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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. © 2004 Elsevier B.V. All rights reserved.
Tako Boris Fouotsa, Laurane Chloé Angélina Marco, Andrea Basso