Last modified: Tue 7 August 15:15:54 IST 2018
MA6011 — Cryptographic Mathematics
News
I have taught this module at UL in 2014 and 2015.
Contact Information
Name |
Dr. Bernd Kreussler |
Office |
N29 (Mary Immaculate College) |
Telephone |
(061) 204578 |
Email |
bernd.kreussler@mic.ul.ie |
WWW |
www.maths.mic.ul.ie/kreussler/ |
Outline content of the lecture given in 2015
- Motivation
- Pythagorean Triples
- Divisibility
- Solving Linear Equations in Integers
- Fundamental Theorem of Arithmetic
- Sieve of Eratosthenes
- Congruences
- Fermat's Little Theorem
- Euler's Formula
- Chinese Remainder Theorem
- Primes
- Calculations involving large powers
- Calculating k-th roots modulo m
- RSA Cryptosystem
- Pseudoprimes
- Primitive Roots
- The ElGamal Cryptosystem
- Solving the Discrete Logarithm Problem
- Squares
- Quadratic Reciprocity
- Elliptic Curves
- Addition of points on Elliptic Curves
- Elliptic curves mod p
- Elliptic Curves in Cryptography
- Number of points on an elliptic curve
- Edwards Curves
- Abelian Groups
- Calculating Discrete Logarithms
- Factoring Large Integers
Textbooks
- J. Silverman, A Friendly Introduction to Number Theory,
(Springer) 2001
- N. Koblitz, A Course in Number Theory and Cryptography
(Springer) 1994
- J. Buchmann, Introduction to Cryptography
(Springer) 2004
- J. Hoffstein, J. Pipher, J. Silverman, An Introduction to
Mathematical Cryptography (Springer) 2008
- C. Paar, J. Pelzl, Understanding Cryptography
(Springer) 2010
- L. Washington, Elliptic Curves, Number Theory and Cryptography
(Chapman & Hall) 2008
Mary Immaculate College, South Circular Road, Limerick, Ireland,
Tel: +35361 204300