Sample/practice exam 7 December 2019, questions and answers PDF

Preview

Summary

INSE 6110 Review1) Consider the Affine cipher studied in class. Can the set (=4 and =7 )be used as anencryption key (Yes, No)? Why?2) In Affine cipher if the attacker was able to capture the following plaintext: IF=(8, 5) andcorresponding ciphertext PQ=(15, 16). Find the key set ( and  )3) Is on...

Description

INSE 6110 Review 1) Consider the Affine cipher studied in class. Can the set (=4 and =7 )be used as an encryption key (Yes, No)? Why? 2) In Affine cipher if the attacker was able to capture the following plaintext: IF=(8, 5) and corresponding ciphertext PQ=(15, 16). Find the key set ( and  ) 3) Is one time pad a secure cryptosystem? 4) Consider the Hill cipher studied in class. if the attacker was able to capture the following plaintexts: IF=(8, 5) and corresponding ciphertext YD=(24, 3) and PQ=(15, 16) and corresponding ciphertext DJ=(3, 9). Can you Find the key Matrix for this cipher. IF yes, find the key if no explain why. 5 3 Answer (yes,K=𝐾 = [ ] 2 1 5) Suppose that users Alice and Bob carry out the Diffie-Hellman key agreement protocol with p = 101 and g = 17. Suppose that Alice chooses x = 19 and Bob chooses y = 13. Show the computations performed by both Alice and Bob, and determine the key that they will share. Ans. Alice -> Bob g^x mod p=6 Bob -> Alice g^y mod p=65 Shared key = g^(xy) mod p=14 6) Suppose that users Alice and Bob carry out the Diffie-Hellman key agreement protocol with p = 17 and g = 3. Suppose that Alice chooses x = 5 and Bob chooses y = 15. Check that Alice and Bob Have the same key (Show all the computations performed by both Alice and Bob).

7) Suppose that users Alice and Bob carry out the 3-pass Diffie-Hellman protocol with p = 101. Suppose that Alice chooses a1 = 19 and Bob chooses b1 = 13. If Alice wants to send the secret message m=5 to Bob, show all the messages exchanged between Alice and Bob Ans. a2=a1 ^ (-1) mod (p-1) =79 b2=77 Alice -> Bob m^a1 mod p =37 Bob -> Alice 80 Alice to Bob 56 Bob evaluates obtains m by evaluating 56^b2 mod p =5 8) Suppose that users Alice and Bob carry out the 3-pass Diffie-Hellman protocol with p = 11. Suppose that Alice chooses a1 = 3 and Bob chooses b1 = 9. If Alice wants to send the secret message m=5 to Bob, show all the messages exchanged between Alice and Bob

9) Consider an RSA system with p=7, q=11 and e=13. Find the plaintext corresponding to c=17 using CRT. Ans. d=37 and m=52 10) Consider an RSA system in which the attacker knows that n1 and n2 has the form n1=pq1=16637 and n2=pq2=17399. Show how the attacker can break this system. 11) Consider an RSA system with n=143, e1=7 and e2=17. Suppose the same message m was sent to the two users above and the attacker observed the ciphertext c 1=42 and c2=9. Show how the attacker can recover the message.

12) Consider an RSA that is using twin primes. If n=10403 and e=8743. Show how the adversary can recover the message corresponding to c=99. Ans. p(p+2)=n -> p=101 q=103 , Ф(n)=10200. d=e^(-1) mod Ф(n)=7 -> m=c^d mod n=9366 13) Consider an RSA system where the public key of three users (i.e., (n,e) are given by: (319,3), (697,3) and (1081,3). If the same message was sent to the three users. Show how the attacker can recover m by observing the ciphertexts c1=128, c2=34 and c3=589. Ans. This is an example of the low exponent attack explained in class. The attacker uses the Chinese remainder theorem to solve for m3 mod (n1 n2 n3). Just denote m3 by x. Then this is equivalent to solving for x that satisfies x=128 mod 319, x=34 mod 697 and x=589 mod 1081. Using CRT we get x=4913 -> m=4913^(1/3)=17

14) Factor N = 26797 using the fact that Ф(N)= 26460. Ans. (By solving a quadratic equation in p or q, we get p=127, q=211) 15) Factor N=77 using the fact that 682=22 mod N Answer(p=7, q=11) 16) Let S(x) be given by x 0123 S(x) 3102 Use this S-box to construct a toy SPN (similar to the one explained in the class) with 2 rounds and a block size of 4 bits. Assume all the round keys are zeroes. Determine the output corresponding to p=(0000) Would increasing the number of rounds of the above SPN add any security? Why?

17) Verify the encryption/decryption operation for the 2 round Feistel cipher shown?

L

R

1

Encryption

2

Decryption...