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第四讲 古典替换密码

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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第四讲 古典替换密码

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  1. 第四讲 古典替换密码

  2. 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

  3. 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)

  4. 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

  5. 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

  6. 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

  7. 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)

  8. 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

  9. 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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