Question

A) Describe how an attacker can obtain the one-time pad that is used to encrypt a message, given both the message and the ciphertext, and explain why your method works.
b) Suppose that two equal-sized messages M1 and M2 are encrypted with the same one-time pad and let C1 and C2 be the resulting ciphertexts. Suppose further that an attacker captures both ciphertexts C1 and C2, and knows one of the two messages, say M1. Based on Part a), describe how the attacker can obtain the other message M2, and explain why your method works.

c) Let’s think about a more realistic situation than part b) that the attacker captures both ciphertexts C1 and C2, but does not know message M1. Based on part b), can you provide an example showing that the attacker can still obtain the message M2 ? You can do research online and find approaches. By answering this question, you can have an idea on how an attacker can do in practice and why the one-time pad cannot be used more than once.

Answer 1

Answer:

(a)

Assuming the one-time pad P is used to XOR the message M to get ciphertext C, the following holds:

M ⊕ P = C

P = C ⊕ M

this is a basic property of how XOR works.

(b)

P = M1 ⊕ C1

then M2 = C2 ⊕ P

(c)

The attacker can make assumptions about the message (e.g., presence of certain words and spaces) and then calculate which pad would be needed to get them in the ciphertexts. He then has two ciphertexts that should yield valid content, making it much more easy to guess the pad.

Explanation: