Course content

The course gives an introduction to modern cryptography and the underlying number theory. Topics covered include: Classical ciphers; modern symmetric cryptography; public-key cryptography and digital signatures; RSA, ElGamal and Diffie-Hellman; basic number theory; primality testing; integer factorisation; discrete logarithms.

Learning outcome

1. Knowledge. The student has an overview of the most important classical cryptosystems and how to break them. The student is familiar with the main ideas in the applications of symmetric and asymmetric cryptography, and with the main strategies for breaking cryptosystems based on discrete logarithms and factorization. The student has an overview of elementary number theory.

2. Skills. The student masters the basic algorithms for modular arithmetic and is able to compute discrete logarithms and factorize integers using various algorithms. Moreover, the student is able to break various classical ciphers, and has a certain intuition regarding how to attack cryptosystems.

Learning methods and activities

Lectures and exercises. Written examination counts 100% towards the final grade. 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.

Recommended previous knowledge

TMA4110/4115 Calculus 3 or equivalent background.

Course materials

Will be announced at the start of the semester.

Credit reductions