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9.2

Block-cipher encryption, probability question

Asked by younoeme in Math & Science, Probability & Statistics

Tags: block, encryption, algorithm

I was looking at this question in a book that I am reading, and it seemed intriguing.  I am an algorithms person, not too strongly inclined towards math, but though an answer to this would be curious enough.

Question:  consider a block encryption algorithm that encrypts blocks on lenght n, and let N = 2^n. Say we have t plaintext-ciphertext pairts P[i], C[i] = E[K](P[i]) where we assume that the key K selects one of the N! possible mappings.  Imagine that we wish to find K by exhaustive search.  We could generate key K' and test whether C[i] = E[K'](P[i]) for 1 <= i <= t.  If K' encrypts each P[i] to its proper C[i] then we have evidence that K = K'.  However, it may be the case that the mappings E[K](X) and E[K'](X) exactly agree on the t plaintext-ciphertext pairs P[i], C[i] and agree on no other pairs.

a)  What is the probability that E[K](X) and E[K'](X) are in fact distinct mappings?
b)  What is the probability that E[K](X) and E[K'](X) agree on anohter t' plaintext-ciphertext pairs where 0 <= t' <= N - t?

Seems a little complicated, but actually really isn't.  I understand the question and the point behind it, but just dont have the mathematical skills to compute it.  Any help is much appreciated.

Thank you..
[+][-]09/26/04 08:44 PM, ID: 12157388Accepted Solution

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Zones: Math & Science, Probability & Statistics
Tags: block, encryption, algorithm
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Solution Provided By: ozo
Participating Experts: 2
Solution Grade: A
 
[+][-]09/26/04 08:47 PM, ID: 12157397Expert Comment

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[+][-]09/26/04 10:28 PM, ID: 12157752Expert Comment

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[+][-]09/26/04 11:22 PM, ID: 12157940Expert Comment

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[+][-]09/26/04 11:36 PM, ID: 12157993Expert Comment

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[+][-]09/27/04 09:04 AM, ID: 12161532Author Comment

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[+][-]09/27/04 02:18 PM, ID: 12164477Author Comment

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[+][-]09/27/04 05:18 PM, ID: 12165498Expert Comment

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