Gröbner Bases, Coding, and Cryptography


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About this book

The information security landscape has many levels, including cryptographic aspects, technical aspects, legal aspects and management. Topics of research include network security, software development and key agreement protocols. LDPC codes have been attracting attention over the recent decade. Originally introduced in the seminal work of Gallager in the sixties, they were re discovered soon after the famous TURBO codes.

Among several developments, the workgroup at the Claude Shannon Institute has come up with a family of LDPC codes that are derived from what are called geometries.


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Testing the performance of several members of this family has led to results suggesting that these codes might be useful in various applications like general communications as well as data storage. The standard method applied is known as store and forward, whereby intermediate nodes store and forward a copy of incoming data to some adjacent nodes. The publication of the seminal paper showed that allowing coding or mixing of data to occur at the nodes, rather than simply routing would result in improved network throughput for many networks.


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Network coding has since generated much interest from experts in information theory, coding theory, complexity theory, cryptography and wireless communications. It is an extremely general theory and can be applied to any communications network. Researchers at the Claude Shannon Institute study bounds on network codes, the random network coding model, and minimizing noiseless broadcasts from a server where each receiver has side information.

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It is well known that multiple antenna wireless communication can potentially achieve a very high data rate. One way to achieve this is via space-time block codes. The basic design criteria for space-time block codes can be met using codes constructed using algebraic number theory. Researchers at the Claude Shannon Institute have studied constructions of multi-block space-time codes, and constructions of space-time codes using quadratic forms.

Gröbner bases for public key cryptography

Copyright Claude Shannon Institute. Contact shannon ucd.


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  4. Costas Arrays and Finite Fields Costas arrays are used in radar, sonar, and frequency hopping multiaccess communications systems. Information Security The information security landscape has many levels, including cryptographic aspects, technical aspects, legal aspects and management.

    Coding Session, First Poster Session:

    Space-Time Codes It is well known that multiple antenna wireless communication can potentially achieve a very high data rate. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.

    source site Skip to main content Skip to table of contents. Advertisement Hide. Front Matter Pages Pages An Introduction to Linear and Cyclic Codes.

    Grobner Bases - Bernd Stumfels [1998]

    Decoding Cyclic Codes: the Cooper Philosophy. Algebraic Geometry Codes from Order Domains.

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    Gröbner Bases, Coding, and Cryptography Gröbner Bases, Coding, and Cryptography
    Gröbner Bases, Coding, and Cryptography Gröbner Bases, Coding, and Cryptography
    Gröbner Bases, Coding, and Cryptography Gröbner Bases, Coding, and Cryptography
    Gröbner Bases, Coding, and Cryptography Gröbner Bases, Coding, and Cryptography
    Gröbner Bases, Coding, and Cryptography Gröbner Bases, Coding, and Cryptography
    Gröbner Bases, Coding, and Cryptography Gröbner Bases, Coding, and Cryptography
    Gröbner Bases, Coding, and Cryptography Gröbner Bases, Coding, and Cryptography

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