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Quadratics
The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows the browser to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders. Th...
Algebraic Number Theory
Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.
RSA and Public-Key Cryptography
Although much literature exists on the subject of RSA and public-key cryptography, until now there has been no single source that reveals recent developments in the area at an accessible level. Acclaimed author Richard A. Mollin brings together all of the relevant information available on public-key cryptography (PKC), from RSA to the latest applic
Advanced Number Theory with Applications
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and mo
An Introduction to Cryptography
Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides a solid foundation in cryptographic concepts that features all of the requisite background material on number theory and algorithmic complexity as well as a historical look at the field. With numerous additions and restructured material, this edition
Fundamental Number Theory with Applications
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in i
Algebraic Number Theory
From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin's popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theor...
Computational Algebra and Number Theory
Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.
Multivariate Public Key Cryptosystems
Multivariate public key cryptosystems (MPKC) is a fast-developing area in cryptography. This book systematically presents the subject matter for a broad audience and is the first book to focus on this exciting new topic. Information security experts in industry can use the book as a guide for understanding what is needed to implement these cryptosystems for practical applications, and researchers in both computer science and mathematics will find it a good starting point for exploring this new field. It is also suitable as a textbook for advanced-level students.
