Generating anomalous elliptic curves

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.


Published in:
Information Processing Letters, 93, 5, 225-230
Year:
2005
Keywords:
Note:
Elliptic curves;Discrete logarithm problem;Trace of frobenius;Complex multiplication;Anomalous curve;
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 Record created 2007-01-18, last modified 2018-03-17

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