We improve several elliptic curve multiplication algorithms secure against side channel attacks (SCA). While some efficient SCAresistant algorithms were developed that apply only to special classes of curves, we are interested in algorithms that are suitable for general elliptic curves and can be applied to the recommended curves found in various standards. We compare the running time and memor...

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.