Rating:
(5 reviews)
Author: Jeffrey Hoffstein
ISBN : 0387779930
New from $39.89
Format: PDF
Direct download links available Free An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) [Hardcover] for everyone book with Mediafire Link Download Link
An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises.
It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.
Direct download links available for Free An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) [Hardcover]
- Series: Undergraduate Texts in Mathematics
- Hardcover: 524 pages
- Publisher: Springer; 2008 edition (September 2, 2008)
- Language: English
- ISBN-10: 0387779930
- ISBN-13: 978-0387779935
- Product Dimensions: 1.2 x 6.1 x 9.1 inches
- Shipping Weight: 2 pounds (View shipping rates and policies)
Free An Introduction to Mathematical Cryptography
At least for the chapters that were studied by this reviewer, the authors of this book give an effective introduction to the mathematical theory used in cryptography at a level that can be approached by an undergraduate senior in mathematics. The field of cryptography is vast of course, and a book of this size could not capture it effectively. The topics of primary importance are represented however, and the authors do a fine job of motivating and explaining the needed concepts.
The authors give an elementary overview of elliptic curves over the complex numbers, and most importantly over finite fields whose characteristic is greater than 3. The case where the characteristic is equal to 2 is delegated to its own section. In discussing the arithmetic of elliptic curves over finite fields, the authors give a good motivation for Hasse's formula, which gives a bound for the number of points of the elliptic curve (over a finite field), but they do not go into the details of the proof. The Hasse formula is viewed in some texts as a "Riemann Hypothesis" for elliptic curves over finite fields, and was proven by Hasse in 1934. This reviewer has not studied Hasse's proof, but a contemporary proof relies on the Frobenius map and its separability, two notions that the authors do not apparently want to introduce at this level of book (however they do introduce the Frobenius map when discussing elliptic curves over F2). Separability is viewed in some texts in elliptic curves as more of a technical issue, which can be ignored at an elementary level. It arises when studying endomorphisms of elliptic curves of fields of non-zero characteristic, and involves defining rational functions.