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# 第四讲 古典替换密码 - PowerPoint PPT Presentation

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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. 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. 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. 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

• 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

• 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)

• 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

• 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