Copy Detection Patterns (CDP) have received significant attention from academia and industry as a practical mean of detecting counterfeits. Their security level against sophisticated attacks has been studied theoretically and practically in different research papers, but for reasons that will be explained below, the results are not fully conclusive. In addition, the publicly available CDP datasets are not practically usable to evaluate the performance of authentication algorithms. In short, the apparently simple question: "are copy detection patterns secure against copy?", remains unanswered as of today. The primary contribution of this paper is to present a publicly available dataset of CDPs including multiple types of copies and attacks, allowing to systematically compare the performance level of CDPs against different attacks proposed in the prior art. The specific case in which a CDP is the same for an entire batch of prints, which is of practical importance as it covers applications with widely used industrial printers such as offset, flexo and rotogravure, is also studied. A second contribution is to highlight the role played by the CDP detector and its different processing steps. Indeed, depending on the specific processing involved, the detection performance can widely outperform the CDP bit error rate which has been used as a reference metrics in the prior art.