Summer Semester 2010/11
Mathematical Foundations of Cryptography MAT3602
Course content:
What is a cryptographic system. Examples of classic monoalphabetic substitution and permutation ciphers. Polialphabetic ciphers.
Affine and Hill's ciphers.
Cryptoanalysis of monoalphabetic substitution ciphers and the Vigenere cipher.
Elements of Shannon information theory.
Cipher maschines - Enigma.
Cryptoanalysis of Enigma.
Mathematical foundations of asymmetric systems.
RSA as a basic asymmetric system.
Probabilistic test of primality.
Cryptoanalysis of RSA - selected methods.
Finite fields, indecomposable polynomials over finite fields. Eliptic curves.
Asymeetric system based on finite fields.
Standards DES and AES
Learning outcomes: Basic knowledge about cryptographic systems
(in Polish) Rodzaj przedmiotu
Course coordinators
Bibliography
a) basic references:
1. J. A. Buchmann, Introduction to cryptography, Wydawnictwo Naukowe PWN
2. Neal Koblitz, Algebraic aspects of cryptography, Wydawnictwo Naukowo-Techniczne, Warszawa 2000.
3. Neal Koblitz, Number theory and cryptography, Wydawnictwo Naukowo-Techniczne, Warszawa 1995.
4. Douglas R. Stinson, Cryptography in theory and practice, Wydawnictwa Naukowo-Techniczne, Warszawa 2005.
b) supplementary references:
1. Josef Pieprzyk, Thomas Hardjono, Jennifer Seberry, Teoria bezpieczeństwa systemów komputerowych, Wydawnictwo Helion, Warszawa 2006.
2. Paulo Ribenboim, Mała księga wielkich liczb pierwszych, Wydawnictwo Naukowo-Techniczne, Warszawa 1997.
3. Simon Singh, Księga szyfrów, Wydawnictwo Albatros Andrzej Kuryłowicz, Warszawa 2001.
4. Michael Welschenbach, Kryptografia w C i C++, MIKOM, Warszawa 2002.