Leprevost, FranckMonnerat, JeanVarrette, SebastienVaudenay, Serge2007-01-182007-01-182007-01-18200510.1016/j.ipl.2004.11.008https://infoscience.epfl.ch/handle/20.500.14299/239712WOS:0002266967000036210In 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.Problem solvingFinite element methodCryptographyComputational methodsParameter estimationAlgorithmsTheorem provingElliptic curvesDiscrete logarithm problemTrace of frobeniusComplex multiplicationAnomalous curvetext::journal::journal article::research article