Algorithms for Numbers and Public-Key Cryptography

Professors: Jean-Sébastien Coron

The goal of the course is to learn the basics of computational number theory and public-key cryptography.

The course takes place in room A14.
  1. Friday, March 7th, 2014, 14:00-16:30
    Course: Basics of C programming. Euclid's algorithm
    Exercise: Simple exercises. Implementation of Euclid's algorithm.
  2. Friday, March 14th, 2014, 14:00-16:30
    Course: Basics of C programming. Modular arithmetic
    Exercise: Implementation of Euclid's extended algorithm.
  3. Friday, March 21st, 2014, 14:00-16:30
    Course: Computing with large integers. Modular exponentiation.
    Exercise: Implementation of large addition and multiplication.
  4. Wednesday, March 26th, 2014, 8:00-10:30 in room B15
    Course: Computing with large integers: modular reduction. Euler function.
    Exercise: Implementation of modular reduction for large integers.
  5. Friday, April 4th, 2014, 14:00-16:30
    Course: The RSA algorithm. Primality testing.
    Exercise: Implementation of RSA light. Implementation of primality testing.
  6. Friday, April 11th, 2014, 14:00-16:30
    Course: Discrete-log groups and applications.
    Exercise: Implementation of DL groups.
  7. Friday, May 2nd, 2014, 14:00-16:30
    Course: Polynomial arithmetic and application to secret-sharing.
    Exercise: Implementation of polynomial arithmetic.
  8. Friday, May 9th, 2014, 10:30-13:00. Room C17
    Course: 30 years of attacks against RSA.
    Exercise: implementation of RSA
  9. Friday, May 9th, 2014, 14:00-16:30
    Course: security proof for RSA signatures.
    Exercise: implementation of RSA-FDH and fault attacks.
  10. Friday, May 16th, 2014, 10:30-13:00. Room C17
    Course: Discrete-log based cryptography
    Exercise: implementation of EC El-Gamal
  11. Friday, May 16th, 2014, 14:00-16:30
    Course: Identity-based encryption.
    Exercise: implementation of IBE
  12. Friday, May 23rd, 2014, 10:30-13:00. Room C17
    Course: How to hash into Elliptic-Curves
    Exercise: Implementation of Icart's function
  13. Friday, May 23rd, 2014, 14:00-16:30.
    Course: Side-channel attacks and countermeasures
  14. Friday, June 6th, 2014, 14:00-16:30.
    Course: Security proof of Boneh-Franklin IBE
Homework: big integer library and implementation of RSA.
This homework is due June 23rd, 2014. It will make 100% of the final grade, with a bonus for students who have completed the exercises from the course.