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 repeat from start after end of key is reached

2. Vigen è re 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 = k 1 k 2... k d 数学表示： Encryption is done using E ki (a): a -> a + k i (mod 26) Decryption is done using D ki (a): a -> a - k i (mod 26)

3. Vigen è re 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 è re 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 类似 Vigenère 密码，但顺序相反 数学描述 : Encryption is done using E ki (p): p -> k i - p (mod 26) Decryption is done using D ki (c): c -> k i - c (mod 26) eg. if using a single key letter of 'd' have translation alphabet Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ Cipher: DCBAZYXWVUTSRQPONMLKJIHGFE

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 E ki (a): a -> a - k i (mod 26) Decryption is done using D ki (a): a -> a + k i (mod 26) eg. Variant-Beauford key 'c' (shift left 2 places) same as Vigenère key 'y' (shift right 24 places)

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 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 = , 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