商品描述
In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.
Rather than simply combining number theory and modern algebra, this textbook features the interdisciplinary characteristics of cryptography―revealing the integrations of mathematical theories and public-key cryptographic applications. Incorporating the complexity theory of algorithms throughout, it introduces the basic number theoretic and algebraic algorithms and their complexities to provide a preliminary understanding of the applications of mathematical theories in cryptographic algorithms.
Supplying a seamless integration of cryptography and mathematics, the book includes coverage of elementary number theory; algebraic structure and attributes of group, ring, and field; cryptography-related computing complexity and basic algorithms, as well as lattice and fundamental methods of lattice cryptanalysis.
The text consists of 11 chapters. Basic theory and tools of elementary number theory, such as congruences, primitive roots, residue classes, and continued fractions, are covered in Chapters 1-6. The basic concepts of abstract algebra are introduced in Chapters 7-9, where three basic algebraic structures of groups, rings, and fields and their properties are explained.
Chapter 10 is about computational complexities of several related mathematical algorithms, and hard problems such as integer factorization and discrete logarithm. Chapter 11 presents the basics of lattice theory and the lattice basis reduction algorithm―the LLL algorithm and its application in the cryptanalysis of the RSA algorithm.
Containing a number of exercises on key algorithms, the book is suitable for use as a textbook for undergraduate students and first-year graduate students in information security programs. It is also an ideal reference book for cryptography professionals looking to master public-key cryptography.
商品描述(中文翻譯)
在《公鑰密碼學的數學基礎》中，作者整合了超過20年的研究和教學經驗，幫助學生彌合數學理論與密碼實踐之間的鴻溝。本書提供了支持公鑰密碼學的基本數論和代數知識的理論結構。
本教科書不僅僅是將數論和現代代數結合，而是展現了密碼學的跨學科特性，揭示了數學理論與公鑰密碼應用的整合。全書貫穿了算法的複雜性理論，介紹了基本的數論和代數算法及其複雜性，以提供對數學理論在密碼算法中應用的初步理解。
本書無縫整合了密碼學和數學，涵蓋了初等數論；群、環和域的代數結構及其屬性；與密碼學相關的計算複雜性和基本算法，以及格和格密碼分析的基本方法。
本書共由11章組成。第1至第6章涵蓋了初等數論的基本理論和工具，如同餘、原根、餘數類和連分數。第7至第9章介紹了抽象代數的基本概念，解釋了群、環和域這三種基本代數結構及其性質。
第10章探討了幾個相關數學算法的計算複雜性，以及整數因式分解和離散對數等難題。第11章介紹了格理論的基本知識和格基減少算法——LLL算法及其在RSA算法密碼分析中的應用。
本書包含多個關於關鍵算法的練習，適合作為本科生和資訊安全專業一年級研究生的教科書。對於希望精通公鑰密碼學的密碼學專業人士來說，它也是一本理想的參考書。
