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Modern Cryptography and Elliptic Curves: A Beginner's Guide by Shemanske
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eBay-Artikelnr.:355917903031
Artikelmerkmale
- Artikelzustand
- Publish Year
- 2017
- Book Title
- Modern Cryptography and Elliptic Curves: A Beginner's Guide
- ISBN
- 9781470435820
Über dieses Produkt
Product Identifiers
Publisher
American Mathematical Society
ISBN-10
1470435829
ISBN-13
9781470435820
eBay Product ID (ePID)
237540095
Product Key Features
Number of Pages
252 Pages
Language
English
Publication Name
Modern Cryptography and Elliptic Curves : a Beginner's Guide
Publication Year
2017
Subject
Communication Studies, Computer Science, Number Theory, Geometry / Algebraic
Type
Textbook
Subject Area
Mathematics, Computers, Language Arts & Disciplines
Series
Student Mathematical Library
Format
Trade Paperback
Dimensions
Item Height
0.8 in
Item Weight
11.3 Oz
Item Length
8.5 in
Item Width
5.5 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2017-001191
Dewey Edition
23
Reviews
The main objective of this book, which is mainly aimed at undergraduate students, is to explain the arithmetic of elliptic curves defined over finite fields and to show how those curves can be used in cryptography. In order to do that, the author purposely avoids complex mathematical demonstrations and, instead, presents the concepts in a more descriptive way, suggesting some topics for further exploration by the reader." - Victor Gayoso Martíinez, Mathematical Reviews
Series Volume Number
83
Illustrated
Yes
Dewey Decimal
516.3/52
Table Of Content
Three motivating problems Back to the beginning Some elementary number theory A second view of modular arithmetic: $\mathbb{Z}_n$ and $U_n$ Public-key cryptography and RSA A little more algebra Curves in affine and projective space Applications of elliptic curves Deeper results and concluding thoughts Answers to selected exercises Bibliography Index.
Synopsis
This book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). Elements of abstract algebra, number theory, and affine and projective geometry are introduced and developed, and their interplay is exploited. Algebra and geometry combine to characterize congruent numbers via rational points on the unit circle, and group law for the set of points on an elliptic curve arises from geometric intuition provided by Bezout's theorem as well as the construction of projective space. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollard's method of factorization, Diffie-Hellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstra's elliptic curve factorization method and ECC. The only real prerequisite for this book is a course on one-variable calculus; other necessary mathematical topics are introduced on-the-fly. Numerous exercises further guide the exploration., Offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed for an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration.
LC Classification Number
QA567.2.E44S534 2017
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