Copyright © 2004 Elsevier B.V. All rights reserved.
Generating anomalous elliptic curves
Received 22 June 2004;
revised 17 November 2004.
Communicated by M. Yamashita.
Available online 23 December 2004.
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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







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