Algorithmic number theory, and the computational issues related to algebraic curves over various fields and arithmetic rings, is a central theme in our research. This very rich area of mathematics and computer science has already shown its relevance in public key cryptography, with industrial successes including the RSA cryptosystem and elliptic curve cryptography. It is less well-known that very good codes for error correction can be built using the same areas of mathematics; this is also at the heart of the Grace proposal. We believe that geometric interpretation, unification, and transformation gives better insight into the nature and performance of this wide range of problems and algorithms in coding theory and cryptology. Both of these application domains deal with communication systems for securing high-level applications. While cryptography is seen as a part of computer science, coding theory tradition- ally has an electical engineering flavour; but recent developments in computer science have shed new light on coding theory, with new applications more central to computer science.
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