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TitleGenus 2 point counting over prime fields
Author(s) Pierrick Gaudry, Éric Schost
TypeArticle in Journal
AbstractFor counting points of Jacobians of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof’s genus 1 algorithm. We propose various practical improvements to this method and illustrate them with a large scale computation: we counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-of-the-art security level of approximately 2 128 and desirable speed properties. This curve and its quadratic twist have a Jacobian group whose order is 16 times a prime.
KeywordsPoint counting, Hyperelliptic curves, Schoof–Pila algorithm
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717111001386
LanguageEnglish
JournalJournal of Symbolic Computation
Volume47
Number4
Pages368 - 400
Year2012
NoteSpecial Issue for Joachim von zur Gathen at 60
Edition0
Translation No
Refereed No
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