什么字母变换表
  • 密钥的第I个字母指定第I个字母表ith letter of key specifies ith alphabet to use
  • 依次使用每个字母表use each alphabet in turn
  • repeat from start after end of key is reached
2 vigen re cipher
2. Vigenère Cipher
  • 最简单的多字母替换密码(Vigenère Cipher)
  • ——多重 caesar ciphers
  • 密钥是多字母长度 K = k1 k2 ... kd
  • 数学表示:
  • Encryption is done using
    • Eki(a): a -> a + ki (mod 26)
  • Decryption is done using
    • Dki(a): a -> a - ki (mod 26)
3 vigen re example
3. Vigenère Example
  • write the plaintext out
  • under it write the keyword repeated
  • then using each key letter in turn as a caesar cipher key
  • encrypt the corresponding plaintext letter
  • Plaintext THISPROCESSCANALSOBEEXPRESSED
  • Keyword CIPHERCIPHERCIPHERCIPHERCIPHE
  • Plaintext VPXZTIQKTZWTCVPSWFDMTETIGAHLH
3 vigen re example1
3. Vigenère Example
  • C -> CDEFGHIJKLMNOPQRSTUVWXYZAB
  • I -> IJKLMNOPQRSTUVWXYZABCDEFGH
  • P -> PQRSTUVWXYZABCDEFGHIJKLMNO
  • H -> HIJKLMNOPQRSTUVWXYZABCDEFG
  • E -> EFGHIJKLMNOPQRSTUVWXYZABCD
  • R -> RSTUVWXYZABCDEFGHIJKLMNOPQ
  • ABCDEFGHIJKLMNOPQRSTUVWXYZ
  • to map the above plaintext letters.
  • \'T\' uses key \'C\' maps to \'V\'
  • \'H\' uses key \'I\' maps to \'P\'
  • \'I\' uses key \'P\' maps to \'X\'
  • etc
4 beauford cipher
4. Beauford Cipher
  • 类似 Vigenère密码,但顺序相反
  • 数学描述:
  • Encryption is done using
    • Eki(p): p -> ki - p (mod 26)
  • Decryption is done using
    • Dki(c): c -> ki - c (mod 26)
  • eg. if using a single key letter of \'d\' have translation alphabet
  • Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ
  • Cipher: DCBAZYXWVUTSRQPONMLKJIHGFE
5 variant beauford cipher
5. Variant-Beauford Cipher
  • 类似 Vigenère密码,但是移位向左
  • 实际上是Vigenère 逆密码 (decrypts it)
  • 数学表示:
  • Encryption is done using
    • Eki(a): a -> a - ki (mod 26)
  • Decryption is done using
    • Dki(a): a -> a + ki (mod 26)
  • eg. Variant-Beauford key \'c\' (shift left 2 places)
  • same as Vigenère key \'y\' (shift right 24 places)
6 autokey cipher
6. Autokey Cipher
  • 更多的字母替换表可以提高密码的安全性
  • Vigenère 提出了自动密钥密码( autokey cipher )
  • 密钥字作为消息的前缀组成密钥
  • knowing keyword can recover the first few letters
  • then use these in turn on the rest of the message
  • eg. given key "DECEPTIVE" and message "WE ARE DISCOVERED SAVE YOURSELF"
  • key: DECEPTIVEWEAREDISCOVEREDSAV
  • plaintext: WEAREDISCOVEREDSAVEYOURSELF
  • ciphertext: ZICVTWQNGKZEIIGASXSTSLVVWLA
problems with autokey ciphers
Problems with autokey ciphers
  • Autorkey cipher 看起来好象比较安全
  • 实际上仍然有语言特征characteristics are used by the key as the message
  • ie. a key of \'E\' will be used more often than a \'T\' etc
  • hence an \'E\' encrypted with a key of \'E\' occurs with probability (0.1275)2 = 0.01663, about twice as often as a \'T\' encrypted with a key of \'T\'
  • given sufficient ciphertext this can be broken
  • if a truly random key as long as the message is used, the cipher will be secure
  • called a Vernam Cipher or One-Time pad, we meet this later
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