Q.3 Suppose you were able to observe ciphertext that you knew had been encrypted

Question

Q.3 Suppose you were able to observe ciphertext that you knew had been encrypted in CBC mode, and you saw that two ciphertext blocks, say c2 and cs, were equal. Why would this leak information? (Hint. What would happen if you knew one of the plaintext blocks, say m2?) Q.4 Given the speed of current ordinary computer, estimate the amount of time necessary to crack a DES encryption by testing all 2 56 possible keys. Make a similar estimate for a 128-bit AES key. Use below instruction for this question. Go to web site https://www.cryptool.org/en/home and download CrypTool 1.4.31 Beta 06 - English version • Encrypt any text with DES-CBC with any key that you select go to analysis select symmetric encryption (modern) select DES-CBC start the Brute Force analysis. • What is the estimated time? Do the same things for AES algorithm. NOTE. Please watch DES and AES animation in this tool kit. (under Indiv. Procedures, select visualization of algorithms)

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Q3)

Answer)

The Cipher block chaining (CBC) method is a method for encryption of the sequence of bits using a cipher key. The plain text in Cipher block chaining (CBC) is XORed with the ciphertext block and then encrypted.

Thus for example, Let us consider C2 and C5 as ciphertext blocks.

M# are the plain text blocks

We know that:

C2 = (M2 XOR C1)

C5 = (M5 XOR C4)

so we have C1 and C4 here in the equation.

Now in conditions when C2=C5,

(M2 XOR C1) = (M5 XOR C4)

Also from the above,

(M2 XOR M5) = (C1 XOR C4)

C2 = C5 and also there is inclusion of the C1 and C4 in our equations.

Thus when we also know the plain text M2 or M5 (one of them), we can put that on the equations and solve the equations, then the value of M5 is also generated and thus plaintext is cracked.

This is the risk in the question.

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