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: Divide the key into two halves: LK and RK; Divide the plaintext into two halves: LT and RT; Then ciphertext= LC||RC where LC=LK XOR RT; and RC = RK XOR LT; where LC, RC, LT, and RT are each 4 bits; Plaintext and ciphertext are each 8 bits. For example, if plaintext=A7 (Hexa) and Key = 6D; then LC=6 ⊕ 7 = 0110 ⊕ 0111 = 0001 = 1 (Hexa); and RC = D ⊕ A = 1101 ⊕ 1010 = 0111 = 7 (Hexa); so Ciphertext = 17 (Hexa). To decryptt, it does the reverse operation: Given ciphertext of C=LC||RC, it finds plaintext T=LT||RT, by finding LT=RC ⊕ RK and RT = LC ⊕ LK. In the above example, LT = 7 ⊕D = 0111⊕1101=1010=A; RT=1 ⊕ 6 = 0001 ⊕ 0110 = 0111=7; So Plaintext=A7 (Hexa). b. Alice and Bob now decide to use Diffie-Hellman Key Exchange (DHKE) (p. 343) with certificates. Both Alice and Bob agree on p=17 and α=4. Alice chooses a=5 and Bob chooses b=3. Answer the following. What is the public key generated by Alice? What is the public key generated by Bob? What is the computed shared key by Alice? What is the computed shared key by Bob? c. Man-in-the-middle attack when Alice and Bob employ Diffie-Hellman key exchange. Here, Carol is the intruder. Compute and complete the unknown entries in the exchanges shown below

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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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: Divide the key into two halves: LK and RK; Divide the plaintext into two halves: LT and RT; Then ciphertext= LC||RC where LC=LK XOR RT; and RC = RK XOR LT; where LC, RC, LT, and RT are each 4 bits; Plaintext and ciphertext are each 8 bits. For example, if plaintext=A7 (Hexa) and Key = 6D; then LC=6 ⊕ 7 = 0110 ⊕ 0111 = 0001 = 1 (Hexa); and RC = D ⊕ A = 1101 ⊕ 1010 = 0111 = 7 (Hexa); so Ciphertext = 17 (Hexa). To decryptt, it does the reverse operation: Given ciphertext of C=LC||RC, it finds plaintext T=LT||RT, by finding LT=RC ⊕ RK and RT = LC ⊕ LK. In the above example, LT = 7 ⊕D = 0111⊕1101=1010=A; RT=1 ⊕ 6 = 0001 ⊕ 0110 = 0111=7; So Plaintext=A7 (Hexa).

b. Alice and Bob now decide to use Diffie-Hellman Key Exchange (DHKE) (p. 343) with certificates. Both Alice and Bob agree on p=17 and α=4. Alice chooses a=5 and Bob chooses b=3. Answer the following.

1. What is the public key generated by Alice?
2. What is the public key generated by Bob?
3. What is the computed shared key by Alice?
4. What is the computed shared key by Bob?

c. Man-in-the-middle attack when Alice and Bob employ Diffie-Hellman key exchange. Here, Carol is the intruder. Compute and complete the unknown entries in the exchanges shown below.

Alice
Carol (Intruder)
p=17 and a= 4 are known to all
Bob
Choose kpri,A =a = 7
Choose kpri,B =b = 5
Alice's public key: kpub,A =A= aª
Bob's public key: kpub,B=B=ab
mod p = ??
mod p = ??
Alice sends A to Bob; intercepted by Carol
Bob sends B to Alice; intercepted by Carol
Carol chooses c=4; computes
A =B =a° 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
Carol derives
Bob derives the shared secret key as
Kl= (B')ª mod p = ??
Kl= A° mod p = ??,
K2= (A')b mod p = ??
and K2= BC 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

Alice
KDC
Bob
KEK: kA = CD (hexa)
KEK: kA = CD (hexa); kg = F1(hexa);
КЕК: kв 3D F1 (hexa);
Alice sends a message to KDC requesting a session key between Alice and Bob
KDC Generates a random session key: kses = B4 (hexa);
YA = ekA(kses) = ??
YB = ekB(kses) = ??
KDC sends yA = ?? to Alice
KDC send yB = ?? to Bob
Děcrypt yA to derive kses using kA = ??
Decrypt yB to derive kses using kg = ??
Message to send,m = E6 (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

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