1. Introduction to the Manual
This manual provides comprehensive information regarding An Introduction to Mathematical Cryptography, a publication by Springer. It details the book's content, structure, target audience, and key mathematical concepts covered. This resource is designed to assist readers in understanding the scope and utility of the book for academic study and self-learning.
Figure 1: Cover of An Introduction to Mathematical Cryptography. This image displays the title, authors (Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman), and publisher (Springer).
2. Overview of Content
This book serves as an introduction to public key cryptography and the essential mathematical principles underpinning it. It is structured into eight chapters, each dedicated to a specific area of mathematical cryptography, complemented by an extensive collection of exercises.
2.1. Key Topics Covered
- Classical cryptographic constructions, including Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, RSA cryptosystem, and digital signatures.
- Fundamental mathematical tools for cryptography: primality testing, factorization algorithms, probability theory, information theory, and collision algorithms.
- Recent cryptographic innovations such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.
2.2. Mathematical Background
Only basic linear algebra is required as a prerequisite. Techniques from algebra, number theory, and probability are introduced and developed within the text as needed, making the book self-contained for readers with limited advanced mathematical background.
3. Target Audience
The book is designed for advanced undergraduate or beginning graduate students in pure and applied mathematics and computer science. It is also suitable for self-study by individuals interested in the mathematical foundations of modern cryptography.
4. Structure and Learning Aids
Each of the eight chapters includes an extensive list of exercises to reinforce understanding. The book also provides a comprehensive bibliography and index. Supplementary materials are available online to further aid learning.
5. About the Authors
- Jeffrey Hoffstein: Professor at Brown University, specializing in number theory, automorphic forms, and cryptography.
- Jill Pipher: Professor at Brown University, focusing on harmonic analysis, elliptic PDE, and cryptography.
- J.H. Silverman: Professor at Brown University, with research interests in number theory, arithmetic geometry, elliptic curves, dynamical systems, and cryptography.
6. Specifications
| Attribute | Detail |
|---|---|
| Publisher | Springer |
| Publication Date | August 12, 2008 |
| Edition | 2008th |
| Language | English |
| Print Length | 524 pages |
| ISBN-10 | 0387779930 |
| ISBN-13 | 978-0387779935 |
| Item Weight | 1.9 pounds |
| Dimensions | 6.25 x 0.25 x 9.25 inches |
7. Support and Further Information
For additional resources, errata, or supplementary materials, please refer to the publisher's official website or academic resources related to the authors. Specific support channels for this publication are typically provided by the publisher, Springer.
For general inquiries about the content, it is recommended to consult academic institutions or libraries that feature this text.
8. Warranty Information
As a published academic text, this product does not typically come with a consumer warranty in the traditional sense. Any concerns regarding print quality, binding, or missing pages should be directed to the retailer or the publisher, Springer, within a reasonable timeframe after purchase. Please retain your proof of purchase for any such claims.
