Computational Number Theory (Hardcover)

Abhijit Das

  • 出版商: CRC
  • 出版日期: 2013-03-18
  • 售價: $4,700
  • 貴賓價: 9.5$4,465
  • 語言: 英文
  • 頁數: 614
  • 裝訂: Hardcover
  • ISBN: 1439866155
  • ISBN-13: 9781439866153
  • 海外代購書籍(需單獨結帳)

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商品描述

Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry.

Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. A dedicated chapter on the application of number theory in public-key cryptography incorporates recent developments in pairing-based cryptography.

With an emphasis on implementation issues, the book uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.

商品描述(中文翻譯)

《計算數論》是根據作者受歡迎的研究生課程所發展而成,提供了對數論算法的完整介紹。本書避免了高級代數,是專為工程領域的高年級本科生和初級研究生設計的自包含教材。同時,它也適合對這個領域新手的研究人員和工業密碼學實踐者。

本書不需要先前的數論或複雜代數工具的經驗,涵蓋了數論的許多計算方面,並突出了重要且有趣的工程應用。它首先以非常基礎的水平介紹了整數和多項式的算術,從而建立了計算數論的基礎。然後討論了橢圓曲線、素性測試、整數因子分解算法、離散對數計算和稀疏線性系統的方法。本書還展示了數論工具在密碼學和密碼分析中的應用。專門的一章介紹了數論在公鑰密碼學中的應用,包括基於配對的密碼學的最新發展。

本書強調實施問題,使用了免費的數論計算器GP/PARI來演示複雜的算術計算。本書中包含了許多例子和練習,並省略了冗長的證明,使材料對學生和實踐者易於理解。