# Lightweight, Secure, Similar-Document Retrieval over Encrypted Data
## 4 Scheme Overview
### Private Similarity Computation and Search Queries Stage
Meanwhile, Figure 9 illustrates that increasing the posting vector requires more ranking time since longer vectors require more time to be added. From the foregoing, the time taken to rank files no longer affects the file retrieval process, as it is of intangible value (0.00019 ms) for the overall performance of the scheme and the client response time. Figure 8: Ranking time: increasing the fingerprint items. Figure 7: Effect of collection size on indexing time. ### Fingerprint Security

The fingerprint terms are protected by the secret key \(K_{1}=(b,M)\), where \(b\) is the base number used in Equations (1) and (3). Without knowing \(b\), no party can generate valid fingerprint terms. In this experiment, the resemblance was computed as seen in Equation (4) between a fingerprint set generated by the valid secret key, \(b=50\), and \(1000\) fingerprints generated by \(1000\) different \(b\) values. One of these values is equal to the original. Figure 10 shows that only the valid \(b\) value has the maximum resemblance, although the values aligned to the valid key are \(90\%\), \(80\%\) and \(70\%\). This experiment verifies that fingerprint security is validated for the application of privacy-preserving document retrieval privacy. ### Comparative Performance Analysis

The researchers understand that two protocols in the literature, namely EsPRESSo [14] and GBF [15], are most closely related to the work proposed in this paper. Therefore, to prove the efficiency of the proposed work, the results were compared against EsPRESSo and GBF, while a fair comparison was ensured by adopting \(80\)-bit security parameters across all works. First, the researchers analysed the complexity of the three protocols in terms of the computational and communication costs, the results of which can be seen in Table 3; the computational and communication costs of EsPRESSo and this work are \(O(m)\) while the GBF costs are \(O(m^{2})\). Table 3 shows that the methods proposed in this study require the lowest computational costs compared with the EsPRESSo and GBF methods. Figure 10: Effect of \(b\) on security. \[R=|\text{Inter}|/|\text{Union}|, \tag{4}\]0 Ranking time: increasing the document collection. Furthermore, this study demonstrates a significant performance improvement over the alternative methods, thanks to the generation of the inverted index [20; 21] and the use of a hash table for storage, which provides \(O(1)\) access time. Moreover, this paper's approach uses a Winnowing algorithm to extract only the effective property and exclude others with less effect when retrieving similar documents, which reduces the computational complexity space. The communication costs of this study are higher than the EsPRESSo method since the latter uses Min-Hash, which generates lower communication costs, but it has disadvantages of reducing the accuracy of the similar documents retrieved [27], as it will be explained later in detail in \[R=|\text{Inter}|/|\text{Union}|, \tag{4}\]1 Min-Hash measures approximate similarity, while the approach adopted by this study is designed to measure exact and approximate similarity for DSD. GBF has the highest communication cost because it considers the full set to represent each document. Figure 12 shows the privacy-preserving DSD performance. A single document was compared with the document collection consisting of \(m\) documents. The results of the comparison show that all methods have \(m\) linear complexity. Of the three methods trialled, this study returned the best performance; the method proposed in this study improves the cost speed of document retrieval with \(O(1)\) access time based on the inverted index [20; 21], which includes a set of fingerprint items and their corresponding posting lists. While EsPRESSo performs slightly less efficiently in this regard as long as it uses a Min-Hash function, it is inefficient in retrieving scalable documents, as noted later.