Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Algebra and Number Theory
- Code
- szgelm1u0um17em
- Title
- Computational number theory (l)
- Usual semester
- Spring
- Published semester
- 2025/26/2
- ECTS
- 3
- Language
- hu
- Learning outcomes
- Knowledge: getting familiar with computational number theory Ability: to understand and use computational number theory Attitude: the need to extend the mathematical knowledge, to gain new analytic skills Autonomy and Responsibility: based on the gained knowledge in computational number theory, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Running time of elementary operations and number theory tasks. When n=pq, the determination of p, q is polynomially equivalent to φ(n). Modular exponentiation. Factorization with algebraic identities. Basic concepts of cryptography. RSA, discrete logarithm, the Diffie-Hellmann key exchange system. Prime testing, pseudoprimes. Fermat factorization, the factor base algorithm, the quadratic sieve. Elliptic curves, the analogue of Diffie-Hellmann key exchange. Pseudorandom sequences, their application in connection with the Monte Carlo method and in cryptography.
- Assessment method
- exam
- Bibliography
- lecture notes