Title: Number Theory, Cryptography and Information Security
Professor Song Yan
Department of Computer Science
University of Luton, England.

Abstract
To insure the transactions over the Internet are secure, encryption particularly the public-key encryption is often used. However, the security of almost all public-key cryptographic systems relies on one or more intractable mathematical particularly number-theoretic problems.

In this tutorial, I shall first, from a computational complexity point of view, introduce some important intractable number-theoretic problems such as the Integer Factorization Problems (IFP), the Discrete Logarithm Problems (DLP), the Elliptic Curve Discrete Logarithm Problems (ECDLP) and the Square Root Problem (SQRT), etc. Then, I shall discuss how these problems can be used to design polynomially unbreakable cryptographic systems such as the most famous Rivest-Shamir-Addleman cryptographic system based on IFP (for which its three inventors received the prestigious Turing Award in 2003), DHM (the first public-key system invented by Diffie-Hellman-Merkle in 1976) based on DLP and Elliptic Curve Cryptosystems based on ECDLP.

Some cryptanalytic attacks on these cryptographic systems are also discussed. Finally, I shall discuss the application of cryptography in Internet security and electronic/mobile commerce. No previous experience in number theory and cryptography is assumed and it shall be generally helpful for anyone who is interested in Internet and information security.

Brief cv
Song Yan is currently Professor in Computer Science at the University of Luton, England. He obtained a PhD in Mathematics at the University of York, England. His current research interests include number theory, complexity theory, cryptography and information security. Among many others he published a very successful book Number Theory for Computing (1st Edition, 2000; 2nd Edition, 2002) by Springer-Verlag, which is appraised as ``an excellent and timely addition to the growing body of literature on computational number theory'' by Prof Lakshmivarahan, Fellow of ACM and IEEE, in the ACM Computing Review, Jan 2003.