- Authors:
- Harald Niederreiter,
- Chaoping Xing
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
Cited By
Döttling N and Garg S (2021). Identity-based Encryption from the Diffie-Hellman Assumption, Journal of the ACM, 68:3, (1-46), Online publication date: 30-Jun-2021.- Patanker N and Singh S (2020). On Geometric Goppa Codes from Elementary Abelian p-Extensions of , Problems of Information Transmission, 56:3, (253-269), Online publication date: 1-Jul-2020.
- Guardia G and Pereira F (2017). Good and asymptotically good quantum codes derived from algebraic geometry, Quantum Information Processing, 16:6, (1-12), Online publication date: 1-Jun-2017.
- Coşgun A, Özbudak F and Saygı Z (2016). Further results on rational points of the curve y^{q^n}-y= γx^{q^h+1} - yqn-y= xqh+1-α over Fq, Designs, Codes and Cryptography, 79:3, (423-441), Online publication date: 1-Jun-2016.
- Kritzer P and Niederreiter H (2016). Mixed orthogonal arrays, ( u , m , e , s ) -nets, and ( u , e , s ) -sequences, Discrete Mathematics, 339:9, (2199-2208), Online publication date: 6-Sep-2016.
- Özbudak F and Saygı Z (2016). Explicit maximal and minimal curves over finite fields of odd characteristics, Finite Fields and Their Applications, 42:C, (81-92), Online publication date: 1-Nov-2016.
- Stichtenoth H Recursive towers of function fields over finite fields Proceedings of the Third international conference on Arithmetic of finite fields, (1-6)