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Guide to elliptic curve cryptography

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Termasuk bibliografi dan indeks.

CONTENTS:

1 Introduction and Overview

1.1 Cryptography basics

1.2 Public-key cryptography

1.2.1 RSAsystems

1.2.2 Discrete logarithmsystems

1.2.3 Elliptic curve systems

1.3 Why elliptic curve cryptography?

1.4 Roadmap

1.5 Notes and further references


2 Finite Field Arithmetic

2.1 Introduction to finite fields

2.2 Primefieldarithmetic

2.2.1 Addition and subtraction

2.2.2 Integer multiplication

2.2.3 Integer squaring

2.2.4 Reduction

2.2.5 Inversion

2.2.6 NISTprimes

2.3 Binary field arithmetic

2.3.1 Addition

2.3.2 Multiplication

2.3.3 Polynomial multiplication

2.3.4 Polynomial squaring

2.3.5 Reduction

2.3.6 Inversion and division

2.4 Optimal extension field arithmetic

2.4.1 Addition and subtraction

2.4.2 Multiplication and reduction

2.4.3 Inversion

2.5 Notes andfurther references


3 Elliptic Curve Arithmetic

3.1 Introduction to elliptic curves

3.1.1 Simplified Weierstrass equations

3.1.2 Group law

3.1.3 Group order

3.1.4 Group structure

3.1.5 Isomorphism classes

3.2 Point representation and the group law

3.2.1 Projective coordinates

3.2.2 The elliptic curve y2 = x3 +ax +b

3.2.3 The elliptic curve y2 +xy = x3 +ax2 +b

3.3 Point multiplication

3.3.1 Unknown point

3.3.2 Fixed point

3.3.3 Multiple point multiplication

3.4 Koblitz curves

3.4.1 The Frobenius map and the ring Z[

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Availability

Detail Information

Series Title

null

Call Number

516.3 HAN g

Publisher

New York : Springer., 2010

Collation

xx, 311 hlm.; ilus.; 23 cm.

Language

English

ISBN/ISSN

9781441929297

Classification

516.3

Content Type

-

Media Type

-

Carrier Type

-

Edition

null

Subject(s)

Curves, Elliptic
Cryptography -- Mathematics

Specific Detail Info

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Statement of Responsibility

Darrel Hankerson, dkk.

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