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Short-course on Cryptography / Mini-cours : " Cryptologie "

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NEAL KOBLITZ, University of Washington, Seattle, Washington  98195, USA
Introduction to elliptic curve cryptography

I will introduce the basic ideas of Elliptic Curve Cryptography, describe its advantages over competing systems, and discuss both cryptosystems constructed by analogy with systems based on the multiplicative group of a finite field and also cryptosystems based on the particular properties of elliptic curves.

MIKE MOSCA, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario  N2L 3G1
Quantum computing and quantum cryptography

Information is stored in a physical medium and manipulated by physical processes, so any meaningful theory of information processing (including communication and computation) must refer, at least implicitly, to a realistic physical theory.

Early in the last century, physicists discovered that a new framework was necessary in order to explain basic physical phenomena. This framework is called quantum mechanics. Quantum computation and quantum cryptography are the natural consequences of considering computation and cryptography in this quantum mechanical framework.

Quantum computers seek to exploit the quantum mechanical properties of the bits that comprise them in order to solve problems with a computational complexity much lower than that of the best known classical computer algorithms.

The consequences of quantum theory for cryptography cannot be ignored. E.g. computationally secure cryptography requires that no reasonable algorithmic process could solve a specific computational problem in a feasible amount of time. If quantum theory enables an adversary to solve such problems efficiently, then we can no longer rely on these assumptions.

Quantum theory also offers new primitives for cryptography, such as intrinsic eavesdropper detection which leads to "unconditionally secure" quantum key establishment.

In this lecture, I will describe the basics of quantum information, and summarize the impact on computation and cryptography.

DOUG STINSON, University of Waterloo, Waterloo, Ontario  N2L 3G1
Introduction to cryptography

In this talk, I will give a brief overview of the objectives of cryptography and the tools that are used to achieve these objectives. A short history of the development of modern cryptography will be presented. The evolution of the notion of "security" will be discussed. Some recent trends in cryptography will be mentioned, as well as some possible future directions. This is a relatively non-technical talk.

HUGH WILLIAMS, University of Calgary
Cryptography and number theory

In the last 25 years, computational number theory and cryptography have become closely intertwined. For example, the security of almost all commercially available public-key cryptosystems is based on the presumed difficulty of some mathematical problems such as the integer factorization problem in computational number theory. Number theory provides most of the hard computational problems used to provide the security of cryptographic schemes

In this talk I will describe several techniques, which owe their origin to the application of number theory to cryptography, that have been successfully applied to classical problems arising in computational number theory. In particular, I will discuss the integer factoring problem, the discrete logarithm problem, and the primality testing problem.