TMA4160 - Cryptography


Examination arrangement

Examination arrangement: Home examination
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Home examination 100/100 4 hours

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. Lattices and the LLL algorithm. Diffie-Hellman, public-key encryption (ElGamal, RSA, lattice-based), 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, elliptic curves and lattices. 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 groups and finite fields, the main algorithms for factorization, algorithms for primality testing and lattice algorithms. 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.

Further on evaluation

see «Teaching methods and activities».

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5023 7.5
TMA4155 4.5 01.09.2007

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


Term no.: 1
Teaching semester:  AUTUMN 2020

No.of lecture hours: 4
Lab hours: 1
No.of specialization hours: 7

Language of instruction: English, Norwegian

Location: Trondheim

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

Department with academic responsibility
Department of Mathematical Sciences



Examination arrangement: Home examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Autumn ORD Home examination (1) 100/100

Release 2020-12-16

Submission 2020-12-16

Release 09:00

Submission 13:00

Room Building Number of candidates
Summer UTS Home examination 100/100 INSPERA
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.
  • 1) Merk at eksamensform er endret som et smittevernstiltak i den pågående koronasituasjonen. Please note that the exam form has changed as a preventive measure in the ongoing corona situation.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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