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. Â© 2004 Elsevier B.V. All rights reserved.
Elliptic curves;Discrete logarithm problem;Trace of frobenius;Complex multiplication;Anomalous curve;
Record created on 2007-01-18, modified on 2016-08-08