These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.a). We write the encryption law in CBC-mode for both ciphertexts Ci and Cj.
Ci = Enck(Pi ⨁ Ci-1)
Cj = Enck(Pj ⨁ Cj-1)
Since Ci = Cj => Pi ⨁ Ci-1 and Pj ⨁ Cj-1 get encrypted to the same value.
Thus Pi ⨁ Ci-1 = Pj ⨁ Cj-1
Now, using the basic properties of XOR function (a ⨁ b =c => a⨁ c=b), we obtain:
Pi ⨁ Pj = Ci-1 ⨁ Cj-1
This tells us that, if know the previous two ciphertext blocks (namely Ci-1 and Cj-1 respectively), then we can also find out the XOR between the two original plaintext blocks. In terms of security, this means that two identical ciphertext blocks in CBC mode might lead to data leakage. Even if we do not know actual plaintext blocks, we pull some information about a relationship between them, which might facilitate other cryptographic attacks further....
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