Last modified: Tue 7 August 15:15:54 IST 2018

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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

  1. Motivation
  2. Pythagorean Triples
  3. Divisibility
  4. Solving Linear Equations in Integers
  5. Fundamental Theorem of Arithmetic
  6. Sieve of Eratosthenes
  7. Congruences
  8. Fermat's Little Theorem
  9. Euler's Formula
  10. Chinese Remainder Theorem
  11. Primes
  12. Calculations involving large powers
  13. Calculating k-th roots modulo m
  14. RSA Cryptosystem
  15. Pseudoprimes
  16. Primitive Roots
  17. The ElGamal Cryptosystem
  18. Solving the Discrete Logarithm Problem
  19. Squares
  20. Quadratic Reciprocity
  21. Elliptic Curves
  22. Addition of points on Elliptic Curves
  23. Elliptic curves mod p
  24. Elliptic Curves in Cryptography
  25. Number of points on an elliptic curve
  26. Edwards Curves
  27. Abelian Groups
  28. Calculating Discrete Logarithms
  29. 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