Modern cryptography and elliptic curves (Record no. 55763)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02546nam a22002177a 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20191021124830.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 191018b ||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470454883 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.352 SHE |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Thomas R Shemanske |
| 245 ## - TITLE STATEMENT | |
| Title | Modern cryptography and elliptic curves |
| Remainder of title | : a beginner's guide |
| Statement of responsibility, etc | /Thomas R Shemanske |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Providence, Rhode Island |
| Name of publisher, distributor, etc | : American Mathematical Society |
| Date of publication, distribution, etc | , 2017 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xii, 250 pages |
| Dimensions | ; 22 cm. |
| 490 ## - SERIES STATEMENT | |
| Series statement | Student mathematical library, v. 83. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Contents note | Three Motivating Problems --<br/>Back to the Beginning --<br/>Some Elementary Number Theory --<br/>A Second View of Modular Arithmetic --<br/>Public-Key Cryptography and RSA --<br/>A Little More Algebra --<br/>Curves in Affine and Projective Space --<br/>Applications of Elliptic Curves --<br/>Appendix A: Deeper Results and Concluding Thoughts --<br/>Appendix B: Answers to Selected Exercises |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | <br/>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 | |
| Topical term or geographic name as entry element | Mathematics |
| 655 ## - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Cryptography |
| Non-focus term | Geometry, Algebraic |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Thomas R Shemanske |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Mathematics Departmental Library |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Home library | Current library | Date acquired | Total Checkouts | Full call number | Barcode | Date last seen | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mathematics Departmental Library | Mathematics Departmental Library | 18/10/2019 | 516.352 SHE | M023 | 18/10/2019 | 18/10/2019 | Mathematics Departmental Library |
