Let =19 and =23
a) Set up the Public key = (n,e) and the private key pk = (p,q,d)
b) Encrypt the message m = ‘‘mo", what is the ciphertext c?
c) Decrypt the ciphertext c to obtain the original message m
Answers
Answer:
a) Protocol A performs the following:
1. Decryption of y using symmetric key k1
dk1
(y) = x||H(k2||x).
2. Concatenate k2 and x, where k2 is 2nd secret key (shared).
3. Compute hash of k2||x, that is H(k2||x).
4. Compare computed hash value with the one obtained in 1.
Protocol B performs the following:
1. Decrypt as in 1A, dk(y) = x||sigkpr(H(x)) using shared symmetric key k.
2. Compute H(x)
3. Feed H(x) and sigkpr(H(x)) into verification algorithm, check if signature on H(x) is valid.
Verification algorithm needs public key of the sender.
b) For protocol A we have:
• confidentiality, YES through encryption
• integrity, YES through hashing; changing y lead to invalid pair x
0 and H(k2||x
0
).
• non-repudiation, NO, both Alice (sender) and Bob (receiver) can generate valid message:
y = ek1
(x||H(k2||x)).
For protocol B we have:
• confidentiality, YES through encryption
• integrity, YES through signing; changing y lead to invalid pair x
0 and sigkpr
(H(x
0
)).
• non-repudiation, YES, only sender can send a message with valid signature.
Problem 6
We wish to encrypt a memoryless source with alphabet M = {0, 1, 2} and P(M = 0) =
1/2, P(M = 1) = p, P(M = 2) = 1/2 − p, 0 ≤ p ≤ 1/2. Let the key K = (K0, K1, K2) be
Step-by-step explanation: