Question

1. 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.
2. 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.
3. Let’s think about a more realistic situation than part b) that the attacker captures both ciphertexts C₁ and C_2, but does not know message M_1. 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

Remarks:Add 26 to 2 for C.(Written wrong D).

(c).

The attacker can get M2 without knowing M1. This is called man in the middle attack. Suppose there are two people Bob and Alice. Bob sends message to Alice and the man in the middle(attacker) is trudy. Suppose Bob and alice has common terms g,n and their secret keys are x and y respectively. and trudy also have his secret key z.

1.Bob sends R1,g,n to Alice. (R1=g^xmod n).R1 is the encypted message.

2. Trudy gets it and he forms his message Rz=g^zmod n. and sends Rz,g,n to Alice.

3. Alice message is R2=g^ymod n. So she forms Rz^ymod n as the key. i.e. g^xzmod n. and sends R2 to Bob. but trudy gets it and he keep the secret key of Alice as K_tb=g^yzmod n.

4.Trudy keeps K_ta as Bob's secret.K_ta= g^xzmod n and sends Rz to Bob.

5. Bob forms the key Rz^x mod n=g^xzmod n .

So trudy is successfull in giving his own key to both Bob and Alice and hence can decrypt every message thereafter.