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ORCIDHandbook 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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