Introduction to Cryptography with Mathematical Foundations and Computer Implementations
暫譯: 數學基礎與計算機實現的密碼學導論

Alexander Stanoyevitch

Introduction to Cryptography with Mathematical Foundations and Computer Implementations

相關主題

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今，《帶有數學基礎和計算機實現的密碼學導論》提供了一個集中於密碼學核心概念的導覽。本書並不是對密碼學主題的百科全書式處理，而是按時間順序劃分密碼學概念，根據需要發展數學內容。

本書以引人入勝但又嚴謹的風格撰寫，每一章都以清晰的定義和定理介紹重要概念。大量的例子解釋關鍵要點，而圖形和表格則幫助說明更困難或微妙的概念。每一章都以「讀者練習」作為結尾，這些練習的完整解答包含在附錄中。每章末尾還提供精心設計的練習題集，大多數奇數練習題的詳細解答可以在指定的附錄中找到。每章末尾的計算機實現部分指導學生編寫自己的程式。支持網站提供了大量的範例程式以及一些核心程式和演算法的可下載平台獨立小應用頁面。

隨著商業、政府和工業對密碼學的依賴持續增加，並且新的數據傳輸技術不斷出現，密碼學在日常運作中扮演著永久且重要的角色。本書是一部自成體系的二年級水平教材，追溯了該領域的演變，從其起源到現今的密碼系統，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)

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

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