Course content

A brief overview of classical ciphers. Algorithms for primality testing. Basic algorithms for computation of discrete logarithms in cyclic groups. Index-calculus algorithms for computation of discrete logarithms in finite fields. Elliptic curves over finite fields. Algorithms for factorization of integers. Diffie-Hellman, public-key encryption (ElGamal, RSA), digital signatures (RSA, Schnorr).

Learning outcome

1. Knowledge. The student has an overview of the algebra that forms the basis of modern symmetric and asymmetric cryptography, and some knowledge of classical and modern symmetric cryptography. The student is familiar with the theory of finite cyclic groups, finite fields and elliptic curves. Moreover, the student is familiar with the motivation for, the use of and attacks on asymmetric cryptography, and knows the main systems.

2. Skills. The student masters the main algorithms for calculating discrete logarithms in finite cyclic group and finite fields, the main algorithms for factorization, and alorithms for primality testing. The student is able to apply the theory of zeros of polynomials over finite fields to assess the security of relevant cryptosystems. The student has aquired some intuition about how to attack various cryptosystems.

Learning methods and activities

Lectures and exercises. The exercises may involve the use of computers. Retake of examination may be given as an oral examination. The lectures may be given in English. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course is based on TMA4150 Algebra and Number Theory or similar background from algebra, or MA2201 Algebra. Some proficiency in the use of computers.

Course materials

Will be announced at the start of the course.

Credit reductions