By Topic

IEEE Quick Preview
  • Abstract

SECTION I

INTRODUCTION

SMART grid has emerged as a new concept and a promising solution for intelligent electricity generation, transmission, distribution and control [1]. The use of robust two-way communications and distributed computing technology improves the efficiency and reliability of power delivery and usage [2]. Currently, many utility companies begin to use smart grid information systems to collect real-time metering data at their control centers, via a reliable communication network deployed in parallel to the power transmission and distribution grid [3], as shown in Fig. 1. In the smart grid information system, smart meters are deployed at residential users' premises as two-way communication devices [4], [5], which periodically record the power consumption and report their metering data to a local area gateway, e.g., a wireless access point (AP). The gateway then collects and forwards data to a control center. Additionally, metering data in smart grid information systems should be periodically audited to ensure that the billing and pricing statements are presented fairly [6]. Specifically, requesters, such as market analysts, are endowed with the task of querying smart grid information systems for auditing, analysis, accounting or tax-related activities [7]. Thus, to prevent the private and sensitive information in the metering data from disclosure, data confidentiality and privacy should be achieved in financial audit for smart grid.

Figure 1
Fig. 1. The conceptional smart grid architecture.

However, the metering data in smart grid are surging from 10,780 terabytes (TB) in 2010 to over 75,200 TB in 2015 [8], which is far beyond the control center's data management capability. Outsourcing data to cloud servers is a promising approach to relieve the control center from the burden of such a large amount of data storage and maintenance. In this approach, users can store their data on cloud servers and execute computation and queries using the servers' computational capabilities [9]. Nevertheless, cloud servers might be untrusted, and intentionally share sensitive data with the third parties for commercial purposes. Therefore, data confidentiality is important in financial audit for smart grid.

In addition, privacy concerns raise in financial auditing [10]. For instance, utility usage patterns within short intervals may reveal the users' regular daily activities [11]. In particular, data from a single house would reveal the activities of the residents, e.g., when the individual resident is at home, when he/she is watching TV [3]. If an attacker can query these data, data privacy might be violated. Therefore, users' data confidentiality and privacy should be protected and only authorized requesters can query the metering data.

From the requester's perspective, the requester, who manages the data query for financial auditing, needs to frequently query the metering data by using date ranges and/or geographic regions etc. If the query is sensitive, the requesters may prefer to keep their queries from being exposed to servers. As a result, how to operate such range queries with guaranteed query privacy is also significant for smart grid.

In this paper, we propose a Privacy-preserving Range Query (PaRQ) scheme over encrypted metering data for smart grid. The PaRQ addresses the data confidentiality and privacy problem by introducing an HVE technique. The main contributions of this paper are twofold.

  • Firstly, we construct a range query predicate based on the HVE. Specifically, the session keys and the searchable attributes of the encrypted data are hidden in the HVE based range query predicate. When a requester query the cloud server, the session keys, whose encryption vectors are satisfied with the range query vectors, are released to the requester, for decrypting the encrypted metering data.
  • Secondly, we analyze the security strengths and evaluate the performance of the PaRQ. Security analysis demonstrates that the PaRQ can achieve user's data confidentiality and privacy, as well as requester's query privacy. Performance evaluation results show that our PaRQ can reduce the communication and computation overhead, and shorten the response time.

The remainder of this paper is organized as follows. In Section II, we investigate the related works. In Section III, we introduce our system model, security requirements and our design goals. Then, in Section IV, we review some preliminaries. In Section V, we present our PaRQ scheme, followed by its security analysis and performance evaluation in Section VI and Section VII, respectively. Finally, we conclude this paper in Section VIII.

SECTION II

RELATED WORKS

A. Security and Privacy in Smart Grid

Security and privacy are critical to the development of wireless networks [10], especially for the real-time data audit strategy in smart grid. The smart grid interpretability panel-cyber security working group [6]presents some guidelines for smart grid cyber security, including security strategy, architecture, and high-level requirements. Li [11] reviews the cyber security and privacy issues in smart grid and discusses some security and privacy solutions for smart grid. Lu et al. [3] use a super-increasing sequence to structure multidimensional data and encrypt the structured data by the holomorphic paillier cryptosystem technique. Li et al. [12] propose an authentication scheme based on merkle tree for smart grid. Acs and Castelluccia [13] exploit the privacy-preserving aggregation technique of time-series data in smart meters. They employ a differential privacy model in which users add noise to their electricity metering and the aggregator can successfully obtain the sum of the metering with a very large probability. In summary, few works focus on the query, especially range query over encrypted data in smart grid, which is really significant for user's metering data audit.

