Constructive and Destructive Facets of Weil Descent on Elliptic Curves

P Gaudry, FK Hess, NP Smart

Research output: Contribution to journalArticle (Academic Journal)

140 Citations (Scopus)


In this paper we look in detail at the curves which arise in the method of Galbraith and Smart for producing curves in the Weil restriction of an elliptic curve over a finite field of characteristic two of composite degree. We explain how this method can be used to construct hyperelliptic cryptosystems which could be as secure as cryptosystems based on the original elliptic curve. On the other hand, we show that the same technique may provide a way of attacking the original elliptic curve cryptosystem using recent advances in the study of the discrete logarithm problem on hyperelliptic curves. We examine the resulting higher genus curves in some detail and propose an additional check on elliptic curve systems defined over fields of characteristic two so as to make them immune from the methods in this paper.
Translated title of the contributionConstructive and Destructive Facets of Weil Descent on Elliptic Curves
Original languageEnglish
Pages (from-to)19 - 46
Number of pages28
JournalJournal of Cryptology
Volume15 (1)
Publication statusPublished - Jan 2002

Bibliographical note

Publisher: Springer

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