Elliptic curves : (Record no. 2395)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04197nam a22001937a 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240905122958.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240905b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781032307084 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.352 |
| Item number | WAS |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Washington C Lawrence |
| 245 ## - TITLE STATEMENT | |
| Title | Elliptic curves : |
| Remainder of title | number theory and cryptography |
| Statement of responsibility, etc. | Lawrence C. Washington |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2 |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
| Place of publication, distribution, etc. | Boca Raton, FL |
| Name of publisher, distributor, etc. | CRC |
| Date of publication, distribution, etc. | c2008. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Page number | 513 p |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Title | INTRODUCTION<br/>THE BASIC THEORY<br/>Weierstrass Equations<br/>The Group Law<br/>Projective Space and the Point at Infinity<br/>Proof of Associativity<br/>Other Equations for Elliptic Curves<br/>Other Coordinate Systems<br/>The j-Invariant<br/>Elliptic Curves in Characteristic 2<br/>Endomorphisms<br/>Singular Curves<br/>Elliptic Curves mod n<br/>TORSION POINTS<br/>Torsion Points<br/>Division Polynomials<br/>The Weil Pairing<br/>The Tate–Lichtenbaum Pairing<br/>Elliptic Curves over Finite Fields<br/>Examples<br/>The Frobenius Endomorphism<br/>Determining the Group Order<br/>A Family of Curves<br/>Schoof’s Algorithm<br/>Supersingular Curves<br/>The Discrete Logarithm Problem<br/>The Index Calculus<br/>General Attacks on Discrete Logs<br/>Attacks with Pairings<br/>Anomalous Curves<br/>Other Attacks<br/>Elliptic Curve Cryptography<br/>The Basic Setup<br/>Diffie–Hellman Key Exchange<br/>Massey–Omura Encryption<br/>ElGamal Public Key Encryption<br/>ElGamal Digital Signatures<br/>The Digital Signature Algorithm<br/>ECIES<br/>A Public Key Scheme Based on Factoring<br/>A Cryptosystem Based on the Weil Pairing<br/>Other Applications<br/>Factoring Using Elliptic Curves<br/>Primality Testing<br/>Elliptic Curves over Q<br/>The Torsion Subgroup: The Lutz–Nagell Theorem<br/>Descent and the Weak Mordell–Weil Theorem<br/>Heights and the Mordell–Weil Theorem<br/>Examples<br/>The Height Pairing<br/>Fermat’s Infinite Descent<br/>2-Selmer Groups; Shafarevich–Tate Groups<br/>A Nontrivial Shafarevich–Tate Group<br/>Galois Cohomology<br/>Elliptic Curves over C<br/>Doubly Periodic Functions<br/>Tori Are Elliptic Curves<br/>Elliptic Curves over C<br/>Computing Periods<br/>Division Polynomials<br/>The Torsion Subgroup: Doud’s Method<br/>Complex Multiplication<br/>Elliptic Curves over C<br/>Elliptic Curves over Finite Fields<br/>Integrality of j-Invariants<br/>Numerical Examples<br/>Kronecker’s Jugendtraum<br/>DIVISORS<br/>Definitions and Examples<br/>The Weil Pairing<br/>The Tate–Lichtenbaum Pairing<br/>Computation of the Pairings<br/>Genus One Curves and Elliptic Curves<br/>Equivalence of the Definitions of the Pairings<br/>Nondegeneracy of the Tate–Lichtenbaum Pairing<br/>ISOGENIES<br/>The Complex Theory<br/>The Algebraic Theory<br/>Vélu’s Formulas<br/>Point Counting<br/>Complements<br/>Hyperelliptic Curves<br/>Basic Definitions<br/>Divisors<br/>Cantor’s Algorithm<br/>The Discrete Logarithm Problem<br/>Zeta Functions<br/>Elliptic Curves over Finite Fields<br/>Elliptic Curves over Q<br/>Fermat’s Last Theorem<br/>Overview<br/>Galois Representations<br/>Sketch of Ribet’s Proof<br/>Sketch of Wiles’s Proof |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves.<br/><br/>New to the Second Edition<br/><br/>Chapters on isogenies and hyperelliptic curves<br/>A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues<br/>A more complete treatment of the Weil and Tate–Lichtenbaum pairings<br/>Doud’s analytic method for computing torsion on elliptic curves over Q<br/>An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems<br/>Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Curves, Elliptic Number theory Cryptography |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Dewey Decimal Classification |
| Koha item type | Books |
| 952 ## - LOCATION AND ITEM INFORMATION (KOHA) | |
| -- | 7369 |
| 952 ## - LOCATION AND ITEM INFORMATION (KOHA) | |
| -- | 7370 |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Collection code | Home library | Current library | Shelving location | Date acquired | Source of acquisition | Cost, normal purchase price | Inventory number | Total Checkouts | Full call number | Barcode | Date last seen | Cost, replacement price | Price effective from | Currency | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | Non-fiction | IIITDM Kurnool | IIITDM Kurnool | ELECTRONICS COMMUNICATION ENGINEERING | 05.09.2024 | Technical Bureau India | 2995.00 | TB1352 DT 23-08-2024 | 516.352 WAS | 0006351 | 05.09.2024 | 2995.00 | 05.09.2024 | INR | Books | |||||
| Dewey Decimal Classification | Not For Loan | Reference | IIITDM Kurnool | IIITDM Kurnool | Reference | 05.09.2024 | Technical Bureau India | 2995.00 | TB1352 DT 23-08-2024 | 516.352 WAS | 0006352 | 05.09.2024 | 2995.00 | 05.09.2024 | INR | Reference |