B. Range Query

Recently, the problem of querying encrypted data has been deeply investigated in both cryptography and database communities. One of the widely studied approaches is public key encryption with keyword search (PEKS) [14]. PEKS can protect users' data privacy and certain query privacy. However, most of PEKS schemes, such as the Searchable Encryption Scheme for Auction (SESA) [15], only can be applied for equality checks. Range query over the encrypted data with numeric attributes is more difficult, and most of the existing literatures cannot achieve data and query privacy simultaneously.

Roughly speaking, there are four categories of solutions that have been developed for range queries: order-preserving encryption (OPE), bucketization (Bucket), HVE and special data structure traversal. OPE-based technique [16] is to ensure that the order of plaintext data is preserved in the ciphertext domain. This allows direct translation of range predicate from the original domain to the domain of the ciphertext. However, the coupling distribution of plaintext and ciphertext domains might be exploited by attackers to guess the scope of the corresponding plaintext for a ciphertext [17]. Bucket-based technique [18] uses distributional properties of the datasets to partition and index data for efficient querying while trying to keep the information disclosure to a minimum. Queries are evaluated in an approximate manner where the returned set of records may contain some false positives.

In an HVE-based approach [19], two vectors over attributes are associated with a ciphertext and a token, respectively. Under the predicate translator, the ciphertext matches the token if and only if the two vectors are component-wise equal. Several HVE schemes [20], [21], [22] have been proposed in literatures. All of them use bilinear groups equipped with bilinear maps, and each constructs a proper method to hide attributes in an encrypted vector. However, it is expensive to compute exponentiation and pairing in a composite-order group. Jong [20] proposes a new HVE scheme that not only works in prime-order groups, but also requires a shorter token size and fewer pairing computations. However, Jong's scheme cannot be directly applied in the smart grid applications where data are high in dimension, variety or both.

Some specialized data structured for range query evaluation are trying to preserve notions of semantic security of the encrypted data, such as Formula${\rm B}+{\rm tree}$ etc. Recently, Shi et al. [23] propose a searchable encryption scheme that supports multidimensional range queries over encrypted data (MRQED). The MRQED utilizes an interval tree structure to form a hierarchical representation of intervals for each dimension and stores multiple ciphertexts corresponding to a single data value on the server, i.e., each one corresponds to a range. If it is applied to a single-dimensional data with values belonging to a domain of size Formula$N$. The ciphertext representation is Formula$O(logN)$ times the actual data. If the MRQED is applied to a piece of data with Formula$l$ dimensions, each query requires Formula$l$ times complexity to execute.

SECTION III

SYSTEM MODEL, SECURITY REQUIREMENTS AND DESIGN GOAL

In this section, we formalize the system model, and identify the security requirements and our design goals.

A. System Model

Our focus is on how to outsource residential users' metering data to a cloud server in encrypted form and how to operate a range query over the encrypted metering data with the help of the control center (CC). Specifically, we consider a typical residential area, as shown in Fig. 2, which is composed of a CC, two cloud servers: the Formula$CS_{1}$ and Formula$CS_{2}$, a requester Formula$S$ and some residential users Formula$\BBU=\{U_{1},U_{2},\ldots,U_{v}\}$.

Figure 2
Fig. 2. System model of PaRQ.

A residential user is the data owner, who encrypts his data by using a secret session key before outsourcing the data to the CSs. There are two cloud servers: Cloud Server 1 Formula$(CS_{1})$ stores data ciphertexts; Cloud Server 2 Formula$(CS_{2})$ stores session key's ciphertexts and indexes. Both servers are semi-trusted, honest but curious. We assume that either the Formula$CS_{1}$ or Formula$CS_{2}$ might be compromised and controlled by an adversary seeking to link users' ciphertexts with their keys, but the adversary cannot control both CSs. The control center is a trusted proxy (it operates on behalf of the utility companies), which can help users to deposit their data to cloud servers and generate query tokens for requesters to retrieve data from the servers. The requester can query the encrypted data on the cloud servers by depositing his entitling tokens to the Formula$CS_{2}$.

