| 000 -LEADER |
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| fixed length control field |
a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
220322b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470435820 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.352 |
| Item number |
SHE |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Shemanske, Thomas R. |
| 245 ## - TITLE STATEMENT |
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| Title |
Modern cryptography and elliptic curves : a beginner's guide |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
2017 |
| Place of publication, distribution, etc |
Providence : |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xii, 250 p. ; |
| Other physical details |
ill., |
| Dimensions |
22 cm |
| 365 ## - TRADE PRICE |
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| Price amount |
52.00 |
| Price type code |
USD |
| Unit of pricing |
78.80 |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Student mathematical library ; |
| Volume number/sequential designation |
v. 83 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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 Bézout'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. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geometry, Algebraic |
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| Topical term or geographic name as entry element |
Curves, Elliptic |
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| Topical term or geographic name as entry element |
Quantum theory Axiomatics |
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| Topical term or geographic name as entry element |
Abstract algebra |
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| Topical term or geographic name as entry element |
Number theory |
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| Topical term or geographic name as entry element |
Affine, projective geometry |
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| Topical term or geographic name as entry element |
Chinese Remainder Theorem |
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| Topical term or geographic name as entry element |
Fundamental Theorem Of Finite Abelian Groups |
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| Topical term or geographic name as entry element |
Torsion point |
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| Topical term or geographic name as entry element |
Crypto systems |
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| Topical term or geographic name as entry element |
Factoring |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
|
| Item type |
Books |