Algebraic Curves in Cryptography (Hardcover)

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.

在密碼學中，代數曲線的應用範圍遠不止於橢圓曲線或公鑰密碼學，然而這些其他應用領域在文獻中尚未得到系統性的涵蓋。為了填補這一空白，《代數曲線在密碼學中的應用》探討了代數曲線在各種密碼學應用中的豐富用途，例如秘密分享、防偽碼和廣播加密。

這本自成一體的書籍適合數學和計算機科學的研究人員和研究生閱讀，是第一批專注於涉及代數曲線的密碼學主題的書籍之一。在提供代數曲線的必要背景知識後，作者們討論了錯誤更正碼，包括代數幾何碼，並介紹了橢圓曲線。書中其餘章節涵蓋了密碼學中的選定主題（除了橢圓曲線密碼學）。所涵蓋的主題包括秘密分享方案、驗證碼、防偽碼、金鑰分發方案、廣播加密和序列。每個章節都以介紹材料開始，然後介紹代數曲線的應用。