Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations.
This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.
Coding theory and cryptography allow secure and reliable data transmission, which is at the heart of modern communication. Nowadays, it is hard to find an electronic device without some code inside. Gröbner bases have emerged as the main tool in computational algebra, permitting numerous applications, both in theoretical contexts and in practical situations.
This book is the first book ever giving a comprehensive overview on the application of commutative algebra to coding theory and cryptography. For example, all important properties of algebraic/geometric coding systems (including encoding, construction, decoding, list decoding) are individually analysed, reporting all significant approaches appeared in the literature. Also, stream ciphers, PK cryptography, symmetric cryptography and Polly Cracker systems deserve each a separate chapter, where all the relevant literature is reported and compared. While many short notes hint at new exciting directions, the reader will find that all chapters fit nicely within a unified notation.
The idea of the Gröbner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the...
This book constitutes the refereed proceedings of the 12th International Conference on Code-Based Cryptography, CBCrypto 2024, held in Zurich, Switzerland, during May 25–26, 2024.The 5 full papers...
As algebra becomes more widely used in a variety of applications and computers are developed to allow efficient calculations in the field, so there becomes a need for new techniques to further this...
This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra,...
The ninth in the series of IMA Conferences on Cryptography and Coding was held (as ever) at the Royal Agricultural College, Cirencester, from 16-18 Dec- ber 2003. The conference's varied programme of...
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