Cloud computing is a technology that provides users with a large storage space and an enormous computing power. However, the outsourced data are often sensitive and confidential, and hence must be encrypted before being outsourced. Consequently, classical search approaches have become obsolete and new approaches that are compatible with encrypted data have become a necessity. For privacy reasons, most of these approaches are based on the vector model which is a time consuming process since the entire index must be loaded and exploited during the search process given that the query vector must be compared with each document vector. To solve this problem, we propose a new method for constructing a secure inverted index using two key techniques, homomorphic encryption and the dummy documents technique. However, 1) homomorphic encryption generates very large ciphertexts which are thousands of times larger than their corresponding plaintexts, and 2) the dummy documents technique that enhances the index security produces lots of false positives in the search results. The proposed approach exploits the advantages of these two techniques by proposing two methods called the compressed table of encrypted scores and the double score formula. Moreover, we exploit a second secure inverted index in order to manage the users' access rights to the data. Finally, in order to validate our approach, we performed an experimental study using a data collection of one million documents. The experiments show that our approach is many times faster than any other approach based on the vector model.