Guidelines:
- Homework assignments are annunced on the Blackbord with their deadlines, and must be submitted as PDF through the Blackboard. Assignments submitted by emails are NOT graded.
- Before solving the homework problems, you are expected to do the weekly reading assignments and understand the related material.
- An asterisk (*) indicates supplementary reading material.
- The homework PDF file must have a header on the first page, and a header for each question. See HW-format. Please follow this format when you submit your homework in order to be graded. See also an example of a HW_Sample, which can be used as a template for your homework.
- Late submission is subjected to a 50% penalty if it is submitted by the cut-off time (usually 48 hours after the announced deadline).
- Resubmission: If you submit a wrong file, or modify the solution after submission, you can resubmit within the deadline (at most twice). Only the latest submission on the Blackboard will be graded and late penalty may apply if resubmitted after the deadline.
- Class SN (CSN): You may find your Class-SN here if applicable, otherwise use your short name as spelled in the class.
Reading Assignment [Weeks 1-2]: Introduction to Cryptography, Modular Arithmetic
Forouzan: Chapters 1 and 2 (all)
Stallings: Chapter 2.
Rosen: Sections* 4.1-4.3
Homework Assignment HW1:
Forouzan: Chapter 1. Exer: 1, 2, 7, 8(a).
Forouzan: Chapter 2. Exer: 12(a,b), 16(b), 18(b,c), 25, 26, 32(a, b), 36(c), 40(b).
Total: 12 exercises.
Reading Assignment [Weeks 3-4]: Traditional symmetric-key ciphers, Types of attack, Blockcipher, DES.
Forouzan: Chapter 3
Forouzan: Sections 5.1, (6.1-6.4)*
Stallings: Chapter 3*, 4*
Additional ppt slides on: Blockcipher and DES.
Homework Assignment HW2:
Forouzan: Chapter 3. Exer: 11, 12, 13, 14, 18.
Stallings: Chapter 3. Problem: 3.
Forouzan: Chapter 5. Exer: 8, 14, 24, 27.
Forouzan: Chapter 6. Exer: 9, 10.
Total: 12 exercises.
Reading Assignment [Weeks 5-6]: AES, Group Theory, Subgroups, Cyclic Groups, Primitive Roots.
Stallings: Chapter 6, Section 7.1*
Forouzan: Chapter 7*.
LNGT: Sections 1, 2.
Additional material on AES: P5.AES, AES_Demo.
Homework Assignment HW3:
LNGT: Section 1. Exer: 3, 4, 5, 6(c,d), 7(b,c).
LNGT: Section 2. Exer: 3(a,b,c,f,g), 6(a,b), 7(a,b,c), 8(a,b), 9.
Additional Problems:
EP#1. Answer the following questions about AES:
(a) What are the main advantages and disadvantage of 3DES?
How does AES keep the advantages and eliminate the disadvantages?
(b) What are the main requirements of AES stated by NIST?
(c) Briefly describe the 4 stages in the AES round?
(d) The 4 stages in the AES round together provide high security. Explain the weakness of each stage alone.
(e) What are the main strength points of the design of the S-box in AES?
EP#2. Compare DES, 3DES and the three AES versions in terms of: block size, number of rounds, the main key length, and the round-key length. (Use a 5x4 table)
Total: 12 exercises.
Reading Assignment [Weeks 7-8]: Permutation Groups, Cayley Theorem, Entropy, Perfect Secrecy, One-Time Pad.
LNGT: Sections 3.
Forouzan: Appendix F.2.
Bellare: Sections 1.4.3, and 2.2.
Homework Assignment HW4:
LNGT: Section 3. Exer: 1, 2, 3(a,b,c), 4(a,b,c), 5, 6(c,e), 7, 8.
Bellare: Chapter 2. Problems: 2.1, 2.2.
Additional Problems:
EP#1. Alice wants to choose a random month m (between 0 and 11) to go for a secret mission. Instead of using a psudorandom number generator, she decides to flip a fair coin 11 times, and set m to be the number of times she gets heads.
(a) Find the probablity that the secret mission will be in January (m = 0).
(b) Find the probabilyt that the secret mission will be in July (m = 6).
(c) Compute the entropy of m as computed by Alice's algorithm?
(d) Compute the enrtopy of a purely (uniformly) random variable x between 0 and 11, and compare it with m in (c). Which one is better? Explain.
EP#2.
Assume Alice and Bob are using an XOR symmetric scheme to communicate messages of length 1024 bits, and they obtain the shared key from a random bit generator G.
In each of the following cases, determine whether the scheme is a perfectly secured Shannon chiper if it is known that every key of length 1024 bits generated by G contains:
(a) exactly 512 ones and 512 zeros?
(b) more ones than zeroz, about 75% ones and 25% zeros?
(c) at least 1 one and 1 zero? (i.e. the other 1022 bits remain random).
Justify your answer in each case.
Total: 12 exercises.
Reading Assignment [Weeks 9-11]: Publick-Key, RSA, Diffie-Hellman, Quadratic Resiudes, Shor's Algorithm, BB84.
Sallings: Sections 9.1, 9.2, 10.1.
Forouzan: Sections 9.3*, 9.5, (10.1-10.2)*
Yanofsky: Sections 6.5, 9.1, 9.2.
Additional ppt slides on: Shor's Algorithms.
Homework Assignment HW5:
Stallings: Chapter 9. Problem: 2(b), 8.
Forouzan: Chapter 10. Exer: 14, 17.
Yanofsky: Chapter 6. Exer: 6.5.3, 6.5.5, 6.5.7.
Yanofsky: Chapter 9. Exer: 9.2.1, 9.2.2.
Additional Problems:
EP#1. Find all square roots of 92 modulo n, show work for credit, where:
(a) n = 103
(b) n = 127
(c) n = 133 (for ICS562 only)
EP#2. Suppose Alice and Bob use RSA with the same modulus n, and each user has a different pair of public/private keys assigned by a trusted party. Explain a possible risk in this scheme
EP#3. Alice and Bob exchange keys in Diffie-Hellman scheme, with p = 19, g = 2. If Alice chooses a random value x = 16, and receives 13 from Bob.
(a) What value Alice should send to Bob?
(b) Compute the exchanged key.
(c) Explain the man-in-the-middle attack on Diffie-Hellman key exchange scheme.
Total: 12 exercises.
Reading Assignment [Weeks 12-14]: B92, EPR, Post-Quantum Cryptography, Lattices, Coin-Flipping, Quantum OTP.
Yanofsky: Sections 9.3, 9.4.
Lattices: Sections 1 and 2.
Bellare: Section 1.2.3.
Classnotes on Lattice-based cryptography, Coin flipping and Quantum OTP.
Homework Assignment HW6: (Optional)
See hw6.pdf
Total: 9 exercises.