Nowadays, data is becoming more and more confidential and sensitive, hence the growing need for encryption. But once data is encrypted, so are the keywords needed to search for it. So people are faced with the challenging task of searching encrypted data with encrypted keywords, often with several encrypted keywords at the same time.

Methods exist today to search encrypted data with encrypted keywords, but these methods can only verify the integrity of single keyword search results; thus, when using multiple keywords, searches must be conducted with each single keyword, validated, and only when every single search passes validation can the whole search be thought of as validated.

This paper presents an encryption scheme that can encrypt data and keywords, search these data with multiple keywords all at once, and directly verify the integrity of the whole search. It does so by verifying the integrity of the results for each single keyword, as the other methods do, but then computing the final intersection among all results before giving the final answer. Moreover, doing it server-side also lowers data communication overhead.

The paper introduces the elements the method is based upon and gives their formal definitions. The authors then describe the security model of the whole method, where they demonstrate how it cannot leak (unintentionally reveal) any information and is thus very hard to break or forge. Next, the paper presents the method in detail. First, a dynamic searchable encryption space is built as a list of encrypted keywords with plain, unencrypted pointers; this way the server is only required to traverse the pointers, and only the results of this traversal need to be verified. At this point, the paper shows the explicit construction of this list of pointers as well as the formal mathematical proof of its security. The method is finally applied to a few real-world cases and these experimental results are included.