Study On Public Key Encryption With Multi-Keywords Search

With the growing of the information and the development of the cloud computation, more and more people will store their important data into a server owning huge storage spaces. For protecting some sensitive data, it is very useful for encrypting these data be-fore uploading them. This will bring a problem of how to make keyword search over en-crypted data efficiently without leaking the information of the data. This results that public encryption scheme which supports keywords search becomes a hot research topic. The ex-isting works mainly concentrate upon two aspects. The first aspect is constructing a scheme which supports more complex search, such as disjunctive keyword search, boolean keyword search, range search and so on. The second one is improving the existing schemes such that these schemes are more secure and more effective. Nevertheless the existing works are still needed to be improved on the function, efficiency and security. Therefore, in this paper, our aim is to construct a effective public key encryption scheme which supports more complex search, and the research results are as follows:(1) According to the relation between the roots and coefficient of an equation of degree n with one unknown quantity, a method of converting the keyword set of index and the query keyword set into vector sets is proposed. The vectors generated by this approach involves the information of keywords. Based on the vector sets and the bilinear pairing function, a public key encryption with disjunctive keyword search (PEDK) scheme is given. Compared with the existing PEDK schemes, the proposed scheme is more efficient in both time and space complexity. Moreover, based on the concept of indistinguishability against chosen keyword attack(IND-CKA), we propose a new security definition called O-security, and give a proof of the security of the proposed scheme under O-security.(2) The number of the keyword is limited in many applications, based on this back-ground, we design a method which can change the keyword set of index and the query keyword set into a "0-1" string whose length is N, where N is the number of keywords which can be used. By applying this approach and an IPE scheme, we give a scheme called public key encryption with conjunctive and disjunctive keyword search (PECDK), and prove that this scheme is secure under IND-CKA. This is the first scheme which supports not only conjunctive but also disjunctive keyword search over the encrypted data.(3) Based on the property that the range can be compressed, we give a method which can convert a range into a group of "0-1-*" strings. By making use of this method and an IPE scheme, we propose a new MPKRQ scheme. Compared with the pre-vious scheme, our scheme is not only adaptively secure, but also needs less test time and smaller trapdoor size. Moreover, since the proposed scheme is based on the IPE scheme, the given scheme will be improved when a high efficiency IPE scheme appears. This reflect that the proposed scheme has good extensibility.(4) In the general searchable public encryption scheme, the relationship between the data sender and data receiver is more-to-one. For the special application scenarios in which the relationship between the data sender and data receiver is more-to-more, by using dual encryption system, dual pairing vector system, and a tool which can convert composite order paring-based encryption scheme into a prime order one, we present a fully secure CP-ABE scheme in prime order group. Compared with the previous schemes, the proposed scheme still has some advantages on the time and space complexity.