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regarding one time pads,can someone show with an example...

<< Back to: Cryptography FAQ (01/10: Overview)

Question by suhas
Submitted on 1/15/2004
Related FAQ: Cryptography FAQ (01/10: Overview)
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regarding one time pads,can someone show with an example how, if the same pad is used  for encrypting two different plain texts, it can be broken very easily


Answer by Anal Srivastava
Submitted on 4/19/2004
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One time pad can be broken if the attacker has atleast 1 plaintext-ciphertext pair. Its pretty simple. One time pad takes XOR of a random sequence of bits (called key) with the plaintext to produce the cipertext, so we can describe this mathematically as

C = P xor K

where C = ciphertext
      P = plaintext
      K = key

if we xor with the plaintext on both sides, we get

P xor C = P xor P xor K

P xor P on the rhs will yield 0, and anything xored with 0 returns the same

so we have effectively

K = P xor C

now if the attacker has even one plaintext-ciphertext pair then he can produce the key that was used for encryption.

For any other cipertext encrypted using the same key, its easy to get the palintext, simply xor the key with the ciphertext, the result would be the plaintext.

Following works out an example, (for simplicity only 4 bits are taken)

lets assume M = 0101, K = 1101
then C = 1000

Suppose attacker knows M & C
then key = 0101 xor 1000 = 1101 which is the original key.

now any new ciphertext (encrypted with the same key) can be decrypted.

 

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