9. Alice wishes to regularly send Bob a plaintext message P1 or P2. On each occa
ID: 3876743 • Letter: 9
Question
9. Alice wishes to regularly send Bob a plaintext message P1 or P2. On each occasion she chooses to send either P1 or P2, but on average she chooses the plaintext P1 twice as often as she chooses the plaintext P2. Each time, Alice uses a (very simple) symmetric cryptosystem, with the same fixed key K, to encrypt the plaintext. When she chooses P1, the ciphertext is C1 = EK (P1); when she chooses P2, the ciphertext is C2 = EK (P2). Suppose that an attacker knows that the only possible plaintext messages are P1 and P2.
(a) Suppose that the attacker does not know that Alice chooses P1 twice as often as P2. What observation will the attacker, who can only see the
ciphertexts sent from Alice to Bob, make?
(b) Suppose that the attacker learns that Alice chooses P1 twice as often as she chooses P2. What does the attacker now learn?
(c) Explain how homophonic encoding can be used in this case to make it more difficult.
Single plaintext letters can be replaced by any of several different ciphertext letters.
Explanation / Answer
a) Attacker will make the observation that a single message appears twice as frequently as the other message. So if one comes in his hold he can decrypt that the complete system.
b) Attacker now learns that the message sent more frequently is the P1 and the message sent less frequently is P2. So he can decrypt or attack on the system with knowing even the cipher text and plain text. So his ultimate aim is to recognize the encryption and decryption mechanism.
c) Homophonic encoding is basically assigning more than one symbol to a letter of plain text. Thus making it enigmatic for attacker the decide which one is P1 and which one is P2. Thus he would not be even able to map the correct cipher text to the plain text hence used in this case makes it more difficult.
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