The CC consists of two main components: a ciphertext forwarder, and a query translator which always operates within the secure environment. The forwarder on the CC needs to add a unique index to the data ciphertexts and the session key's ciphertexts. To preserve the query privacy, the requester's query needs to be translated into two tokens, so that the Formula$CS_{2}$ can evaluate this query without disclosing its real value.

B. Security Requirements

We identify the security requirements for our PaRQ. In our security model, the CC is trustable, and residential users Formula$\BBU=\{U_{1},U_{2},\ldots,U_{v}\}$ are honest as well. However, there exists an adversary Formula${\cal A}$ in the system intending to eavesdrop and invade the database on cloud servers to steal the individual users' reports. In addition, Formula${\cal A}$ can also launch some active attacks to threaten the data privacy and query privacy. Therefore, in order to prevent Formula${\cal A}$ from learning the users' data and to detect its malicious actions, the following security requirements should be satisfied in range query applications for smart grid.

  • Data Confidentiality: The residential user can utilize symmetric or asymmetric cryptography to encrypt the data before outsourcing, and successfully prevent the unauthorized entities, including eavesdroppers and cloud servers, from prying into the outsourced data.
  • Data privacy: Individual residential users' data should not be accessed by unauthorized requesters. It means that only requesters with authorized query tokens can access the Formula$CS_{2}$, and they can obtain the correct session keys when their query vectors in the tokens are satisfied with the encryption vectors. Thus, only the authorized requester can decrypt the encrypted metering data.
  • Query privacy: As requesters usually prefer to keep their queries from being exposed to others, thus, the biggest concern is to hide their queries into tokens to protect the query privacy. Otherwise, if the query includes some sensitive information, such as “Formula$5\leq priority\leq 7$”, then the Formula$CS_{2}$ could know the requester is querying some important users' metering data. Then, the requester or the query results could be traced or analyzed by the curious server Formula$CS_{2}$.

C. Designing Goal

To enable effective range query over encrypted metering data under the aforementioned model, our design goal is to develop a privacy-preserving range query scheme over encrypted data for smart grid, and to achieve the security of the data and efficient range query as follows.

  • The security requirements should be guaranteed in the proposed scheme. As stated above, if the smart grid does not consider the security, the residential users' privacy could be disclosed, and the real-time power metering reports could be stealed. Therefore, the proposed scheme should achieve the data confidentiality and privacy, as well as the query privacy.
  • The performance efficiency should be achieved in the proposed scheme. As range query are operated over encrypted multidimensional data, compared with existing schemes, the proposed PaRQ scheme should improve the communication, computation and response time complexities.
SECTION IV

PRELIMINARIES

In this section, we briefly describe the basic definitions and properties of bilinear pairings and HVE, which serves as the basis of the PaRQ.

A. Bilinear Pairing

Bilinear pairing is an important cryptographic primitive [24]. Let Formula$\BBG_{1}$ and Formula$\BBG_{2}$ be two cyclic multiplication groups of prime order Formula$q$. Let Formula$a$ and Formula$b$ be elements of Formula$Z_{q}^{\ast}$. We assume that the discrete logarithm problem (DLP) in both Formula$\BBG_{1}$ and Formula$\BBG_{2}$ are hard. Formula$g$ is a generator of Formula$\BBG_{1}$. A bilinear pairing is a map Formula$e:\BBG_{1}\times\BBG_{1}\rightarrow\BBG_{2}$ with the following properties.

  1. Bilinear: Formula$e(g^{a},h^{b})=e(g,h)^{ab}$ for any Formula$(g,h)\in\BBG_{1}^{2}$.
  2. Non-degenerate: Formula$e(g,h)\ne 1_{\BBG_{2}}$ whenever Formula$g$, Formula$h\ne 1_{\BBG_{1}}$.
  3. Computable: There is an efficient algorithm to compute Formula$e(g,h)\in\BBG_{2}$ for all Formula$(g,h)\in\BBG_{1}^{2}$.

Definition 1

A bilinear parameter generator Formula${\cal G}en$ is a probabilistic algorithm that takes a security parameter Formula$\kappa$ as input, and outputs a 5-tuple Formula$(q, g,\BBG_{1},\BBG_{2}, e)$.

