Comparing Invariants for Class Fields of Imaginary Quadratic Fields

摘要

Class fields of imaginary quadratic number fields can be constructed from singular values of modular functions, called class invariants. From a computational point of view, it is desirable that the associated minimal polynomials be small. We examine different approaches to measure the size of the polynomials. Based on experimental evidence, we compare two families of class invariants suggested in the literature with respect to these criteria. Our results lead to more efficient constructions of elliptic curves for cryptography or in the context of elliptic curve primality proving (ECPP).