Suppose an attacker who does not know k is given r, c = Enck(r) and r 0 , c0 = Enck(r 0 ) for random r = r 0 . Show that (r, r0 ⊕ c, c0 ) is accepted by the decryption algorithm.
Question
Suppose an attacker who does not know k is given r, c = Enck(r) and r 0 , c0 = Enck(r 0 ) for random r = r 0 . Show that (r, r0 ⊕ c, c0 ) is accepted by the decryption algorithm.
Solution
The question seems to be about a cryptographic system where Enck(r) represents the encryption of a random number r using a key k. The symbol ⊕ represents the XOR operation.
Let's break down the problem:
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We are given r, c = Enck(r) and r0 , c0 = Enck(r0) for random r = r0. This means that we have two pairs of random numbers and their corresponding encrypted values.
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We are asked to show that (r, r0 ⊕ c, c0) is accepted by the decryption algorithm.
To show this, we need to understand how the decryption algorithm works. In general, a decryption algorithm takes an encrypted message and a key, and produces the original message.
Let's denote the decryption algorithm as Deck(c), which should return the original message r.
We need to show that Deck(r0 ⊕ c) = r. Since r = r0, r0 ⊕ c = r ⊕ c.
Now, we know that for any value x, x ⊕ x = 0 and x ⊕ 0 = x. Therefore, r ⊕ c = r ⊕ Enck(r) = r ⊕ (r ⊕ k) = (r ⊕ r) ⊕ k = 0 ⊕ k = k.
So, Deck(r0 ⊕ c) = Deck(k). Since the decryption algorithm uses the key k to decrypt the message, it will accept k as input and return the original message.
Therefore, (r, r0 ⊕ c, c0) is accepted by the decryption algorithm.
Similar Questions
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Discuss Cryptography
Write a program to perform encryption and decryption using wrapper class Encryption phase with shift n = En (x) = (x+n)mod 26Decryption phase with shift n = Dn (x) = (x-n)mod 26
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