An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)

Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman

  • 出版商: Springer
  • 出版日期: 2014-09-11
  • 售價: $3,150
  • 貴賓價: 9.5$2,993
  • 語言: 英文
  • 頁數: 538
  • 裝訂: Hardcover
  • ISBN: 1493917102
  • ISBN-13: 9781493917105
  • 相關分類: 資訊安全
  • 立即出貨(限量) (庫存=1)

買這商品的人也買了...

商品描述

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.

The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:
 

  • classical cryptographic constructions, such as DiffieHellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures;
     
  • fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;
     
  • an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.
     

The second edition of An Introduction

to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

 

商品描述(中文翻譯)

這本自成一體的現代密碼學入門書強調公鑰密碼系統和數位簽章方案背後的數學理論。本書著重於這些關鍵主題,同時發展讀者所需的構建和安全分析各種密碼系統的數學工具。讀者只需要基本的線性代數知識;本書會引入和發展代數、數論和概率等技巧。這本書為數學和計算機科學學生提供了理解現代密碼學數學基礎的理想入門。本書包含了廣泛的參考文獻和索引;補充材料可在線上獲得。

本書涵蓋了被認為是數學密碼學核心的各種主題。關鍵主題包括:
- 古典密碼學結構,如Diffie-Hellman金鑰交換、離散對數密碼系統、RSA密碼系統和數位簽章;
- 密碼學的基本數學工具,包括素性測試、因數分解算法、概率論、資訊論和碰撞算法;
- 對重要的密碼學創新進行深入探討,如橢圓曲線、基於橢圓曲線和配對的密碼學、格和基於格的密碼學,以及NTRU密碼系統。

第二版的《數學密碼學入門》對數位簽章的內容進行了重大修訂,包括更早地介紹了RSA、Elgamal和DSA簽章,以及關於基於格的簽章和拒絕抽樣的新材料。許多章節為了更清晰而進行了重寫或擴充,特別是在資訊論、橢圓曲線和格的章節,而附加主題的章節則擴充了數字現金和同態加密的部分。書中還新增了許多新的習題。