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I have a ciphertext encoded with One Time Pad. I do not know the key. How can I find the possible keys which when decoded, will result in a meaningful plain text?

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Take the ciphertext you have and the message you want, xor them. That gives you the key which decrypts the message to that given message. Obviously this only works with OTPs, not with short key stream-ciphers. –  CodesInChaos Aug 16 '13 at 9:38
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2 Answers

The interesting property for the one time pad is that every plausible plaintext (given the length constraint, i.e. of same length as the ciphertext, maybe including some padding) has a corresponding key which produces a certain ciphertext.

As mentioned in the comment by CodesInChaos, this key can be retrieved by simply XORing both plaintext and ciphertext (if you are using the XOR variant of the one time pad ... for the addition variant you'll have to subtract).

Also, assuming a random key, every plaintext has the same probability, given the ciphertext, as it has without knowing the ciphertext (apart from the length).

This is known as perfect secrecy – you can get no information from the ciphertext about the plaintext which you didn't know before (apart from the length, but this can be hidden to a certain degree by padding, too).

Every cryptosystem with the perfect secrecy property must have a key as least as long as the messages, and each key must be used only once. This is why a one-time pad or other perfect encryption systems are not used often in practice.

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You will need more than one ciphertext encrypted with the same key to do that. The one time pad is perfectly secret if the key is used only once (Which is why its called the one time pad).

The only way for you to find the actual key without more ciphertexts is to try all possible key combinations (i.e. brute force it), but this could take a long long time if your ciphertext is also long.

If you manage to get more than one ciphertext, you could XOR the two ciphertexts together and use crib dragging techniques to determine the contents of the plaintext. This is possible because the xor of two ciphertexts is the same as xoring the two plaintexts together:

Let:
c1 = p1 xor k
c2 = p2 xor k

Then:
c1 xor c2 = (p1 xor k) xor (p2 xor k)
c1 xor c2 = p1 xor k xor p2 xor k          (associative property of xor)
c1 xor c2 = p1 xor p2 xor k xor k          
c1 xor c2 = p1 xor p2 xor 0                (k xor k = 0)
c1 xor c2 = p1 xor p2                      (x xor 0 = x)

See the link i posted to see how this relationship can be used to uncover the plaintext.

Also, notice that the above property would not hold if i had two keys k1, k2 instead of just k.

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You may want to reread the question, which was how to find the key (pad) which will map a given ciphertext to a given plaintext (or a given ciphertext to meaningful plaintext for some definition of "meaningful", not sure how best to interpret it). –  Thomas Aug 16 '13 at 13:13
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As far as i understood the OP wants to figure out what the key of some ciphertext is? Figuring out the plaintext would reveal the key in the process. There is no mention of having both the ciphertext and the plaintext which is why i answered the question as i did. If its the case where both the plaintext and ciphertext are available then it can simply be found by xoring the plaintext and ciphertext together. –  Michael Aquilina Aug 16 '13 at 13:31
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