CS 463/563: Cryptography for Cyber Security
Fall 2021
Homework #11: Due: November 21, 2021
Points: 20
Q1. Shared session key establishment using a Key Distribution Center (KDC). Using the following table, illustrate how Alice can initiate a secure session with Bob with the help of KDC. Here, KEKs are the long term key establishment keys used to transport the session keys across the network securely. Assume the encryption process to be as follows: Block (LB || RB) is 8 bits; Encryption Key (LK||RK) is 8 bits; Ciphertext = LC|| RC where LC=LB ⊕ RK; and RC=RB ⊕ LK; For example, if plaintext=A7 (Hexa) and Key = 6D; then LC=A ⊕ D = 1010 ⊕ 1101 = 0111 = 7 (Hexa); and RC = 7 ⊕
6 = 0111 ⊕ 0110 = 0001 = 1 (Hexa); so Ciphertext = 71 (Hexa). To decrypt, it does the reverse
operation: Given ciphertext of C=LC||RC, it finds plaintext B=LB||RB, by finding LB=LC ⊕ RK and RB =
RC ⊕ LK.
Alice KDC Bob
KEK: kA = A6 (hexa) KEK: kA = A6 (hexa); kB = D8(hexa); KEK: kB = D8 (hexa);
Alice sends a message to KDC requesting a session key between Alice and Bob
Generate a random session key: kses = 7B (hexa);
yA = ekA(kses) = ??
yB = ekB(kses) = ??
KDC sends yA = ?? to Alice
KDC send yB = ?? to Bob
Decrypt yA to derive kses
using kA =
Decrypt yB to derive kses
using kB =
Message to send, m = 45
(Hexa)
Encrypyt m using session key,
y = ekses(m)
Alice sends y to Bob
Decrypt y using session key to
get m =
Verify that this is the message
sent by Alice
Q2. [Points 10] Man-in-the-middle attack when Alice and Bob employ Diffie-Hellman key exchange.
Alice Carol (Intruder) Bob
p=17 and α= 4 are known to all
Choose kpri,A =a = 7 Choose kpri,B =b = 8
Alice’s public key: kpub,A = A= αa
mod p =
Bob’s public key: kpub,B = B=αb mod
p =
Send A to Bob; intercepted by Carol
Send B to Alice; intercepted by Carol
Carol chooses c=6; computes
A’ = B’ =αc mod p
Carol sends A’ to Bob as if it is A from Alice
Carol sends B’ to Alice as if it is from Bob
Alice derives the shared secret key as
K1= B’a mod p
Carol derives K1= Ac mod
p, K2= Bc mod p,
Bob derives the shared secret key as
K2= A’b mod p
Session 1 established with key K1: verify that Alice and Carol have
derived the same key K1
Session 2 established with key K2; verify that Carol and Bob have
derived the same key K2
