Xiaoyun Wang - Böcker

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.

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.

This book constitutes the refereed proceedings of the 10th International Conference on Practice and Theory in Public-Key Cryptography, PKC 2007, held in Beijing, China in April 2007. The 29 revised full papers presented together with two invited lectures are organized in topical sections on signatures, cryptanalysis, protocols, multivariate cryptosystems, encryption, number theoretic techniques, and public-key infrastructure.

This book constitutes the proceedings of the 17th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2011, held in Seoul, Korea, in December 2011. The 40 revised papers included in this volume were carefully reviewed and selected from 266 submissions. The contributions are organized in topical sections on lattices and quantum cryptography; public key encryption; database privacy; hash function; symmetric key encryption; zero knowledge proof; universal composability; foundation; secure computation and secret sharing; public key signature; and leakage resilient cryptography.

This book constitutes the refereed proceedings of the 10th International Conference on Cryptology and Network Security, CANS 2011, held in Sanya, China, in December 2011. The 18 revised full papers, presented were carefully reviewed and selected from 65 submissions. The book also includes two invited talks. The papers are organized in topical sections on symmetric cryptanalysis, symmetric ciphers, public key cryptography, protocol attacks, and privacy techniques.

This book constitutes the refereed proceedings of the 18th International Conference on the Theory and Application of Cryptology and Information Security, Asiacrypt 2012, held in Beijing, China, in December 2012. The 43 full papers presented were carefully reviewed and selected from 241 submissions. They are organized in topical sections named: public-key cryptography, foundation, symmetric cipher, security proof, lattice-based cryptography and number theory, hash function, cryptographic protocol, and implementation issues.

This book takes China Mobile's "5G +" plan as the mainline, introduces three major scenarios, nine indicators, system architecture and basic principles of 5G, and systematically explains the essence of China Mobile's "5G +" for the first time.