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Mathematical Foundations of Public Key Cryptography by Xiaoyun Wang
English | 30 Oct. 2015 | ISBN: 1498702236 | 236 Pages | AZW4/PDF (True) | 5.32 MB

In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research & teaching experience to help students bridge the gap between math theory & crypto practice.
The book provides a theoretical structure of fundamental number theory & algebra knowledge supporting public-key cryptography.

Rather than simply combining number theory & modern algebra, this textbook features the interdisciplinary characteristics of cryptography―revealing the integrations of mathematical theories & public-key cryptographic applications. Incorporating the complexity theory of algorithms throughout, it introduces the basic number theoretic & algebraic algorithms & their complexities to provide a preliminary underst&ing of the applications of mathematical theories in cryptographic algorithms.

Supplying a seamless integration of cryptography & mathematics, the book includes coverage of elementary number theory; algebraic structure & attributes of group, ring, & field; cryptography-related computing complexity & basic algorithms, as well as lattice & fundamental methods of lattice cryptanalysis.

The text consists of 11 chapters. Basic theory & tools of elementary number theory, such as congruences, primitive roots, residue classes, & 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, & fields & their properties are explained.

Chapter 10 is about computational complexities of several related mathematical algorithms, & hard problems such as integer factorization & discrete logarithm. Chapter 11 presents the basics of lattice theory & the lattice basis reduction algorithm―the LLL algorithm & 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 & first-year graduate students in information security programs. It is also an ideal reference book for cryptography professionals looking to master public-key cryptography.
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