Cryptology and Error Correction: An Algebraic Introduction and Real-World Applications
暫譯: 密碼學與錯誤更正：代數入門及其實際應用

Childs, Lindsay N.

Cryptology and Error Correction: An Algebraic Introduction and Real-World Applications
  • 出版商: Springer
  • 出版日期: 2019-05-02
  • 售價: $2,490
  • 貴賓價: 9.5 折 $2,366
  • 語言: 英文
  • 頁數: 351
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3030154513
  • ISBN-13: 9783030154516

    • 海外代購書籍(需單獨結帳)

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商品描述

This text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for understanding these methods. The objective is to provide a thorough understanding of RSA, Diffie-Hellman, and Blum-Goldwasser cryptosystems and Hamming and Reed-Solomon error correction: how they are constructed, how they are made to work efficiently, and also how they can be attacked. To reach that level of understanding requires and motivates many ideas found in a first course in abstract algebra--rings, fields, finite abelian groups, basic theory of numbers, computational number theory, homomorphisms, ideals, and cosets. Those who complete this book will have gained a solid mathematical foundation for more specialized applied courses on cryptology or error correction, and should also be well prepared, both in concepts and in motivation, to pursue more advanced study in algebra and number theory.

This text is suitable for classroom or online use or for independent study. Aimed at students in mathematics, computer science, and engineering, the prerequisite includes one or two years of a standard calculus sequence. Ideally the reader will also take a concurrent course in linear algebra or elementary matrix theory. A solutions manual for the 400 exercises in the book is available to instructors who adopt the text for their course.


商品描述(中文翻譯)

本書仔細介紹了全球廣泛使用的密碼學和錯誤更正方法，以及理解這些方法所必需的抽象代數和數論概念。目標是提供對 RSA、Diffie-Hellman 和 Blum-Goldwasser 密碼系統以及 Hamming 和 Reed-Solomon 錯誤更正的透徹理解：它們是如何構建的、如何高效運作的，以及如何受到攻擊。達到這種理解水平需要並激發許多在抽象代數初級課程中出現的概念——環、域、有限阿貝爾群、數的基本理論、計算數論、同態、理想和陪集。完成本書的讀者將獲得堅實的數學基礎，以便於更專門的應用課程，如密碼學或錯誤更正，並且在概念和動機上也應該為進一步深入學習代數和數論做好充分準備。

本書適合用於課堂教學、線上學習或獨立學習。針對數學、計算機科學和工程的學生，先修課程包括一至兩年的標準微積分課程。理想情況下，讀者還應同時修習線性代數或初級矩陣理論的課程。對於採用本書作為課程教材的教師，提供了 400 道習題的解答手冊。

作者簡介

Lindsay N. Childs is Professor Emeritus at the University of Albany where he earned recognition as a much-loved mentor of students, and as an expert in Galois field theory. Capping his tenure at Albany, he was named a Collins Fellow for his extraordinary devotion to the University at Albany and the people in it over a sustained period of time. Post University of Albany, Professor Childs has taught a sequence of online courses whose content evolved into this book. Lindsay Childs is author of A Concrete Introduction to Higher Algebra, published in Springer's Undergraduate Texts in Mathematics series, as well as a monograph, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory (American Mathematical Society), and more than 60 research publications in abstract algebra.


作者簡介(中文翻譯)

Lindsay N. Childs 是阿爾巴尼大學的名譽教授，他因為深受學生喜愛的導師身份以及在 Galois 場理論方面的專業知識而獲得認可。在阿爾巴尼大學任職期間，他因對大學及其人員的卓越奉獻而被授予 Collins Fellow 的榮譽。離開阿爾巴尼大學後，Childs 教授教授了一系列的線上課程，其內容最終演變成這本書。Lindsay Childs 是 A Concrete Introduction to Higher Algebra 的作者，該書發表於 Springer's Undergraduate Texts in Mathematics 系列，此外，他還撰寫了專著 Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory（美國數學學會出版），以及超過 60 篇有關抽象代數的研究出版物。

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