B. HEV Based Query Predicate

The concept of HVE is proposed by Boneh and Waters [19]. HVE is a type of predicate encryption where two vectors over attributes are associated with a ciphertext and a token, respectively. At a high level, the ciphertext matches the token if and only if the two vectors are component-wise equal. There are two character sets Formula$\sum$ and Formula$\sum_{\ast}=\sum\cup\{\ast\}$ in the setting of HVE. Here Formula$\sum$ is an arbitrary set of attributes. We assume Formula$\sum=\BBZ_{q}$; ∗ is a special symbol denoting a wildcard component, which means that the component related to ∗ is not involved with any attribute. HVE mainly consists of four phases: key generation, data encryption, token generation and data query.

1) Equality Query

  • In key generation phase, the TA distributes the public/private key pair Formula$(PK,SK)$ to a receiver.
  • In data encryption phase, a user chooses a vector Formula${\bf x}=(x_{1},\ldots,x_{l})\in\sum^{l}$ to characterize its data and encrypts its data Formula$m$ into a ciphertext Formula${\ssr CT}$ using the receiver's public key.
  • In token generation phase, the receiver chooses a vector Formula${\bf w}\!=\!(w_{1},\ldots,w_{l})\!\in\!(\sum_{\ast})^{l}$ to represent his query requirements and generate a query token Formula$T_{w}$. The receiver sends Formula$T_{w}$ to the server.
  • In data query phase, if Formula${\bf x}$ equals to Formula${\bf w}$, the token can decrypt a ciphertext by using the receiver's private keys. The matching condition is defined as following: let Formula$s(w)$ be the set of indexes Formula$i$ such that Formula$w_{i}$ is not a wildcard in the vector Formula${\bf w}=(w_{1},\ldots,w_{l})$. For the vector Formula${\bf x}$ and Formula${\bf w}$, let Formula$P_{\bf w}({\bf x})$ be the following equality predicate: Formula TeX Source $$P_{\bf w}({\bf x})=\cases{1, &if for all $i\in s(w),w_{i}=x_{i},$\cr 0,&otherwise.\cr}\eqno{\hbox{(1)}}$$ Then, the server can disclose the data Formula$m$ if the equality predicate Formula$P_{\bf w}({\bf x})=1$.

2) Comparison Query

If we map the Formula$i$th component Formula$x_{i}\in{\bf x}$ to its domain Formula$\{1,\ldots,n\}$ as in [20], the value of Formula$x_{i}$ is one of the number Formula$j\in\{1,\ldots,n\}$. The key generation phase is same as in the above quality query.

Then, in the data encryption phase, the user builds an encryption vector Formula$\sigma ({\bf x})=(\sigma_{i,j})\in\{0,1\}^{nl}$ for Formula${\bf x}=(x_{1},\ldots, x_{l})\in\{1,\ldots,n\}^{l}$, as follows: Formula TeX Source $$\sigma_{i,j}=\cases{1, &if $x_{i}\geq j,$\cr 0, & otherwise,\cr}\eqno{\hbox{(2)}}$$ where, Formula$i\in\{1,\ldots,l\}$ and Formula$j\in\{1,\ldots,n\}$. For example, Formula$l=3$, Formula$n=5$ and let Formula${\bf x}=(1,3,2)$. Thus Formula${\bf x}=(x_{1},\ldots,x_{l})\in\{1,\ldots,n\}^{l}=\{1,2,3,4,5\}^{3}$ and the corresponding encryption vector Formula$\sigma ({\bf x})=(10000, 11100, 11000)$. Then, the data should be encrypted under the encryption vector Formula$\sigma ({\bf x})$.

Next, in the token generation phase, the user builds a query vector Formula$\sigma^{\ast}({\bf w})=(\sigma_{i,j}^{\ast})\in\{0,1,\ast\}^{nl}$ for Formula${\bf w}=(w_{1},\ldots, w_{l})\in\{1,\ldots,n\}^{l}$ as follows: Formula TeX Source $$\sigma_{i,j}^{\ast}=\cases{1, &if $w_{i}=j,$\cr\ast, &otherwise.\cr}\eqno{\hbox{(3)}}$$ Similarly, we assume Formula$l=3$, Formula$n=5$ and Formula${\bf w}=(w_{1},\ldots,w_{l})\in\{1,\ldots,n\}^{l}=\{1,2,3,4,5\}^{3}$. If the receiver's query condition is Formula$P=({x}_{1}\geq 1)\wedge ({x}_{2}\geq 3)\wedge ({x}_{3}\geq 1)$, i.e., Formula${\bf w}=(1,3,1)$. Thus the query vector Formula$\sigma^{\ast}({\bf w})=(1\ast\ast\ast\ast,\ast\ast 1\ast\ast,1\ast\ast\ast\ast)$. Note that, the number of the elements in Formula$\sigma^{\ast}({\bf w})$ is Formula$nl$.

