公钥密码学的数学基础（英文版）-JobPlus

[书籍] 公钥密码学的数学基础（英文版）

作者: 王小云

出版社: 科学出版社

简介: In Mathematical Foundations of Public Key Cryptography， the authors present theresults of more than 20 years of research and teaching experience to help studentsbridge the gap between math theory and crypto practice. The book provides a theoreticalstructure of fundamental number theory and algebra knowledge supporting public-keycryptography. Rather than simply combining number theory and modem algebra， this textbookfeatures the interdisciplinary characteristics of cryptography——revealing the integrationsof mathematical theories and public-key cryptographic applications. Incorporating thecomplexity theory of algorithms throughout， it introduces the basic number theoreticand algebraic algorithms and their complexities to provide a preliminary understandingof the applications of mathematical theories in cryptographic algorithms. Supplying a seamless assimilation of cryptography and mathematics， the bookincludes coverage of elementary number theory; algebraic structure and attributes ofgroup， ring， and field; cryptography-related computing complexity and basic algo-rithms， as well as lattice and fundamental methods of lattice cryptanalysis. The text consists of 11 chapters. Basic theory and tools of elementary numbertheory， such as congruences， primitive roots， residue classes， and continued fractions，are covered in Chapters 1-6. The basic concepts of abstract algebra are introduced inChapters 7-9， where three basic algebraic structures of groups， rings， and fields and theirproperties are explained. Chapter 10 is about computational complexities of several related mathematicalalgorithms， and hard problems such as integer factorization and discrete logarithm.Chapter 11 presents the basics of lattice theory and the lattice basis reductionalgorithm——the LLL algorithm and its application in the cryptanalysis of the RSA algo-rithm. Containing a number of exercises on key algorithms， the book is suitable for use asa textbook for undergraduate students and first-year graduate students in informationsecurity programs. It is also an ideal reference book for cryptography professionalslooking to master public-key cryptography.

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