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Handbook of Elliptic and Hyperelliptic Curve Cryptography
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General Information
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Type.................: Ebook
Part Size............: 6,913,834 bytes
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Posted by............: ~tqw~
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Release Notes
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The discrete logarithm problem based on elliptic and hyperelliptic curves has
gained a lot of popularity as a cryptographic primitive. The main reason is that
no subexponential algorithm for computing discrete logarithms on small genus
curves is currently available, except in very special cases. Therefore curve-
based cryptosystems require much smaller key sizes than RSA to attain the same
security level. This makes them particularly attractive for implementations on
memory-restricted devices like smart cards and in high-security applications.
Table of Contents
1 Introduction to public-key cryptography 1
I Mathematical background
2 Algebraic background 19
3 Background on p-adic numbers 39
4 Background on curves and Jacobians 45
5 Varieties over special fields 87
6 Background on pairings 115
7 Background on Weil descent 125
8 Cohomological background on point counting 133
II Elementary arithmetic
9 Exponentiation 145
10 Integer arithmetic 169
11 Finite field arithmetic 201
12 Arithmetic of p-adic numbers 239
III Arithmetic of curves
13 Arithmetic of elliptic curves 267
14 Arithmetic of hyperelliptic curves 303
15 Arithmetic of special curves 355
16 Implementation of pairings 389
IV Point counting
17 Point counting on elliptic and hyperelliptic curves 407
18 Complex multiplication 455
V Computation of discrete logarithms
19 Generic algorithms for computing discrete logarithms 477
20 Index calculus 495
21 Index calculus for hyperelliptic curves 511
22 Transfer of discrete logarithms 529
VI Applications
23 Algebraic realizations of DL systems 547
24 Pairing-based cryptography 573
25 Compositeness and primality testing - factoring 591
VII Realization of discrete logarithm systems
26 Fast arithmetic in hardware 617
27 Smart cards 647
28 Practical attacks on smart cards 669
29 Mathematical countermeasures against side-channel attacks 687
30 Random numbers - generation and testing 715
Product Details
* ISBN: 1584885181
* ISBN-13: 9781584885184
* Format: Hardcover, 808pp
* Publisher: CRC Press
* Pub. Date: July 2005
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Install Notes
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PDF Reader
*******************************************************************************
Handbook of Elliptic and Hyperelliptic Curve Cryptography
*******************************************************************************
-------------------------------------------------------------------------------
General Information
-------------------------------------------------------------------------------
Type.................: Ebook
Part Size............: 6,913,834 bytes
-------------------------------------------------------------------------------
Post Information
-------------------------------------------------------------------------------
Posted by............: ~tqw~
-------------------------------------------------------------------------------
Release Notes
-------------------------------------------------------------------------------
The discrete logarithm problem based on elliptic and hyperelliptic curves has
gained a lot of popularity as a cryptographic primitive. The main reason is that
no subexponential algorithm for computing discrete logarithms on small genus
curves is currently available, except in very special cases. Therefore curve-
based cryptosystems require much smaller key sizes than RSA to attain the same
security level. This makes them particularly attractive for implementations on
memory-restricted devices like smart cards and in high-security applications.
Table of Contents
1 Introduction to public-key cryptography 1
I Mathematical background
2 Algebraic background 19
3 Background on p-adic numbers 39
4 Background on curves and Jacobians 45
5 Varieties over special fields 87
6 Background on pairings 115
7 Background on Weil descent 125
8 Cohomological background on point counting 133
II Elementary arithmetic
9 Exponentiation 145
10 Integer arithmetic 169
11 Finite field arithmetic 201
12 Arithmetic of p-adic numbers 239
III Arithmetic of curves
13 Arithmetic of elliptic curves 267
14 Arithmetic of hyperelliptic curves 303
15 Arithmetic of special curves 355
16 Implementation of pairings 389
IV Point counting
17 Point counting on elliptic and hyperelliptic curves 407
18 Complex multiplication 455
V Computation of discrete logarithms
19 Generic algorithms for computing discrete logarithms 477
20 Index calculus 495
21 Index calculus for hyperelliptic curves 511
22 Transfer of discrete logarithms 529
VI Applications
23 Algebraic realizations of DL systems 547
24 Pairing-based cryptography 573
25 Compositeness and primality testing - factoring 591
VII Realization of discrete logarithm systems
26 Fast arithmetic in hardware 617
27 Smart cards 647
28 Practical attacks on smart cards 669
29 Mathematical countermeasures against side-channel attacks 687
30 Random numbers - generation and testing 715
Product Details
* ISBN: 1584885181
* ISBN-13: 9781584885184
* Format: Hardcover, 808pp
* Publisher: CRC Press
* Pub. Date: July 2005
-------------------------------------------------------------------------------
Install Notes
-------------------------------------------------------------------------------
PDF Reader