CS 463/563: Cryptography for Cyber Security
Fall 2021
Homework #11: Due: November 21, 2021
Points: 20
Q1. [Points 10] 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
KEK: kA = A6 (hexa)
KEK: kA = A6 (hexa); 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);
Bob
KEK: kB = D8 (hexa);
yA = ekA(kses) = ??
yB = ekB(kses) = ??
KDC sends yA = ?? to Alice
Decrypt yA to derive kses
using kA =
KDC send yB = ?? to Bob
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 ?= 4 are known to all
Choose kpri,A =a = 7
Choose kpri,B =b = 8
Aliceàpublic key: kpub,A = A= ?a
Bobàpublic key: kpub,B = B=?b mod
mod p =
p=
Send A to Bob; intercepted by Carol
Send B to Alice; intercepted by Carol
Carol chooses c=6; computes
A= B=?c mod p
Carol sends A4o Bob as if it is A from Alice
Carol sends B4o Alice as if it is from Bob
Alice derives the shared secret key as
Bob derives the shared secret key as
Carol derives K1= Ac mod
a
c
K1= B-od p
K2= A mod p
p, K2= 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
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