Algebraic Curves in Cryptography

San Ling, Huaxiong Wang, Chaoping Xing

June 13, 2013 by Chapman and Hall/CRC
Reference - 340 Pages - 15 B/W Illustrations
ISBN 9781420079463 - CAT# C7946
Series: Discrete Mathematics and Its Applications

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  • Illustrates various kinds of algebraic curves in a broad range of cryptographic applications, including secret sharing, authentication codes, frameproof codes, key distribution, broadcast encryption, and sequences for stream ciphers
  • Requires minimal background in advanced mathematics and cryptography
  • Provides the required fundamentals on algebraic curves
  • Offers a brief introduction to elliptic curves and applications


The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sharing, frameproof codes, and broadcast encryption.

Suitable for researchers and graduate students in mathematics and computer science, this self-contained book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected topic in cryptography (other than elliptic curve cryptography). The topics covered include secret sharing schemes, authentication codes, frameproof codes, key distribution schemes, broadcast encryption, and sequences. Chapters begin with introductory material before featuring the application of algebraic curves.