Algebraic Geometry in Coding Theory and Cryptography (eBook)

Harald Niederreiter, Chaoping Xing (Autoren)

eBook Download: PDF

2009
272 Seiten
Princeton University Press (Verlag)
978-1-4008-3130-2 (ISBN)

Infos

This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books

Autor

Harald Niederreiter is professor of mathematics and computer science at the National University of Singapore. Chaoping Xing is professor of mathematics at the Nanyang Technological University in Singapore. They are the authors of Rational Points on Curves over Finite Fields: Theory and Applications.

Produkt-Details

• Erscheint lt. Verlag: 21.9.2009
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Kryptologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geografie / Kartografie
• Themenwelt: Technik
• Schlagworte: abelian group • Addition • Affine space • affine variety • Algebraically closed field • algebraic closure • Algebraic Curve • Algebraic element • algebraic equation • algebraic extension • Algebraic function field • Algebraic Geometry • Algebraic Structure • algebraic variety • algorithm • arithmetic • asymptotic analysis • Big O notation • Characterization (mathematics) • character theory • ciphertext • Closed set • coding theory • complex number • Computation • computational complexity theory • Coprime integers • Cryptanalysis • cryptography • cryptosystem • digital signature • discrete logarithm • discrete valuation • Discrete valuation ring • Divisor • ElGamal encryption • ElGamal signature scheme • Elliptic Curve • Elliptic Curve Cryptography • Equation • Euclidean space • existential quantification • Explicit formulae (L-function) • Field Extension • Field of fractions • finite field • Function field • Function (mathematics) • Galois extension • Generator Matrix • Group homomorphism • Homomorphism • hyperelliptic curve • Integer • integral domain • Invertible matrix • Irreducible element • irreducible polynomial • Jacobian matrix and determinant • linear algebra • linear code • Local ring • logarithm • McEliece cryptosystem • minimal polynomial • monic polynomial • Multiplicative group • Niederreiter cryptosystem • Noetherian • Number Theory • Parameter (computer programming) • Parity-check matrix • Plane curve • polynomial • polynomial ring • Prime number • Principal ideal domain • Projective line • projective space • projective variety • Quasi-Monte Carlo method • Quasi-projective variety • rational function • Resolution of Singularities • Riemann–Roch theorem • Row and column spaces • RSA (cryptosystem) • scientific notation • Set (mathematics) • Special case • Subring • Theorem • time complexity • Topological space • Topology • Upper and lower bounds • Valuation ring • Variable (mathematics) • Vector Space • Zariski topology
• ISBN-10: 1-4008-3130-X / 140083130X
• ISBN-13: 978-1-4008-3130-2 / 9781400831302