Computations in class groups of imaginary quadratic number fields

The most crucial question when using a cryptographic scheme is how to select the cryptographic parameters such that the scheme is "secure" and reasonably efficient at the same time. In this article that question will be considered for cryptographic schemes based on class groups of imaginary quadratic number fields. Specifically, an algorithm is investigated that is very similar to the (p - 1) factoring algorithm. This algorithm is already known to be asymptotically inferior to the IQ-MPQS algorithm. However, based on rough running time estimates of both algorithms, there has been the suspicion that for parameters within range of cryptographic relevance the algorithm was competing with the IQ-MPQS. In this article it is clearly shown that this is not even remotely the case