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Elliptic Curve Public Key Cryptosystems Softcover reprint of the original 1st ed. 1993 [Pehme köide]

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Elliptic Curve Public Key Cryptosystems Softcover reprint of the original 1st ed. 1993Suurem pilt
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Püsilink: https://www.kriso.ee/db/9781461364030.html
Märksõnad:
Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems.
Elliptic Curve Public Key Cryptosystems provides an up-to-date and self-contained treatment of elliptic curve-based public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems.
Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject.

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Springer Book Archives
Foreword ix
Preface xi
1 Introduction to Public Key Cryptography
1(14)
1.1 Private Key Cryptography
1(2)
1.2 Diffie-Hellman Key Exchange
3(1)
1.3 Public Key Cryptography
4(1)
1.4 Trapdoor One-Way Functions Based on Groups
5(5)
1.4.1 Group Order as a TOF
6(1)
1.4.2 RS A Cryptosystem
6(1)
1.4.3 Exponentiation as a TOF
7(3)
1.5 NIST Digital Signature Standard
10(3)
1.6 Elliptic Curve Cryptosystems
13(1)
1.7 Notes
14(1)
2 Introduction to Elliptic Curves
15(20)
2.1 Definitions
15(2)
2.2 Group Law
17(2)
2.3 The Discriminant and j-Invariant
19(1)
2.4 Curves over K, char(K) ≠ 2, 3
20(1)
2.5 Curves over K, char(K) = 2
21(2)
2.6 Group Structure
23(5)
2.7 Divisor Theory
28(4)
2.8 Elliptic Curves over Zn
32(2)
2.9 Notes
34(1)
3 Isomorphism Classes of Elliptic Curves over Finite Fields
35(5)
3.1 Introduction
35(2)
3.2 Isomorphism Classes of Curves over Fq, char(Fq) ≠ 2, 3
37(2)
3.3 Isomorphism Classes of Non-Supersingular Curves over F2m
39(1)
3.4 Isomorphism Classes of Supersingular Curves over f2m, m odd
40(1)
3.5 Isomorphism Classes of Supersingular Curves over F2m, m even
41(5)
3.6 Number of Points
46(2)
3.7 Notes
48
4 The Discrete Logarithm Problem
40(21)
4.1 Algorithms
49(5)
4.1.1 Square Root Methods
50(1)
4.1.2 Pohlig-Hellman Method
51(1)
4.1.3 Index Calculus Method
52(2)
4.1.4 Index Calculus Method for Elliptic Curves
54(1)
4.2 Reducing Some Logarithm Problems to Logarithms in a Finite Field
54(5)
4.2.1 Singular Elliptic Curves
55(2)
4.2.2 Another Class of Genus 0 Curves
57(2)
4.3 Notes
59(2)
5 The Elliptic Curve Logarithm Problem
61(22)
5.1 The Weil Pairing
61(7)
5.1.1 Definition
62(1)
5.1.2 Computing the Function of a Principal Divisor
63(3)
5.1.3 Computing the Weil Pairing
66(2)
5.2 Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field
68(9)
5.2.1 The Reduction
69(3)
5.2.2 Supersingular Curves
72(5)
5.2.3 Non-Supersingular Curves
77(1)
5.3 Cryptographic Implications
77(2)
5.4 Finding the Group Structure
79(2)
5.5 Notes
81(2)
6 Implementation of Elliptic Curve Cryptosystems
83(18)
6.1 Field Arithmetic in F2m
83(3)
6.2 Selecting a Curve and Field K
86(4)
6.3 Projective Coordinates
90(1)
6.4 ElGamal Cryptosystem
91(1)
6.5 Performance
92(1)
6.6 Using Supersingular Curves
93(4)
6.7 Elliptic Curve Cryptosystems over Zn
97(1)
6.8 Implementations
98(1)
6.9 Notes
99(2)
7 Counting Points on Elliptic Curves Over F2m
101(16)
7.1 Some Basics
102(1)
7.2 Outline of Schoof's Algorithm
103(1)
7.3 Some Heuristics
104(7)
7.3.1 Finding an Eigenvalue of φ, if One Exists
105(1)
7.3.2 Schoof's Algorithm
106(1)
7.3.3 Determining t modulo l = 2c
107(2)
7.3.4 Baby-step Giant-step Algorithm
109(1)
7.3.5 Checking Results
110(1)
7.4 Implementation and Results
111(4)
7.5 Recent Work
115(1)
7.6 Notes
116(1)
Bibliography 117(10)
Index 127