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Author: Jeffrey Hoffstein
ISBN : B00DWKP0V4
New from $11.26
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Free download Free An Introduction to Mathematical Cryptography from with Mediafire Link Download LinkThis self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.Download latest books on mediafire and other links compilation Free An Introduction to Mathematical Cryptography
- File Size: 8142 KB
- Print Length: 540 pages
- Publisher: Springer; 2008 edition (April 11, 2013)
- Sold by: Amazon Digital Services, Inc.
- Language: English
- ASIN: B00DWKP0V4
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- Amazon Best Sellers Rank: #142,376 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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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.