A course for Undergraduates at the
School of Mathematics
Fudan University Shanghai
from February 24 to March 28 in 2014
Prof. Dr. sc. math. ETH Albert Fässler
Bern University of Applied Sciences, Switzerland
Email: albert-faessler@bluewin.ch
The subject concerns Applied Mathematics, using results from classical elementary number theory and some algorithms.
The course is based on the book by Buchmann Johannes, Introduction to Cryptography.
It contains a sufficient amount of exercises, supporting the learning process. Copies will be given at the beginning of the course.
Additional written information and demonstrations with a computer algebra system will support theory and exercices.
By experience, the talk will be given in slow English.
No prerequisite necessary.
Contents:
Euclidian Algorithm and its efficiency, Modular Arithmetic, used Finite groups and fields, Fermat’s Little Theorem, Fast exponentiation.
Symmetric and asymmetric cryptosystems, encryption, decryption, perfect secrecy.
The RSA-system including digital signatures and the Diffie-Hellman Key Exchange as representative examples of Public-Key Cryptosystems will be treated with its aspects of efficiency and security. The generation of huge primes with a probabilistic algorithm is included.
Supplementary (if time allows): Introduction to Elliptic Curves which serve for higher security than with integer arithmetic and/or Zero Knowledge Proofs.
December 2013 Albert Fässler
