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2005 - 2006
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Coding Theory and Cryptography
August 2005 - July 2006
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Coding Theory and Cryptography are two areas of interest which incorporates
use of Mathematics in an essential way. The Mathematical aspects of these
topics are fairly sophisticated. It is fascinating to observe that a
remarkably large body of Mathematics has been (and is being) developed
to tackle the questions in these areas. Hoping to enthuse researchers
to learn more about Mathematics currently in vogue in selected topics
in Coding Theory and Cryptography, The Mathematics Initiative has decided
to declare August 2005 to July 2006 as a special year in the Mathematical
aspects of Coding Theory and Cryptography.
Some of the mathematical tools required in Coding Theory and
Cryptography are:
- Theory of Finite Fields for classical error-correcting codes and
construction of some Cryptosystems.
- Computational Number Theory for the implementation and analysis of
public-key cryptosystems.
- Theory of Algebraic function fields for the construction of
Algebraic-Geometric Codes.
- Exponential sums form a powerful tool in both Coding
Theory and Cryptography.
- Algebraic Geometry of curves particularly for Elliptic curve
Cryptography.
During the special year, apart from running short
courses and seminars on these (and related) topics, it is proposed
to have workshops and conference. In particular it is proposed to
conduct two workshops one each on Coding
Theory and Cryptography. In the workshop on Coding Theory it is proposed
to cover topics from Finite Fields, Algebraic Space-Time Codes, Low
Density Parity Check Codes and Codes on Graphs. Also there will be special
lectures on Combinatorial aspects of Codes, Codes arising from Finite
Geometries, Codes arising from Algebraic geometry, Pseudo-random
sequences. In the Workshop on Cryptography we expect to cover topics from
Equations over Finite Fields, Exponential sums, Algorithms in Algebraic Number
Theory and Public-key Cryptosystems. There will be special lectures on
Elliptic Curve Cryptography. It is hoped that graduate students, motivated
researchers wanting to be active in these areas will benefit from these
workshops. It is also hoped that people working in Industry will make use
of these workshops. To encourage researchers in these areas it is proposed to
host two conferences - one on Coding Theory and the other on Cryptography -
where the participants will present their original work.
As part of the programme, the
following activities are planned:
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