Generating anomalous elliptic curves

Autor:	Serge Vaudenay, Jean Monnerat, Franck Leprévost, Sébastien Varrette
Rok vydání:	2005
Předmět:	Finite element method Pure mathematics Edwards curve Complex multiplication Anomalous curve Theoretical Computer Science Computational methods Parameter estimation Elliptic curves Theorem proving Mathematics Discrete mathematics Problem solving Sato–Tate conjecture Elliptic divisibility sequence Twists of curves Supersingular elliptic curve Computer Science Applications Trace of frobenius Signal Processing Cryptography Counting points on elliptic curves Schoof's algorithm Discrete logarithm problem Algorithms Division polynomials Information Systems
Zdroj:	Information Processing Letters. 93:225-230
ISSN:	0020-0190
DOI:	10.1016/j.ipl.2004.11.008
Popis:	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. Â© 2004 Elsevier B.V. All rights reserved.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd469fe88c90295bb2f503b10b8b1437 https://doi.org/10.1016/j.ipl.2004.11.008 Zobrazit plný text záznamu Full Text from ScienceDirect