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Handbook of Elliptic and Hyperelliptic Curve Cryptography 2005
- Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, Frederik Vercauteren:

Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman and Hall/CRC 2005, ISBN 978-1-58488-518-4 - Roberto Maria Avanzi, Tanja Lange:

Introduction to Public-Key Cryptography. 1-15 - Christophe Doche, David Lubicz:

Algebraic Background. 18-37 - David Lubicz:

Background on p-adic Numbers. 39-44 - Gerhard Frey, Tanja Lange:

Background on Curves and Jacobians. 45-85 - Gerhard Frey, Tanja Lange:

Varieties over Special Fields. 87-113 - Sylvain Duquesne, Gerhard Frey:

Background on Pairings. 115-124 - Gerhard Frey, Tanja Lange:

Background on Weil Descent. 125-132 - David Lubicz, Frederik Vercauteren:

Cohomological Background on Point Counting. 133-141 - Christophe Doche:

Exponentiation. 144-168 - Christophe Doche:

Integer Arithmetic. 169-199 - Christophe Doche:

Finite Field Arithmetic. 201-237 - Frederik Vercauteren:

Arithmetic of p-adic Numbers. 239-263 - Christophe Doche, Tanja Lange:

Arithmetic of Elliptic Curves. 267-302 - Sylvain Duquesne, Tanja Lange:

Arithmetic of Hyperelliptic Curves. 303-353 - Christophe Doche, Tanja Lange:

Arithmetic of Special Curves. 355-387 - Sylvain Duquesne, Gerhard Frey:

Implementation of Pairings. 389-404 - Reynald Lercier, David Lubicz, Frederik Vercauteren:

Point Counting on Elliptic and Hyperelliptic Curves. 406-453 - Gerhard Frey, Tanja Lange:

Complex Multiplication. 455-473 - Roberto Maria Avanzi:

Generic Algorithms for Computing Discrete Logarithms. 476-494 - Roberto Maria Avanzi, Nicolas Thériault:

Index Calculus. 495-509 - Roberto Maria Avanzi, Nicolas Thériault:

Index Calculus for Hyperelliptic Curves. 511-527 - Gerhard Frey, Tanja Lange:

Transfer of Discrete Logarithms. 529-545 - Gerhard Frey, Tanja Lange:

Algebraic Realizations of DL Systems. 546-572 - Sylvain Duquesne, Tanja Lange:

Pairing-Based Cryptography. 573-590 - Roberto Maria Avanzi, Henri Cohen:

Compositeness and Primality Testing Factoring. 591-614 - Kim Nguyen, Andrew Weigl:

Fast Arithmetic in Hardware. 616-646 - Bertrand Byramjee, Andrew Weigl:

Smart Cards. 647-667 - Bertrand Byramjee, Jean-Christophe Courrège, Benoit Feix:

Practical Attacks on Smart Cards. 669-685 - Tanja Lange:

Mathematical Countermeasures against Side-Channel Attacks. 687-714 - Tanja Lange, David Lubicz, Andrew Weigl:

Random Numbers Generation and Testing. 715-735 - References. 737-775


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