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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. --- Cryptography. --- Gro ̈bner bases. --- Grèobner bases --- Coding theory --- Cryptography --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Gröbner bases. --- Gröbner basis theory --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Mathematics. --- Data encryption (Computer science). --- Computers. --- Computer science --- Algebra. --- Discrete mathematics. --- Combinatorics. --- Discrete Mathematics. --- Data Encryption. --- Mathematics of Computing. --- Theory of Computation. --- Commutative algebra --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Computer science. --- Information theory. --- Cryptology. --- Communication theory --- Communication --- Cybernetics --- Informatics --- Science --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Combinatorics --- Mathematical analysis --- Computer science—Mathematics. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace --- Grobner bases.