We investigate the use of energy dispersive x-ray coherent scatter computed tomography (ED-CSCT) as a non-invasive diagnostic method to differentiate between type I and type II breast calcifications. This approach is sensitive to the differences of composition and internal crystal structure of different types of microcalcifications. The study is carried out by simulating a CSCT system with a scanning pencil beam, considering a polychromatic x-ray source and an energy-resolving photon counting detector. In a first step, the multidimensional angle and energy distributed CSCT data is reduced to the projection-space distributions of only a few components, corresponding to the expected target composition: adipose, glandular tissue, weddellite (calcium oxalate) for type I calcifications, and hydroxyapatite for type II calcifications. The maximum-likelihood estimation of scatter components algorithm used, operating in the projection space, takes into account the polychromatic source, the detector response function and the energy dependent attenuation. In the second step, component images are reconstructed from the corresponding estimated component projections using filtered backprojection. In a preliminary step the coherent scatter differential cross sections for hydroxyapatite and weddellite minerals were determined experimentally. The classification of type I or II calcifications is done using the relative contrasts of their components as the criterion. Simulation tests were carried out for different doses and energy resolutions for multiple realizations. The results were analyzed using relative/receiver operating characteristic methodology and show good discrimination ability at medium and higher doses. The noninvasive CSCT technique shows potential to further improve the breast diagnostic accuracy and reduce the number of breast biopsies.