(in Polish) Algorytmy teorii liczb i kryptografii 0800-ALGLICZB

1. Sieve of Eratosthenes
2. Gaussian and Eisenstein primes
3. Euclid algorithm, Bezout identity
4. Factorisation algorithms
5. Primality testing algorithms
6. Exponentiation by squaring
7. Algorithms for computing discrete logarithms
8. El-Gamal and RSA cryptosystems
9. Cryptanalysis by frequency analysis
10. Performing the group operation of elliptic curves
11. El-Gamal cryptosystem on elliptic curves

Total student workload

30 hours of classes 30 hours of work alone

Learning outcomes - knowledge

Gaussian and Eisenstein primes Caesar and Vigenere codes Al-Kindi frequency analysis and Kasickis period analysis

Learning outcomes - skills

Skills on algorithmic thinking Practical understanding of number theory and the theory of rings and number fields Practical understanding of algorithms of number theory Practical understanding of algorithms of cryptography and cryptoanalysis Elementary skills on visualising results graphically

Learning outcomes - social competencies

None

Teaching methods

Supervised programming

Exploratory teaching methods

- practical
- laboratory

Type of course

elective course

Prerequisites

Lecture on discrete mathematics Python course - passed or attended parallelly

Course coordinators

Gniewomir Sarbicki

Assessment criteria

Colloquia in the last class, extra points for homework

Practical placement

None

Bibliography

Kenneth A. Ross, Charles R. B. Wright Matematyka Dyskretna PWN 2005
J. Jaworski, Z. Palka, J. Szymański Matematyka Dyskretna dla Informatyków
A. Szepietowski Matematyka Dyskretna
S. G. Krantz Discrete Mathematics Demystified
Kenneth A. Rosen Handbook of discrete and combinatorial mathematics
Władysław Narkiewicz Teoria Liczb PWN 2003
Jerzy Rutkowski Algebra abstrakcyjna w zadaniach PWN 2006
A. I. Kostrykin Wstęp do algebry PWN 2005
A. Chrzęszczyk Algorytmy teorii liczb i kryptografii w przykładach Wydawnictwo BTC 2010
N. Koblitz Wykład z teorii liczb i kryptografii WNT Warszawa 2006
N. Koblitz Algebraiczne aspekty kryptografii WNT Warszawa 2000

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 0800-ALGLICZB in USOSweb