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National Mathematics Initiative (NMI)
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2005 - 2006

Coding Theory and Cryptography

August 2005 - July 2006

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:

  1. Theory of Finite Fields for classical error-correcting codes and construction of some Cryptosystems.

  2. Computational Number Theory for the implementation and analysis of public-key cryptosystems.

  3. Theory of Algebraic function fields for the construction of Algebraic-Geometric Codes.

  4. Exponential sums form a powerful tool in both Coding Theory and Cryptography.

  5. 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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