ITC8240 Cryptography

Course information

Code: ITC8240 Cryptography

ECTS: 6

Assessment: examination

Instructors:

• Ahto Buldas ahto dot buldas at ttu dot ee
• Jaan Priisalu jaan dot priisalu at ttu dot ee
• Aleksandr Lenin aleksandr dot lenin at ttu dot ee

Schedule

Lecture: Tue 12:00 - 13:30 @U06A-201

Exercise:

 *  Wed 17:45 - 19:15 @SOC-417
 *  Wed 19:30 - 21:00 @SOC-417
 *  Fri 14:00 - 15:30 @ICT-A1

Announcements

06.09.2018 Math test results are available here.

19.10.2018 Practice lessons on November 7th (IVCM 11,12) and 9th (IAPM 11,12) are cancelled.

Lectures

1. Simple Ciphers and Attacks and Elementary Number Theory

2. Application Problems and Protocol Issues

3. Theory of Unbreakable Ciphers

4. Breaking Imperfect Ciphers

5. Key Establishment

Exercises

Weeks 2,3: Modular Projection

• Exercises and Solution
• Proofs of relevant theorems.

Week 4: Theory of Unbreakable Ciphers

• Theory of Probability (notes)
• Probabilistic Cipher Model (notes)

Weeks 5,6: Breaking historical ciphers

• Exercises part1 and Solution
• Exercises part2 and Solution

Week 7: Key establishment protocols

• Homework Due date: Mon, Nov 5th
• Exercises and Solution. The 3SAT model of graph 3-colorability can be seen here 3sat.

Week 8: Groups

• Exercises and Solution

Week 9: RSA, Chinese Remainder Theorem

• Chinese Remainder Theorem (theory)
• Exercises

Week 10: First written test

• List of topics to prepare for the test

Week 11: Primality Testing, CRT, RSA weaknesses

• Exercises and Solution

Week 12: Strong primality tests

• Exercises and Solution

Week 13: Factoring and plain RSA insecurity (again)

• Exercises and Solution

Week 14: RSA-CRT fault attacks, DDH assumption

• Solution

Week 15: Topics for the test

   1. Modular exponential function: finding primitive elements in simple cases
   2. Diffie-Hellman key establishment
   3. Man in the middle attack against Diffie-Hellman key establishment
   4. O- and o- notations
   5. The notion of S-security and security bits
   6. RSA setup: given prime numbers, find suitable public and private exponents
   7. RSA setup: given a public exponent, find suitable prime numbers or determine if given primes are ok for RSA
   8. Probabilistic prime number tests: given the required reliablility of the test, compute the number of trials
   9. Common modulus RSA: how to reconstruct the message if the same message is sent to two users in encrypted form
   10. Chinese reminder theorem
   11. Finding square roots of 1
   12. Factoring with square roots of 1
   13. Small public modulus attack against pure RSA
   14. Blind signatures and Chaum’s digital cash
   15. Homomorphic property of RSA and related weaknesses