In the data query phase, let Formula$s(\sigma^{\ast}(w))$ denotes the set of all indexes Formula$k$ which satisfies Formula$\sigma_{k}^{\ast}\ne\ast$, where Formula$k\in\{1,\ldots,nl\}$. Let Formula$P_{\sigma^{\ast}({\bf w})}(\sigma ({\bf x}))$ be the following comparison predicate: Formula TeX Source $$\eqalignno{& P_{\sigma^{\ast}({\bf w})}(\sigma ({\bf x}))\cr &\quad=\cases{1, & if for all $ i\in s(\sigma^{\ast}(w)),\sigma^{\ast}(w_{i})=\sigma (x_{i}),$\cr 0, & otherwise.}&{\hbox{(4)}}}$$ Finally, the server can disclose the data Formula$m$ if the comparison predicate Formula$P_{\sigma^{\ast}({\bf w})}(\sigma ({\bf x}))=1$.

SECTION V

THE PROPOSED PARQ SCHEME

In this section, we present the details of the PaRQ. There are three major phases in our scheme: construction of the range query predicate phase, encrypted data deposit phase and range query phase. Firstly, we introduce the construction of the range query predicate phase.

A. Construction of the Range Query Predicate

Inspired by the equality predicate and comparison predicate, we can extend them to support range query predicate. Specifically, we can achieve the opposite semantics of the above comparison query, i.e., Formula$x_{i}\leq j$, by constituting the vectors Formula$\sigma ({\bf x})$ in a reverse manner as (5). Formula TeX Source $$\sigma_{i,j}=\cases{1, &if $x_{i}\leq j,$\cr 0, & otherwise.\cr}\eqno{\hbox{(5)}}$$ Thus, the HVE scheme can support range queries, such as Formula$a\leq x_{i}\leq b$. Table Iillustrates notations used in this paper. The key generation phase is same as above in the quality query.

Table 1
TABLE I THE NOTATIONS USED IN THIS PAPER.

In the data encryption phase, the residential user should define two encryption vectors: Formula$\sigma_{\geq}({\bf x})$ and Formula$\sigma_{\leq}({\bf x})$ as (2) and (5) when Formula$x_{i}\geq j$ and Formula$x_{i}\leq j$, respectively. The receiver can obtain the correct data if and only if both conditions Formula$x_{i}\geq a$ and Formula$x_{i}\leq b$ hold. If the encrypted data in HVE is Formula$\Omega$, the residential user Formula$U_{i}\in\BBU$ should split Formula$\Omega$ into two parts by the following steps: 1) randomly chooses a polynomial Formula$f(x)=a^{\prime}x+\Omega$, where Formula$a'$ is a random coefficient. 2) Formula$U_{i}$ chooses two random integers and computes two data shares Formula$\Omega_{L}$ and Formula$\Omega_{R}$, i.e., Formula$\Omega$ is divided into two parts: Formula$\Omega_{{\ssr L}}$ and Formula$\Omega_{{\ssr R}}$. Formula$U_{i}$ encrypts Formula$\Omega_{{\ssr L}}$ and Formula$\Omega_{{\ssr R}}$ under vectors Formula$\sigma_{\geq}({\bf x})$ and Formula$\sigma_{\leq}({\bf x})$, respectively.

