Alice and Bob use the Diffie-Hellman key exchange protocol to negotiate a shared secret. They agree on two parameters, where p = 17 and g = 4. Alice selects 3 as her private key (i.e., the secret number). Bob selects 6 as his private key (i.e., the secret number). A.1. What is the public key sent from Alice to Bob? (25%) A.2. What is the public key sent from Bob to Alice? (25%) A.3. What is the negotiated shared key (i.e., the shared secret)? (50%) Question-B: An RSA system was used to encrypt the message M, and its corresponding ciphertext C is 9 (C=9). Both e (the public key) and n (n=pq) are publicly known, where e = 23 and n = 143. Since n=143 is not carefully chosen and its factoring process is relatively easy, we can crack the system to determine the original message M manually. B.1: What is p and q? (25%) B.2: What is the private key? You can use the following reference to speed up your calculation. (25%) Calculation Reference 23 * 44 = 1012 23 * 45 = 1035 23 * 46 = 1058 23 * 47 = 1081 B.3: What is the original message M? Please show how you derive the answer. You can use python or scientific calculator to assist your computation here. (50%)
Alice and Bob use the Diffie-Hellman key exchange protocol to negotiate a shared secret. They agree on two parameters, where p = 17 and g = 4.
Alice selects 3 as her private key (i.e., the secret number).
Bob selects 6 as his private key (i.e., the secret number).
A.1. What is the public key sent from Alice to Bob? (25%)
A.2. What is the public key sent from Bob to Alice? (25%)
A.3. What is the negotiated shared key (i.e., the shared secret)? (50%)
Question-B:
An RSA system was used to encrypt the message M, and its corresponding ciphertext C is 9 (C=9). Both e (the public key) and n (n=pq) are publicly known, where e = 23 and n = 143. Since n=143 is not carefully chosen and its factoring process is relatively easy, we can crack the system to determine the original message M manually.
B.1: What is p and q? (25%)
B.2: What is the private key? You can use the following reference to speed up your calculation. (25%)
| Calculation Reference |
| 23 * 44 = 1012 |
| 23 * 45 = 1035 |
| 23 * 46 = 1058 |
| 23 * 47 = 1081 |
B.3: What is the original message M? Please show how you derive the answer. You can use python or scientific calculator to assist your computation here. (50%)
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