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Seminars given
October 25, 2002 - Efficient arithmetic on (hyper-)elliptic curves over finite fields
by Tanja Lange
| Abstract: | The talk will be concerned with arithmetic on elliptic and hyperelliptic curves. We show how fast the arithmetic can get by clever choices of the coordinates and present special kinds of curves which allow even faster arithmetic using the Frobenius endomorphism. For elliptic curves this has been used to achieve fast arithmetic for the past years. However, so far arithmetic in the ideal class group of hyperelliptic curves was performed using Cantor's algorithm which needs several inversions per group operation. Meanwhile inversion-free systems have been studied allowing even hardware implementations and depending on the system hyperelliptic curves can even be faster than elliptic curves. |
Publications
Daniel V. Bailey, Brian Baldwin, Lejla Batina, Daniel J. Bernstein, Peter Birkner, Joppe W. Bos, Gauthier van Damme, Giacomo de Meulenaer, Junfeng Fan, Frank Gurkaynak, Tim Güneysu, Thorsten Kleinjung, Tanja Lange, Nele Mentens, Christof Paar, Francesco Regazzoni, Peter Schwabe, and Leif Uhsadel. The Certicom Challenges ECC2-X, Workshop on Special Purpose Hardware for Attacking Cryptographic Systems (SHARCS'09), September 2009 PDF BibTeX
Mathieu Ciet, Tanja Lange, Francesco Sica, and Jean-Jacques Quisquater. Improved Algorithms for Efficient Arithmetic on Elliptic Curves Using Fast Endomorphisms, In Eli Biham, editor(s), Advances in Cryptology - EUROCRYPT 2003, Warsaw, Poland, Volume 2656 of Lecture Notes in Computer Science, Springer-Verlag, May 2003 PDF BibTeX
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