In the token generation phase, the requester's range query are defined with two vectors: Formula$\sigma_{\geq}^{\ast}({\bf w})$ and Formula$\sigma_{\leq}^{\ast}({\bf w})$ when Formula$w_{i}=a$ and Formula$w_{i}=b$, respectively. Let Formula$s(\sigma_{\geq}^{\ast}(w))$ be the set of all indexes Formula$k$ which satisfies Formula$\sigma_{\geq}^{\ast}(w_{k})\ne\ast$, and Formula$s(\sigma_{\leq}^{\ast}(w))$ be the sets of all indexes Formula$k^{\prime}$ which satisfy Formula$\sigma_{\leq}^{\ast}(w_{k^{\prime}})\ne\ast$. Here, Formula$k, k^{\prime}\in (1,\ldots,nl)$. Finally, in the data query phase, the server checks two comparison predicates Formula$P_{\sigma_{\geq}^{\ast}({\bf w})}(\sigma_{\geq}({\bf x}))$ and Formula$P_{\sigma_{\leq}^{\ast}({\bf w})}(\sigma_{\leq}({\bf x}))$, which can be generated as (4). The server can obtain Formula$\Omega_{{\ssr L}}$ if Formula$\sigma_{g}(x_{k})$ and Formula$\sigma_{\geq}^{\ast}(w_{k})$ are equal for all Formula$k\in s(\sigma_{\geq}^{\ast}(w))$, i.e., Formula$P_{\sigma_{\geq}^{\ast}({\bf w})}(\sigma_{\geq}({\bf x}))=1$. Similarly, the server can obtain Formula$\Omega_{{\ssr R}}$ if Formula$\sigma_{\leq}(x_{k^{\prime}})$ and Formula$\sigma_{\leq}^{\ast}(w_{k^{\prime}})$ are equal for all Formula$k^{\prime}\in s(\sigma_{\leq}^{\ast}(w))$, i.e., Formula$P_{\sigma_{\leq}^{\ast}({\bf w})}(\sigma_{\leq}({\bf x}))=1$. The range query predicate can be denoted as follows: Formula TeX Source $$\eqalignno{&P_{(\sigma_{\geq}^{\ast}({\bf w}),\sigma_{\leq}^{\ast}({\bf w}))}(\sigma_{\geq}({\bf x}),\sigma_{\leq}({\bf x}))\cr& =\cases{1, \quad {\rm if} P_{\sigma_{\geq}^{\ast}({\bf w})}(\sigma_{\geq}({\bf x}))=1, and, P_{\sigma_{\leq}^{\ast}({\bf w})}(\sigma_{\leq}({\bf x}))=1\cr 0, \quad {\rm otherwise}.}\cr&&{\hbox{(6)}}}$$ Finally, if Formula$P_{(\sigma_{\geq}^{\ast}({\bf w}),\sigma_{\leq}^{\ast}({\bf w}))}(\sigma_{\geq}({\bf x}),\sigma_{\leq}({\bf x}))=1$ the server can recover Formula$\Omega_{{\ssr L}}$ and Formula$\Omega_{{\ssr R}}$. Then, the data Formula$\Omega$ can be computed.

The main procedures of range query on encrypted data in smart grid are illustrated in Fig. 3. The CC is not only the data forwarder but also the query translator. In the encrypted data deposit phase, before outsourcing his data, a residential user Formula$U_{i}$ encrypts his data Formula$m$ into a ciphertext Formula${\ssr C}$ by randomly choosing a secret session key Formula$ks$. At the same time, Formula$U_{i}$ hides Formula$ks$ and Formula$m$'s searchable attributes into another ciphertext Formula${\ssr CT}$ by using the HVE range query predicate and the CC's pubic key Formula$PK$. Note that, Formula$\Omega=ks$ in our PaRQ. Then, Formula$U_{i}$ deposits both ciphertexts Formula${\ssr C}$ and Formula${\ssr CT}$ to the CC. The CC adds an index Formula$Ind$ to both Formula${\ssr C}$ and Formula${\ssr CT}$. Then the CC transmits Formula$\{Ind,{\ssr C}\}$ to the Formula$CS_{1}$ and Formula$\{Ind,{\ssr CT}\}$ to the Formula$CS_{2}$.

Figure 3
Fig. 3. Data query procedures (a) Encrypted Data Deposit Phase (ED) (b) Range Query Phase (RQ).

As shown in Fig. 3, when a requester S posts a range query, the query should be translated into query tokens by using the CC's private key. Then, the requester deposits its tokens to the Formula$CS_{2}$ to retrieve the session key Formula$ks$ and index Formula$Ind$. The session keys whose encryption vectors are satisfied with the range query vectors and their indexes can be released to the requester. The requester queries the corresponding ciphertext Formula${\ssr C}$ from Formula$CS_{1}$ by using its received index Formula$Ind$. Then, the requester can recover the original data by using the secret key Formula$ks$ to decrypt Formula${\ssr C}$.

