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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第四讲 古典替换密码

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6009078

第四讲 古典替换密码


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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