Software birthmarks are unique and native characteristics of a binary executable program that can be used for detecting software piracy. API (Application Programming Interface) calls in an MS Windows binary executable can be used as software birthmarks when there are no source codes available to detect software similarity. However, it is inefficient to extract birthmarks from all API calls during the execution of a binary executable. In this paper, we propose an efficient scheme for comparing software similarity. To reduce the number of comparisons used in the proposed scheme, we extract only the core API calls that are explicitly used in different programs. The birthmarks used for comparing the similarity between two programs can be obtained by extracting these core API calls. Our experimental results show that this proposed birthmark scheme using core API calls is efficient for evaluating software similarity.