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Euclidian Distance Improvement
Query Standard Deviation Improvement
100%
90% 35%
80%
30%
70%
Improvement 60% Improvement 20%
25%
50%
40%
15%
30%
20% 10%
5%
10%
0 0
0 3000 6000 9000 12000 15000 18000 21000 24000 27000 30000 0 3000 6000 9000 12000 15000 18000 21000 24000 27000 30000
Number of Queries Number of Queries
Figure 8. Euclidean distance improvement over 30000 queries. Figure 9. Standard deviation improvement of the queries over
30000 queries.
Figure 9 demonstrates that LRSE reduces the standard deviation 25-30%. In other words, identifying the key-
words are 30% more difficult using LRSE. Moreover the reduction amount stays in the same range (25%-30%)
as the number of queries increases which shows the stability of LRSE.

7 RELATED WORK
[1]
The symmetric searchable encryption (SSE) introduced by Song et al. , where each word is encrypted under
a particular two-layered encryption. Afterward, Goh [15] improved the search request time using Bloom filters.
[3]
[4]
Chang et al. and Curtmola et al. then enhanced the security definitions, constructions and proposes some
improvements. However, traditional symmetric encryption schemes only supports exact keyword search and
cannot endure any kind of format inconsistency or minor imperfections. To address this issue, Li et al. [27]
propose a method in which returned documents are designated according to the predefined keywords or the
closest possible matching documents, based on keyword similarity semantics. Kuzu et al. [28] also tackle this
challenge and propose a method with more efficiency and less overhead.

All these approaches support only Boolean search. Thus, finding the most relevant documents for the data
user’s multi-keyword search request is a crucial challenge. To resolve this challenge, Cao et al. [9] introduce
a method that allows data users to apply a multi-keyword search request on the encrypted files with ranking
capability. Cao et al. [9] chose the similarity measure of “coordinate matching”, that is, as many matches as
possible. And to capture the relevance of outsourced documents to the query keywords, the “inner product
similarity” is employed. Later, Fu et al. [10] propose a model that makes the query results more personalized for
each user based on their search history. Considering the user search history, they built a user interest model
for individual users with the help of the semantic ontology WordNet. Moreover, Yu et al. [11] propose a user-
ranked multi-keyword method to prevent data privacy leaks in cloud-ranked methods. They employed the
vector space model and homomorphic encryption. The vector space model helps to provide sufficient search
accuracy, whereas the homomorphic encryption enables users to get involved in the ranking procedure, while
the remaining computing work is done on the server side. In a recent work, Guo et al. [18] propose a multi-
keyword SSE approach which support multi data owners, and to tackle the key management challenges they
exploit a trusted proxy.

However, these schemes function based on the symmetric key encryption, where the same key is employed to
encrypt and decrypt the data. Another approach is to use public key encryption. Boneh et al. [2] defined the
concept of the “public key encryption with keyword search”, and later, several methods [6,29–32] were introduced
to improve the efficiency and system cost of the public-key searchable encryption schemes. Basically, these
methods exercise one key for encryption and another key for decryption. Thus, data users who own the
private key are able to search the outsourced data encrypted by the public key.