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I am a beginner in cryptography. I studied many time pad attack and now I want to solve a popular exercise, It consists 11 ciphertexts (s1,s2,...,s11), that encrypted by a same key and I want to find plaintext(p11) of s11. I know:

p10 ⊕ k = s10
p11 ⊕ k = s11
p10 ⊕ p11 = s10 ⊕ s11

Now, what should I do for getting p11? If assume k = s10 ⊕ s11, so:

s11 ⊕ k = p11
s11 ⊕ (s10 ⊕ s11) = p11

. Is it correct?

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marked as duplicate by Ilmari Karonen, otus, e-sushi Apr 22 '17 at 2:49

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You need to know something about the plaintexts and their structure for an attack, otherwise (more precisely: if you have to assume the $p_i$ are uniform distributed and truly random) knowing $s_1,...s_{11}$ is the very same as having $11$ one-time-pads for the same message (consider $k$ the message and $p_1$ to $p_11$ the keys) - which is still perfectly secure.

If you know for example that the plaintext is English words encoded in ASCII, then you can identify probabilities for the Xor of two plaintexts and start there. However, in that exercise you might be challenged just to try out different things, if they don't tell you anything else. Your best bet is so calculate all $s_i \oplus s_j$ with $i \neq j$ and compare this distribution to the XOR of symbols of natural language.

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