# MinHash-Based Fuzzy Keyword Search of Encrypted Data across Multiple Cloud Servers
## 4 Security and Performance Analysis
### Performance Evaluation  
Performance evaluation of search results in information retrieval involves several evaluation criteria including precision and recall [24] which are defined below.  
\[\text{Precision}=\frac{\text{The number of related files retrieved by the system}}{\text{Total number of files returned by the system}} \tag{8}\]  
\[\text{Recall}=\frac{\text{The number of related files retrieved by the system}}{\text{Total number of relevant documents}} \tag{9}\]  
Figure 9 shows the average accuracy of multiple search results. As discussed before, different hash functions generate hash values with different numbers of bits, thus affecting the accuracy of the search results. The more the number of bits that are correct, the higher the rate of correction. From Figure 9, it can be seen that when the number of returned documents is less than 60, Hmac-SHA1 should be used and the rate of correction of the results is close to 100%. As the number of returned documents increases further, some of the lower-ranked documents will be returned some of which may be irrelevant documents, causing the accuracy of search results to follow a downward trend. Another solution is to use Hmac-MD5 as the hash function. However, since the number of bits in Hmac-MD5 (128 bits) is less than that in Hmac-SHA1 (160 bits), Hmac-MD5 makes the generated fingerprints incapable of better reflecting keyword characteristics. Therefore, the accuracy of the search results when using Hmac-MD5 is lower than that using Hmac-SHA1. In both cases, however, as the number of irrelevant documents returned increases, the accuracy rate will follow a downward trend. This experiment demonstrates that the number of bits generated by the hash function used in the proposed scheme will have an impact on the correction rate of the search results.  
Figure 8: Retrieval efficiency of single server/multiple servers under different segmentation storage mode. (**a**) 10 servers; (**b**) 50 servers; (**c**) 100 servers.  
Figure 10 shows the average rate of recall for multiple search results from which we can see that in the proposed scheme that uses Hmac-SHA1 as the hash function, the recall rate rises as the number of returned documents increases. Because it is the ratio of related documents that are returned to all relevant documents, the recall rate is lower when the number of returned documents is small. Since the ranking algorithm in the proposed scheme can optimize the sorted results, when the number of returned documents reaches 90, the recall rate approaches 100%. The use of Hmac-MD5 results in a lower recall rate as expected for a similar reason. That is, since the number of bits (128 bits) that it generates as the message digest is less than that generated by Hmac-SH1 (160 bits), the resulting fingerprints generated cannot better distinguish between the characteristics of keywords. As the number of returned documents increases, the recall rate will gradually go up after more related documents are returned. The experiment proves that the number of bits generated by the hash function used to generate message digests definitely has an impact on the recall rate of search results.