# Computing

## Discrete Mathematics 2

- Class 45
- Practice 4
- Independent work 101

### Course title

Discrete Mathematics 2

### Lecture type

Elective

### Course code

183494

### Semester

6

### ECTS

5

### Lecturers and associates

### Course objectives

The Euclidean algorithm; Prime numbers.

Linear congruences. The Chinese Remainder Theorem.

Euler's phi-function.

Primitive roots. Solving some polynomial congruences.

The Legendre symbol; The Jacobi symbol.

The Quadratic Reciprocity Law.

Linear Diophantine equations; Pythagorean triples; Pell's equation.

Midterm exam.

Semigroups and groups.

Rings and fields.

Finite fields.

Introduction to cryptography.

Symmetric cryptography.

The RSA cryptosystem. Public-key cryptography.

Final exam.

### Required reading

(.), Andrej Dujella, Uvod u teoriju brojeva, https://web.math.pmf.unizg.hr/~duje/utb/utblink.pdf,

(.), K. H. Rosen: Elementary Number Theory and Its Applications, Addison-Wesley, Reading, 1993.,

(.), D. Žubrinić, Diskretna matematika, Element, 1997.,

(.), Course in Number Theory and Cryptography N. Koblitz Springer 1994,

(.), A. Baker: A Concise Introduction to the Theory of Numbers, Cambridge University Press, Cambridge, 1994.,(.), I. Niven, H. S. Zuckerman, H. L. Montgomery: An Introduction to the Theory of Numbers, Wiley, New York, 1991.,

(.), A. Baker: A Comprehensive Course in Number Theory, Cambridge University Press, Cambridge, 2012.,

(.), Cryptography. Theory and Practice D. R. Stinson CRC Press 2002

#### Online education during epidemiological measures

- Study program duration
- 6 semesters (3 years)
- Semester duration
- 15 weeks of active teaching + 5 examination weeks
- Total number of ECTS points
- 180
- Title
- Bacc.ing.comp (Bachelor of Science in Computing)

**Academic calendar**

#### Minimal learning outcomes

- To solve linear congruence and a system of linear congruences
- Solve some of the polynomial and exponential congruences via prime roots
- Examine the solution existence of quadratic congruence by virtue of the Jacobi symbol
- Solve some basic diophantine equations
- Compute in finite fields
- Apply number theory and group theory in public key cryptography