Codes, Cryptology and Curves with Computer Algebra

This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

這本平衡的書籍涵蓋了保護數位資料的理論和應用方面。讀者將獲得基本理論，並深入了解更多有趣的細節，包括目前的最新技術。讀者將很快熟悉在數據傳輸和數據存儲過程中保護數位資料的方法。書中介紹了基本和高級的錯誤修正碼，並提供了關於它們參數和特性的許多結果。作者解釋了如何將這些碼應用於對稱和公鑰加密系統以及秘密分享。基於多項式系統求解的有趣方法被應用於密碼學和解碼碼。計算機代數系統也被用來理解書中介紹的對象是如何構建的，以及如何檢查它們的特性。這本書適用於攻讀數學、計算機科學、電機工程或物理學碩士學位的學生。