Gröbner bases, coding, and cryptography

Almost every electronic device today contains some form of code, and the systems that keep information accurate and safe as it travels between machines rest on the mathematics explored here. Gröbner bases serve as the principal instrument of computational algebra, and they find use both in abstract theory and in practical engineering problems.

This volume is presented as the first thorough survey of how commutative algebra is applied to error-correcting codes and cryptography. Algebraic and geometric coding schemes are examined one stage at a time, covering construction, encoding, decoding, and list decoding, with the major methods from the research literature reported for each stage.

Stream ciphers, public-key cryptography, symmetric-key cryptography, and Polly Cracker systems each receive a chapter of their own, where the relevant literature is gathered and compared side by side.

Throughout, the author points toward promising new research directions in brief remarks, and every chapter uses the same notation, so the material reads as one connected treatment.