ScienceDirect® Home Skip Main Navigation Links
You have guest access to ScienceDirect. Find out more.
 
Home
Browse
My Settings
Alerts
Help
 Quick Search
 Search tips (Opens new window)
    Clear all fields    
advertisementadvertisement
Information Processing Letters
Volume 93, Issue 5, 16 March 2005, Pages 225-230
 
Font Size: Decrease Font Size  Increase Font Size
 Abstract - selected
Purchase PDF (121 K)

  E-mail Article   
  Add to my Quick Links   
Bookmark and share in 2collab (opens in new window)
Request permission to reuse this article
  Cited By in Scopus (0)
 
 
 
Related Articles in ScienceDirect
View More Related Articles
 
View Record in Scopus
 
doi:10.1016/j.ipl.2004.11.008    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2004 Elsevier B.V. All rights reserved.

Generating anomalous elliptic curves

Franck Leprévosta, E-mail The Corresponding Author, Jean Monneratb, Corresponding Author Contact Information, 1, E-mail The Corresponding Author, Sébastien Varrettea, E-mail The Corresponding Author and Serge Vaudenayb, E-mail The Corresponding Author

aUniversité du Luxembourg, LIASIT, 162 A, Avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg bEPFL, LASEC, CH-1015 Lausanne, Switzerland

Received 22 June 2004; 
revised 17 November 2004. 
Communicated by M. Yamashita. 
Available online 23 December 2004.

Purchase the full-text article



References and further reading may be available for this article. To view references and further reading you must purchase this article.

Abstract

In 1999, Smart has shown how to solve in linear time ECDLP for elliptic curves of trace 1 defined over a prime finite field Fp, the so-called anomalous elliptic curves. In this article, we show how to construct such cryptographically weak curves for primes p of industrial length, using complex multiplication theory.

Keywords: Elliptic curve; Discrete logarithm problem; Trace of Frobenius; Complex multiplication; Anomalous curve; Cryptography


 
Home
Browse
My Settings
Alerts
Help
Elsevier.com (Opens new window)
About ScienceDirect  |  Contact Us  |  Information for Advertisers  |  Terms & Conditions  |  Privacy Policy
Copyright © 2008 Elsevier B.V. All rights reserved. ScienceDirect® is a registered trademark of Elsevier B.V.