Problem 3. (20 points). Remember that in the One Time Pad (OTP) cryptosystem, th

Question

Problem 3. (20 points). Remember that in the One Time Pad (OTP) cryptosystem, the key is as long as the plaintext. A fresh in OTP? random key needs to be generated each time you want to encrypt a new plaintext. Explain why one should never reuse a key Hint: Consider the case where you encrypt plaintext Pi and plaintext F2 (of same bit size) with the same key K, to obtain ciphertexts Ci and C2. What could an adversary learn about Pt and P2 from Ci and C2? In this attack, the adversary has access only to ciphertexts Ci and C2, but not to the key or the plaintexts

Explanation / Answer

The one time pad derives its name for using unique key everytime for encryptying the message.So you wouldn't call it a one time pad if you reused the key. Also the length of the key is as long as message so unless the two messages are of same size you cant have same length of OTP key and even if both are of same length it wont be similar in order to maintain its unique behavior.

The reason we shouldn't reuse a key is because, OTP uses XOR operation to combine key and message. If the key is reused an attacker can mount a known plaintext attack, he can get part of your keystream and decrypt anything that was encrypted using this part of the keystream.
As soon as you start repeating the key stream an attacker can even notice that in a ciphertext only attack as he can simply xor both cipherexts (c1=km1c2=km2c1c2=kkm1m2=m1m2c1=km1c2=km2c1c2=kkm1m2=m1m2) On this an attacker can even mount a simple frequency analysis.

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