Computational Number Theory

Spring 2026

General Information | Announcements | Course Objectives | Course Topics | Lectures | Practical Works | Required Text and Materials | Class Requirements | Exams

General Information

Instructor

Sorin Iftene

Office: C904

E-mail: sorin.iftene @ info.uaic.ro

Class Time and Location

Course - Friday, 8:00-10:00 in C309

Announcements

February 15 -A dedicated Google Classroom Account has been created

https://classroom.google.com/c/NzkzODQzNzMzMjEy?cjc=5u47vjlt

Course Objectives

This course will focus on designing efficient algorithms (and providing complexity analysis) for the most important problems from number theory, with major applications in coding theory and cryptography.

Course Topics

- Representations of Integers and Polynomials

- Basic Operations (addition, subtraction, multiplication, division, (extended) gcd, inverse, Chinese remainder theorem)

- Exponentiation and Multiexponentiation

- Primality Testing (Probabilistic Primality Testing, Primality Testing for Numbers of a Special Form)

- Computing the Order of an Element and Generating Primitive Roots (and Elements of a Certain Order)

- Computing Discrete Logarithms

- Solving Equations over Finite Fields (including computing square roots)

- The Arithmetic of Elliptic Curves

Lectures

- will be announced on the dedicated Google Classroom Account

Practical Works

• four homework assignments will be assigned during the semester

• late assignment submissions will be penalized as follows: a late assignment within one week of the deadline will be penalized by 20%
• assignment submissions more than one week late will not be accepted
• exceptions to these rules will of course be made for serious illness or other emergency circumstances; in these cases, please contact me as soon as you are aware of the problem.

• you must collect a minimum of 50% from the maximum number of points

Required Text and Materials

[1] Abhijit Das. Computational Number Theory. CRC Press, 2013

[2] Hans Riesel. Prime Numbers and Computer Methods for Factorization (2nd Edition). Birkhauser, 2012

[3] F. L. Ţiplea et al. MpNT: A Multi-Precision Number Theory Package. Number Theoretical Algorithms (I). TR03-02, Faculty of Computer Science, Al. I. Cuza University, 2003

[4] R. P. Brent, P. Zimmermann. Modern Computer Arithmetic. Cambridge University Press, 2010

[5] relevant conference or journal articles (will be gradually announced)

Class Requirements

Class participation:  Students are expected to come prepared and actively participate in the courses and practical works.

The course grade will be determined as follows:

presentation of homeworks (during practical works): 35%

midterm exam: 35%

final exam: 30%

(You have to collect at least 50% points from the practical works and at least 50% points from each exam)

Exams

- midterm exam -TBA

- midterm re-evaluation exam -TBA

- final exam - TBA

- final re-evaluation exam - TBA