Introduction to Cryptography with Mathematical Foundations and Computer Implementations

Alexander Stanoyevitch

商品描述

From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in cryptography, it delineates cryptographic concepts in chronological order, developing the mathematics as needed.

Written in an engaging yet rigorous style, each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with "Exercises for the Reader;" complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter, and detailed solutions to most odd-numbered exercises can be found in a designated appendix. The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platform-independent applet pages for some core programs and algorithms.

As the reliance on cryptography by business, government, and industry continues and new technologies for transferring data become available, cryptography plays a permanent, important role in day-to-day operations. This self-contained sophomore-level text traces the evolution of the field, from its origins through present-day cryptosystems, including public key cryptography and elliptic curve cryptography.

商品描述(中文翻譯)

從古代發展的激動人心的歷史到現代,以數學基礎和電腦實現為基礎的《密碼學入門》提供了對密碼學核心概念的專注介紹。本書不是對密碼學主題的百科全書式處理,而是按照時間順序勾勒出密碼學概念,並根據需要發展數學知識。

本書以引人入勝但嚴謹的風格撰寫,每章都用清晰的定義和定理介紹重要概念。眾多例子解釋了關鍵點,圖表則有助於說明更難理解或微妙的概念。每章末尾都有“讀者練習”,這些練習的完整解答包含在附錄中。每章還提供了精心設計的練習題,並且大多數奇數編號的練習題的詳細解答可以在指定的附錄中找到。每章末尾的電腦實現部分引導學生進行編寫自己程序的過程。支持網站提供了大量的示例程序,以及一些核心程序和算法的可下載平台無關的小程序頁面。

隨著商業、政府和工業對密碼學的依賴持續增加,以及新的數據傳輸技術的出現,密碼學在日常運營中扮演著永久而重要的角色。這本自成一體的大二水平教材追溯了該領域的演變,從其起源到現代的密碼系統,包括公鑰密碼學和橢圓曲線密碼學。

目錄大綱

Preface
Chapter 1: An Overview of the Subject
Chapter 2: Divisibility and Modular Arithmetic
Chapter 3: The Evolution of Codemaking Until the Computer Era
Chapter 4: Matrices and the Hill Cryptosystem
Chapter 5: The Evolution of Codebreaking Until the Computer Era
Chapter 6: Representation and Arithmetic of Integers in Different Bases
Chapter 7: Block Cryptosystems and the Data Encryption Standard (DES)
Chapter 8: Some Number Theory and Algorithms
Chapter 9: Public Key Cryptography
Chapter 10: Finite Fields in General, and GF(28) in Particular
Chapter 11: The Advanced Encryption Standard Protocol (AES)
Chapter 12: Elliptic Curve Cryptography
Appendix A: Sets and Basic Counting Principles
Appendix B: Randomness and Probability
Appendix C: Solutions to all Exercises for the Reader
Appendix D: Answers to Selected Exercises(with solution details)
References
Index

目錄大綱(中文翻譯)

前言
第一章:主題概述
第二章:可除性和模數算術
第三章:從計算機時代以前的密碼製作演變
第四章:矩陣和希爾加密系統
第五章:從計算機時代以前的密碼破解演變
第六章:不同進制中整數的表示和算術
第七章:區塊加密系統和數據加密標準(DES)
第八章:一些數論和算法
第九章:公鑰加密
第十章:一般有限域,特別是GF(2^8)
第十一章:高級加密標準協議(AES)
第十二章:橢圓曲線加密
附錄A:集合和基本計數原則
附錄B:隨機性和概率
附錄C:讀者練習的所有習題解答
附錄D:選擇性習題答案(包含解答詳解)
參考文獻
索引