Kurdistan Algebra Project 2026
Part IV
Erbil April 5-16, 2026
Laura Geatti and Lea Terracini
Please contact us for questions!
Program: Review of the ring Z/nZ and its properties. Primality of Large Numbers. Large number factorization.
Cryptography. The RSA Cryptosystem. Digital Signatures. Safety of RSA. Discrete Logarithms. Diffie-Hellman protocol.
Prerequisites: The Algebra course, parts I, II, III. A good working knowledge of modular arithmetic is especially desirable (see Exercises 1 below).
References: - P. Stevenhagen, Algebra 1, Chapter 7.
- PARI/GP
computer algebra system for doing fast computations in number theory.
- VIDEOS of the lectures will be recorded. The links to the videos will be posted on this page.
Contacts: Our email adderesses are
geatti@mat.uniroma2.it lea.terracini@unito.it
- Video1: Introduction to the course link
- Video2: The division algorithm and its applications: the Euclidean algorithm for computing the gcd of two integers, Bezout identity, expressing an integer in different bases.
link
- Video3: Review of the ring Z/n Z link
- Video4: The Euler φ function link
- Video5: Inverses modulo n link
- Video6: Congruences modulo n
link
- Video7: Chinese Remainder Theorem and systems of congruences
link
- Video8: Euler's Theorem, Fermat Little Theorem and prime numbers
link
- Video9: Primality testing and the Prime Number Theorem (part 1)
link PNT: examples pdf
- Video10: Introduction to Cryptography (part 1)
link
- Video11: Introduction to Cryptography (part 2)
link
- Video12: Primality testing and the Prime Number Theorem (part 2)
link
- Video13: RSA examples and digital signatures
link RSA examples pdf
- Video14: The discrete logarithm (Part 1)
link
- Video15: The discrete logarithm (Part 2)
link
- Video16: The discrete logarithm (Part 3)
link
- Video17: Review exercises
link
Exercises
- Exercises 1 (review of modular arithmetic) pdf
- Exercises 1: solutions pdf
- Exercises 2 (the ring Z/n Z, RSA, the discrete logarithm, Diffie-Hellman key exchange) pdf
- Exercises 2: solutions pdf