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Top1. Introduction
Cloud computing, one of the most important computing paradigms emerged in recent years, has become a good means for users to manage data efficiently. By outsourcing the data files into the cloud, the large enterprises as well as individual users can dynamically increase their storage space when required without buying any storage devices, and this also can reduce the costs for purchasing hardware equipment, managing enterprise data and maintaining the system. However, a major issue for cloud computing is the privacy of outsourced data, when data owner outsources the data to the cloud, (s)he may only allow the authorized user to visit the data, though cloud can provide some basic security mechanisms such as firewalls, it is thought untrusted, so privacy-preserving of data owner in the cloud environment is a challenging task, especially on data privacy, security and reliability issues (Song, Wagner, & Perrig, 2000; Ziegeldorf, Morchon, & Wehrle, 2014; Henze et al., 2013).
At present, encryption of sensitive data is the most extensively used methods to fulfill data security in the cloud. That is, data owners place the encrypted data in the cloud, and only the authorized users can decrypt the data and visit them. Up to now, people have proposed many schemes to guarantee the security of data in the cloud using asymmetric or symmetric algorithm (Zhu et al., 2016; Zou et al., 2016; Shaozhang, Shanshan, & Huang, 2015; Li & Ma, 2014; Hadavi & Jalili, 2010). Among them, Hui Zhu et al. (2016) proposed an efficient privacy-preserving location-based services query scheme in outsourced cloud by using symmetric encryption algorithm; in the scheme, the location provider’s data is encrypted and issued to the cloud, and the registered user can get accurate location query results from the cloud server. Qin Zou et al. gave a content-based image retrieval of cloud using comparable encryption algorithm (2016). In asymmetric encryption, Niu Shaozhang et al. presented a security access control for the data in the cloud efficiently by using asymmetric encryption system (2015); Keying Li and Hua Ma proposed an improved multi-authority attribute-based encryption for outsourced data by means of asymmetric and symmetric encryption (2014).
However, complexity of asymmetric or symmetric encryption/decryption operations is extremely high, so they are not efficient facing with the explosive growth in the amount of outsourced data in the number of access. Thus, as an emerging approach for the encryption of outsourced data, secret sharing has attracted much attention for its low computational complexity in recent years (Hadavi & Jalili, 2010; Agrawal et al., 2011; Dautrich & Ravishankar, 2012; Liu & Chang, 2016; Liu, Wu, & Chang, 2014; Hadavi et al., 2015; Hong, Kim, & Chang, 2016). For example, in the schemes proposed by Agrawal (2011), a data file is divided into n sections shared among n cloud storage servers; who has the knowledge of any t or more pieces can recover the file. The developers of these schemes have claimed that they are secure, but Dautrich pointed out the scheme is vulnerable to the collusion attack in which any t colluding servers can recover all files outsourced in the cloud (2012), Recently, Liu et al. proposed a secure secret sharing mechanism based on Shamir’s secret sharing method, the scheme can allow an authorized data user to recover all data files in a specified subset (2014). Mohammad et al. studied the security and search-ability in secret sharing-based data outsourcing, and proposed multiple partitioning methods that enable clients to efficiently search among shared secrets (2015).