The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.

The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.

This graduate coursebook offers a mathematical foundation for modern cryptography for readers with basic knowledge of probability theory.

This comprehensive encyclopedia provides easy access to information on all aspects of cryptography and security. The work is intended for students, researchers and practitioners who need a quick and authoritative reference to areas like data protection, network security, operating systems security, and more.

This book constitutes the proceedings of the 16th IMA International Conference on Cryptography and Coding, IMACC 2017, held at Oxford, UK, in December 2017. The 19 papers presented were carefully reviewed and selected from 32 submissions. The conference focuses on a diverse set of topics both in cryptography and coding theory.

Cryptography plays a key role in ensuring the privacy and integrity of data and the security of computer networks. Introduction to Modern Cryptography provides a rigorous yet accessible treatment of modern cryptography, with a focus on formal definitions, precise assumptions, and rigorous proofs. The authors introduce the core principles of

In the mid-1970s, Whitfield Diffie and Martin Hellman invented public key cryptography, an innovation that ultimately changed the world. Today public key cryptography provides the primary basis for secure communication over the internet, enabling online work, socializing, shopping, government services, and much more. While other books have documented the development of public key cryptography, this is the first to provide a comprehensive insiders’ perspective on the full impacts of public key cryptography, including six original chapters by nine distinguished scholars. The book begins with an original joint biography of the lives and careers of Diffie and Hellman, highlighting parallels and intersections, and contextualizing their work. Subsequent chapters show how public key cryptography helped establish an open cryptography community and made lasting impacts on computer and network security, theoretical computer science, mathematics, public policy, and society. The volume includes particularly influential articles by Diffie and Hellman, as well as newly transcribed interviews and Turing Award Lectures by both Diffie and Hellman. The contributed chapters provide new insights that are accessible to a wide range of readers, from computer science students and computer security professionals, to historians of technology and members of the general public. The chapters can be readily integrated into undergraduate and graduate courses on a range of topics, including computer security, theoretical computer science and mathematics, the history of computing, and science and technology policy.

This book provides the basic theory, techniques, and algorithms of modern cryptography that are applicable to network and cyberspace security. It consists of the following nine main chapters: Chapter 1 provides the basic concepts and ideas of cyberspace and cyberspace security, Chapters 2 and 3 provide an introduction to mathematical and computational preliminaries, respectively. Chapters 4 discusses the basic ideas and system of secret-key cryptography, whereas Chapters 5, 6, and 7 discuss the basic ideas and systems of public-key cryptography based on integer factorization, discrete logarithms, and elliptic curves, respectively. Quantum-safe cryptography is presented in Chapter 8 and offensive cryptography, particularly cryptovirology, is covered in Chapter 9. This book can be used as a secondary text for final-year undergraduate students and first-year postgraduate students for courses in Computer, Network, and Cyberspace Security. Researchers and practitioners working in cyberspace security and network security will also find this book useful as a reference.

This book constitutes the refereed proceedings of the 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2010, held on the French Riviera, in May/June 2010. The 33 revised full papers presented together with 1 invited lecture were carefully reviewed and selected from 188 submissions. The papers address all current foundational, theoretical and research aspects of cryptology, cryptography, and cryptanalysis as well as advanced applications. The papers are organized in topical sections on cryptosystems; obfuscation and side channel security; 2-party protocols; cryptanalysis; automated tools and formal methods; models and proofs; multiparty protocols; hash and MAC; and foundational primitives.

This volume constitutes the refereed proceedings of the 27th Annual International Cryptology Conference held in Santa Barbara, California, in August 2007. Thirty-three full papers are presented along with one important invited lecture. The papers address current foundational, theoretical, and research aspects of cryptology, cryptography, and cryptanalysis. In addition, readers will discover many advanced and emerging applications.