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Advances in Elliptic Curve Cryptography [Minkštas viršelis]

Edited by (Hewlett-Packard Laboratories, Palo Alto, California), Edited by (Hewlett-Packard Laboratories, Bristol), Edited by (University of Toronto)
  • Formatas: Paperback / softback, 298 pages, aukštis x plotis x storis: 229x152x17 mm, weight: 440 g, 11 Tables, unspecified; 7 Line drawings, unspecified
  • Serija: London Mathematical Society Lecture Note Series
  • Išleidimo metai: 25-Apr-2005
  • Leidėjas: Cambridge University Press
  • ISBN-10: 052160415X
  • ISBN-13: 9780521604154
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 298 pages, aukštis x plotis x storis: 229x152x17 mm, weight: 440 g, 11 Tables, unspecified; 7 Line drawings, unspecified
  • Serija: London Mathematical Society Lecture Note Series
  • Išleidimo metai: 25-Apr-2005
  • Leidėjas: Cambridge University Press
  • ISBN-10: 052160415X
  • ISBN-13: 9780521604154
Kitos knygos pagal šią temą:
Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.

This second volume addresses tremendous progress in elliptic curve cryptography since the first volume.

Daugiau informacijos

This second volume addresses tremendous progress in elliptic curve cryptography since the first volume.
Preface ix
Abbreviations and Standard Notation xi
Authors xv
Part
1. Protocols
Elliptic Curve Based Protocols
3(18)
N.P. Smart
Introduction
3(1)
ECDSA
4(4)
ECDH/ECMQV
8(4)
ECIES
12(6)
Other Considerations
18(3)
On the Provable Security of ECDSA
21(20)
D. Brown
Introduction
21(2)
Definitions and Conditions
23(9)
Provable Security Results
32(1)
Proof Sketches
33(3)
Further Discussion
36(5)
Proofs of Security for ECIES
41(28)
A. W. Dent
Definitions and Preliminaries
42(8)
Security Proofs for ECIES
50(8)
Other Attacks Against ECIES
58(3)
ECIES-KEM
61(8)
Part
2. Implementation Techniques
Side-Channel Analysis
69(18)
E. Oswald
Cryptographic Hardware
70(1)
Active Attacks
71(1)
Passive Attacks
72(5)
Simple SCA Attacks on Point Multiplications
77(7)
Differential SCA Attacks on Point Multiplications
84(3)
Defences Against Side-Channel Analysis
87(16)
M. Joye
Introduction
87(1)
Indistinguishable Point Addition Formula
88(5)
Regular Point Multiplication Algorithms
93(4)
Base-Point Randomization Techniques
97(1)
Multiplier Randomization Techniques
98(2)
Preventing Side-Channel Analysis
100(3)
Part
3. Mathematical Foundations
Advances in Point Counting
103(30)
F. Vercauteren
p-adic Fields and Extensions
104(1)
Satoh's Algorithm
105(10)
Arithmetic Geometric Mean
115(6)
Generalized Newton Iteration
121(7)
Norm Computation
128(4)
Concluding Remarks
132(1)
Hyperelliptic Curves and the HCDLP
133(18)
P. Gaudry
Generalities on Hyperelliptic Curves
133(3)
Algorithms for Computing the Group Law
136(4)
Classical Algorithms for HCDLP
140(2)
Smooth Divisors
142(2)
Index-Calculus Algorithm for Hyperelliptic Curves
144(2)
Complexity Analysis
146(3)
Practical Considerations
149(2)
Weil Descent Attacks
151(32)
F. Hess
Introduction -- the Weil Descent Methodology
151(2)
The GHS Attack
153(13)
Extending the GHS Attack Using Isogenies
166(7)
Summary of Practical Implications
173(2)
Further Topics
175(8)
Part
4. Pairing Based Techniques
Pairings
183(32)
S. Galbraith
Bilinear Pairings
183(1)
Divisors and Weil Reciprocity
184(1)
Definition of the Tate Pairing
185(2)
Properties of the Tate Pairing
187(2)
The Tate Pairing over Finite Fields
189(2)
The Weil Pairing
191(1)
Non-degeneracy, Self-pairings and Distortion Maps
192(4)
Computing the Tate Pairing Using Miller's Algorithm
196(1)
The MOV/Frey--Ruck Attack on the ECDLP
197(1)
Supersingular Elliptic Curves
198(3)
Applications and Computational Problems from Pairings
201(2)
Parameter Sizes and Implementation Considerations
203(1)
Suitable Supersingular Elliptic Curves
204(1)
Efficient Computation of the Tate Pairing
205(3)
Using Ordinary Curves
208(7)
Appendix: Proof of Weil Reciprocity
212(3)
Cryptography from Pairings
215(38)
K.G. Paterson
Introduction
215(3)
Key Distribution Schemes
218(3)
Identity-Based Encryption
221(7)
Signature Schemes
228(7)
Hierarchical Identity-Based Cryptography and Related Topics
235(5)
More Key Agreement Protocols
240(2)
Applications and Infrastructures
242(8)
Concluding Remarks
250(3)
Bibliography
253(20)
Summary of Major LNCS Proceedings
271(2)
Author Index 273(4)
Subject Index 277