B. The Encrypted Data Deposit Phase

1) Key Generation

For a single-authority smart grid system, a trusted authority (TA) can bootstrap the whole system. Specifically, in the key generation phase, given the security parameters Formula$\kappa$, TA first generates Formula$(q, g,\BBG_{1},\BBG_{2}, e)$ by running Formula${\cal G}en(\kappa)$. TA randomly chooses a master key Formula$r\in Z_{q}^{\ast}$, and computes the corresponding public key Formula$g^{r}$. Thus, Formula$(g^{r},r)$ is the public/private key pair of the TA. When S applies a query, TA assigns an ID-based key pair Formula$(H_{1}(ID_{S}),H_{1}^{r}(ID_{S}))$, denoted as Formula$(pk_{s}, sk_{s})$, to S. TA selects some random elements Formula$g_{1}$, Formula$g_{2}$, Formula$(h_{1},u_{1},\psi_{1}),\ldots, (h_{nl},u_{nl},\psi_{nl})\in\BBG_{1}$. The TA also picks random numbers Formula$y_{1},y_{2},v_{1},\ldots,v_{nl}, t_{1},\ldots,t_{nl}\in\BBZ_{p}$. Then, TA computes Formula$Y_{1}=g^{y_{1}}$, Formula$Y_{2}=g^{y_{2}}$, Formula$v_{k}=g^{v_{k}}\in\BBG_{1}$ for Formula$k\in (1,\ldots,nl)$. In addition, TA computes Formula$\Gamma=e(g_{1},Y_{1})e(g_{2},Y_{2})\in\BBG_{2}$. Later, TA distributes the HVE public/private key pair Formula$(PK, SK)$ to the CC as follows: Formula TeX Source $$\eqalignno{PK=&\, (g,Y_{1},Y_{2},(h_{1},u_{1},\psi_{1},V_{1},T_{1}),\cr &\quad\ldots,(h_{nl},u_{nl},\psi_{l},V_{nl},T_{nl}))\cr SK=&\,(g_{1},g_{2},y_{1},y_{2},v_{1},\ldots,v_{nl},t_{1},\ldots,t_{nl}).}$$ We assume that the communication channels are secure in our system model. An ID-based signature scheme Formula$Sig(\cdot)$ [25] can be used to authenticate the requester's identity. The details of secure channel establishment is without the scope of this paper. Fig. 4 shows the dataflow of the PaRQ.

Figure 4
Fig. 4. Data flow in our PaRQ scheme.

2) Data Encryption

We denote each data as Formula$m_{i}$. When Formula$U_{i}$ wants to report Formula$m_{i}$ to the cloud server Formula$CS_{1}$, Formula$U_{i}$ randomly generates a session key Formula$ks_{i}$. Then Formula$U_{i}$ encrypts its data into a ciphertext Formula${\ssr CT}_{i}$, where Formula${\ssr CT}_{i}={\ssr Enc}_{ks_{i}}(m_{i})$. Formula${\ssr Enc}(\cdot)$ is a symmetric encryption algorithm, e.g., AES [26].

For each uploading interval Formula TeX Source $$U_{i}\rightarrow CC:\{{\ssr C}_{i},t_{1}\}.$$ In this paper, “Formula$A\rightarrow B:\{C\}$” means “A sends C to B”. Then, the CC adds a unique index Formula$Ind_{i}$ to the data ciphertext and transmits all of them to the Formula$CS_{1}$. Formula TeX Source $$CC\rightarrow CS_{1}:\{{\ssr C}_{i},t_{1},Ind_{i}\}.$$

3) HVE-Based Session Key Encryption

If each data has Formula$l$ searchable attributes, Formula$U_{i}$ chooses a vector Formula${\bf x}_{i}=(x_{i1},\ldots,x_{il})\in\sum^{l}$ to characterize its data Formula$m_{i}$ in different dimensions. To encrypt Formula$ks_{i}$ by using the CC's Formula$PK$ and the vector Formula${\bf x}_{i}$, Formula$U_{i}$ divides each Formula$ks_{i}$ into two parts: Formula$ks_{i{\ssr L}}$ and Formula$ks_{i{\ssr R}}$. Then, Formula$ks_{i{\ssr L}}$ is encrypted by using the encryption vector Formula$\sigma_{\geq}({\bf x}_{i})$; Formula$ks_{i{\ssr R}}$ is encrypted by using the encryption vector Formula$\sigma_{\leq}({\bf x}_{i})$. Thus, the Formula$CS_{2}$ can recover Formula$ks_{i}$ only when both encryption vectors are satisfied with the corresponding query vectors in the range query tokens. The HVE-based session key encryption details are as follows:

