## 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.- Friday, February 19th, 2016, 14:00-16:30

Course: Basics of C programming. Euclid's algorithm

Exercise: Simple exercises. Implementation of Euclid's algorithm. - Friday, March 11th, 2016, 14:00-16:30

Course: Basics of C programming. Chinese Remainder Theorem. Computing with large integers.

Exercise: Implementations. - Friday, March 18th, 2016, 14:00-16:30

Course: Computing with large integers. Modular arithmetic.

Exercise: Implementation of large addition and multiplication. - Friday, March 25th, 2016, 08:00-10:30

Course: The RSA algorithm. Primality testing.

Exercise: Implementation of RSA light. Implementation of primality testing. - Friday, March 25th, 2016, 14:00-16:30

Course: Discrete-log groups and applications.

Exercise: Implementation of DL groups. - Friday, April 8th, 2016, 8:00-10:30

Course: Polynomial arithmetic and application to secret-sharing.

Exercise: Implementation of polynomial arithmetic. - Friday, April 8th, 2016, 14:00-16:30.

Course: 30 years of attacks against RSA.

Exercise: implementation of RSA - Friday, April 22nd, 2016: 14:00-16:30.

Course: security proof for RSA signatures.

Exercise: implementation of RSA-FDH and fault attacks. - Friday, May 6th, 2016, 08:00-10:30.

Course: Discrete-log based cryptography

Exercise: implementation of EC El-Gamal - Friday, May 6th, 2016, 14:00-16:30.

Course: Identity-based encryption.

Exercise: implementation of IBE - Friday, May 13rd, 2016, 14:00-16:30.

Course: Security proof of Boneh-Franklin IBE - Friday, May 20th, 2016, 14:00-16:30.

Course: How to hash into Elliptic-Curves

Exercise: Implementation of Icart's function - Friday, May 27th, 2016, 14:00-16:30.

Course: Side-channel attacks and countermeasures

Homework: big integer library and implementation of RSA.

This homework is due June 30th, 2016. It will make 100% of the final grade, with a bonus for students who have completed the exercises from the course.

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