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# Elliptic Curves In Cryptography

I. Blake, G. Seroussi, N. Smart

Published 1999 · Mathematics, Computer Science

Preface 1. Introduction 2. Finite field arithmetic 3. Arithmetic on an elliptic curve 4. Efficient implementation of elliptic curves 5. The elliptic curve discrete logarithm problem 6. Determining the group order 7. Schoof's algorithm and extensions 8. Generating curves using complex multiplication 9. Other applications of elliptic curves 10. Hyperelliptic curves Appendix A. Curve examples Bibliography Author index Subject index.

This paper references

176: Line 10. Removè, what is no surprise

J. Cryptology

(1999)

114: Footnote. Insert comma afterafter`comments

In reference [37], the author is R

JLMS Math. Comp

(1999)

191{198: The following references have now appeared

Line -5 (of the main text). The inequality should be an equality

Line -11. The sum should run over P 2 C(F q )

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Fast Algorithms for Elliptic Curve Cryptosystems over Binary Finite Field

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T. Wollinger (2003)

The security of PSEC-KEM versus ECIES-KEM

D. Chacon (2005)

Mitigating DOS attacks against signature-based broadcast authentication in wireless sensor networks

P. Ning (2005)

A highly efficient modular multiplication algorithm for finite field arithmetic in GF(P)

Rainer Blümel (2005)

10.1007/978-3-540-30574-3_25

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J. A. Muir (2005)

Merging GF(p) Elliptic Curve Point Adding and Doubling on Pipelined VLSI Cryptographic ASIC Architecture

A. Gutub (2006)

10.1109/ISCAS.2006.1693348

An RNS architecture of an F/sub p/ elliptic curve point multiplier

Dimitrios M. Schinianakis (2006)

10.1007/s10623-005-3297-0

A-Codes from Rational Functions over Galois Rings

G. Bini (2006)

Cost-Effective Implementations of GF (p) Elliptic Curve Cryptography Computations

H. Khali (2007)

10.1017/S0004972700039034

Some remarks on the number of points on elliptic curves over finite prime field

Saiying He (2007)

10.1145/1216919.1216953

Attacking elliptic curve cryptosystems with special-purpose hardware

Tim Güneysu (2007)

10.4218/ETRIJ.03.0303.0014

A Scalable Structure for a Multiplier and an Inversion Unit in GF(2 m )

C. Lee (2003)

10.1596/0-8213-5759-x

Electronic Safety and Soundness: Securing Finance in a New Age

Thomas C. Glaessner (2004)

10.1109/SIPS.2007.4387555

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10.1007/978-0-387-76481-8_13

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L. Batina (2008)

10.1049/iet-cdt:20070077

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A. Byrne (2006)

10.1007/s11859-008-0616-0

Efficient scalar multiplication for elliptic curves over binary fields

Haihua Gu (2008)

10.1109/ICECS.2008.4674785

A modified architecture for Optimal Normal Basis multiplication based on pre-computation

Richard Cupples (2008)

10.1109/PDCAT.2008.70

Operation of Super Long Integers in Cryptographic Applications

Shenghui Su (2008)

10.21917/IJCT.2011.0034

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R. Ganesan (2011)

10.1155/2011/412146

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10.1109/CSA.2013.24

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10.1007/3-540-45708-9_23

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10.1145/1015047.1015051

Elliptic and hyperelliptic curves on embedded μP

Thomas J. Wollinger (2004)

10.1016/j.csi.2003.11.008

A practical authenticated encryption scheme based on the elliptic curve cryptosystem

T. Chen (2004)

10.2316/JOURNAL.202.2005.3.202-1501

A Secure Key Agreement Protocol Using Elliptic Curves

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10.1007/978-3-540-24591-9_18

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10.1109/ICCIT.2007.342

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