J. Sun, H. Xiong and H. Zhang et al. / Information Sciences 507 (2020) 1–15 3
a business trip, due to collaboration requirements, wants to use the phone to access the company server to download the
relevant data. Owing to the variety of content and vast data that is encrypted by IB(B)E and stored in the company’s server.
It is very arduous for Bob to retrieve the data which is in ciphertext mode stored on company’s server. So here we adopt
the IB(B)E-ET to make retrieval effortless. Bob can use his identity as his public key to encrypt his tag UI and delegate the
capability of equality test to the company server to find the data of UI. If this ciphertext is only encrypted with Bob’s public
key, Bob can download and decrypt the ciphertext directly. Suppose that this ciphertext is encrypted with the identities of
the whole UI staffs, Bob needs to blind his private key and send it to the company’s server. Then, the company’s server
converts the broadcast ciphertext into a simpler ciphertext that can be decrypted easily with Bob’s retrieval key. After that,
Bob can effortlessly get the data he wants. Furthermore, our IBBET supports flexible Collaboration Office Automation. If Bob
is a front-end department staff, due to the interaction of project, he requires some data of UI. Because Bob’s identity is not in
the UI department, he cannot download and decrypt these data directly. But he can contact one of the UI department staffs,
say Alice. Alice can use her private key with Bob’s public key to generate a conversion key and send it to the company’s
server. Then the company’s server converts the broadcast ciphertext into the ciphertext which can be only decrypted by
Bob. In this way, Bob can obtain these relevant data and decrypt with his private key.
Paper Outline: Related works in the next section are reviewed, then some preliminaries on bilinear maps, formal defini-
tion system model and security model are presented in Section 3 . Concrete construction for optimized IBPRE-ET is provided
in Section 4 . The proposed collaborative office automation system is described in Section 5 . Section 6 gives the security
analysis of the IBPRE-ET and the designed collaborative office automation system. Afterward, the performance analysis is
discussed in Section 7 . Finally, Section 8 concludes our work.
2. Related works
This section reviews the related works associated with secure access delegation and public key encryption with search
functionality.
2.1. Secure access delegation
As one special kind of public key encryption, proxy re-encryption (shorten as PRE) [5] allows an untrusted proxy to
convert an encryption from one ciphertext into another. During the conversion, the proxy couldn’t read the plaintext hidden
in the ciphertext. By considering the conversion capability associated with PRE, this primitive has been naturally deployed
in the cloud to achieve secure access delegation. So far, PRE has been investigated in terms of improving the efficiency
[3] , enhancing the security [8,18,24,28] , and enriching the functionality [15,18,19] . A survey of PRE could be found in [26] .
Recently, PRE for heterogeneous systems has been suggested by Zhou et. al [38] , where a proxy is able to transform a
ciphertext in the IBBE system to one encryption in the standard IBE system. Despite the work in [38] is the most recent
work in the literature of PKE for heterogeneous systems, it fails to provide search functionality over the encrypted data. That
is to say, the only way for a user to obtain the desired encrypted data is to download all of the ciphertexts and perform
the decryption operation. This paper is mostly related to the research works associated with public key encryption with
keyword search/equality test and secure access delegation.
2.2. Secure search functionality
There exist fruitful research results on searchable encryption, which can be coarsely categorized into symmetry search-
able encryption (SSE) and asymmetric searchable encryption. Song et al. [29] first introduced the conception of SSE scheme.
The modern security definition were developed by Curtmola et al. [9] . They designed the first reversed-index-based SSE
construction that achieves optimal search complexity. Subsequently, the SSE schemes with distinct properties are further
enriched. For example, Kamara et al. [16] designed the first sublinear dynamic SSE scheme and Wu et al. [32] proposed
a forward secure SSE scheme to provide conjunctive queries over encrypted data. As a frequently promising information
retrieval technique, PKE with keyword search (PKE-KS), firstly invented by Boneh et al. [6] , allows a semi-trusted cloud
server to perform search functionality over the encrypted keyword. Specifically, the cloud server with the input of a trap-
door calculated by the receiver is capable of learning nothing other than the fact that whether a given ciphertext contains
the keyword associated with the trapdoor. In light of the search functionality over encrypted data, PKE-KS has been inves-
tigated in a series of distinct environments such as identity-based [1,10] and attribute-based cryptosystems [20,30,34,39] .
In PKE-KS, the trapdoor and the corresponding keyword ciphertext should be generated under the same public key. That
is to say, PKE-KS is not suitable for achieving secure data sharing between multiple users. Fortunately, public key encryp-
tion with equality test (PKE-ET) [36] provides an alternative solution to flexible search functionality over encrypted data.
In PKE-ET, a cloud server is enabled to perform an equivalence test between two messages encrypted distinct public keys.
Different from PKE-KS, PKE-ET can support more flexible search functionality over encrypted data. Thus, this primitive has
been widely investigated along with different research directions such as authorized PKE-ET [22] , identity-based PKE-ET
[23] and attribute-based PKE-ET [41] . Despite PKE-ET seems to be a good solution to provide flexible search functionality
over encrypted data, the IBBE with equality test has not been treated in the literature so far.