TMA4160 - Cryptography


Examination arrangement

Examination arrangement: Written examination
Grade: Letters

Evaluation Weighting Duration Grade deviation Examination aids
Written examination 100/100 4 timer

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

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5023 7.5
TMA4155 4.5

Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  AUTUMN 2013

Language of instruction: English, Norwegian


Subject area(s)
  • Mathematics
  • Technological subjects
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences


Examination arrangement: Written examination

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD Written examination 100/100 2013-12-17 15:00
Room Building Number of candidates

Examination arrangement: Oral examination

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Summer KONT Oral examination 100/100 2014-08-13
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

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