Skip to Main content Skip to Navigation
Journal articles

Constructive and destructive facets of Weil descent on elliptic curves

Abstract : 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 can be used to construct hyperelliptic cryptosystems which could be as secure as a cryptosystem 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.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/inria-00512763
Contributor : Pierrick Gaudry <>
Submitted on : Tuesday, August 31, 2010 - 3:25:03 PM
Last modification on : Thursday, March 5, 2020 - 6:21:45 PM
Document(s) archivé(s) le : Wednesday, December 1, 2010 - 2:51:20 AM

File

weildesc_vZ.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Pierrick Gaudry, Florian Hess, Nigel Smart. Constructive and destructive facets of Weil descent on elliptic curves. Journal of Cryptology, Springer Verlag, 2002, 15, pp.19-46. ⟨10.1007/s00145-001-0011-x⟩. ⟨inria-00512763⟩

Share

Metrics

Record views

319

Files downloads

460