  1. Firstly, Formula$U_{i}$ maps Formula${\bf x}_{i}$ to an encryption vector Formula$\sigma_{\geq}({\bf x}_{i})$ as (2). Then, Formula$U_{i}$ selects two random numbers Formula$r_{i1}$, Formula$r_{i2}\in Z_{p}$ and computes tags for the ciphertext Formula$ks_{i{\ssr L}}$ by using the encryption vector Formula$\sigma_{\geq}({\bf x}_{i})$ as: Formula TeX Source $$\eqalignno{&{\ssr C}^{i}_{{\ssr L}1}=Y_{1}^{r_{i1}},{\ssr C}^{i}_{{\ssr L}2}=Y_{2}^{r_{i1}},\cr &{\ssr C}^{i}_{{\ssr L}3,1}=(h_{1}u_{1}^{\sigma_{\geq}(x_{i1})})^{r_{i1}}V_{1}^{r_{i2}},\cr &\ldots,\cr &{\ssr C}^{i}_{{\ssr L}3,nl}=(h_{nl}u_{nl}^{\sigma_{\geq}(x_{inl})})^{r_{i1}}V_{nl}^{r_{i2}},\cr &{\ssr C}^{i}_{{\ssr L}4,1}=\psi_{1}^{r_{i1}}T_{1}^{r_{i2}},\cr &\ldots,\cr &{\ssr C}^{i}_{{\ssr L}4,nl}=\psi_{nl}^{r_{i1}}T_{nl}^{r_{i2}},\cr &{\ssr C}^{i}_{{\ssr L}5}=g^{r_{i2}},{\ssr C}^{i}_{{\ssr L}6}=\Gamma^{r_{i1}}ks_{i{\ssr L}}.&{\hbox{(7)}}}$$
    Let Formula${\ssr CT}_{i{\ssr L}}=({\ssr C}^{i}_{{\ssr L}1},{\ssr C}^{i}_{{\ssr L}2},{\ssr C}^{i}_{{\ssr L}3,1},\ldots,{\ssr C}^{i}_{{\ssr L}3,nl},{\ssr C}^{i}_{{\ssr L}4,1},\ldots, {\ssr C}^{i}_{{\ssr L}4,nl}, {\ssr C}^{i}_{{\ssr L}5},{\ssr C}^{i}_{{\ssr L}6})$.
  2. Secondly, Formula$U_{i}$ maps Formula${\bf x}_{i}$ to an encryption vector Formula$\sigma_{\leq}({\bf x}_{i})$ as (5). Then, Formula$U_{i}$ selects two random numbers Formula$r^{\prime}_{i1}$, Formula$r^{\prime}_{i2}\in Z_{p}$, and computes tags for the ciphertext Formula$ks_{i{\ssr R}}$ by using the encryption vector Formula$\sigma_{\leq}({\bf x}_{i})$: Formula TeX Source $$\eqalignno{&{\ssr C}^{i}_{{\ssr R}1}=Y_{1}^{r^{\prime}_{i1}},{\ssr C}^{i}_{{\ssr R}2}=Y_{2}^{r^{\prime}_{i1}},\cr &{\ssr C}^{i}_{{\ssr R}3,1}=(h_{1}u_{1}^{\sigma_{\leq}(x_{i1})})^{r^{\prime}_{i1}}V_{1}^{r^{\prime}_{i2}},\cr &\ldots,\cr &{\ssr C}^{i}_{{\ssr R}3,nl}=(h_{nl}u_{nl}^{\sigma_{\leq}(x_{inl})})^{r^{\prime}_{i1}}V_{nl}^{r^{\prime}_{i2}},\cr &{\ssr C}^{i}_{{\ssr R}4,1}==\psi_{1}^{r^{\prime}_{i1}}T_{1}^{r^{\prime}_{i2}},\cr &\ldots,\cr &{\ssr C}^{i}_{{\ssr R}4,nl}=\psi_{nl}^{r^{\prime}_{i1}}T_{nl}^{r^{\prime}_{i2}},\cr &{\ssr C}^{i}_{{\ssr R}5}=g^{r^{\prime}_{i2}},{\ssr C}^{i}_{{\ssr R}6}=\Gamma^{r^{\prime}_{i1}}ks_{i{\ssr R}}.&{\hbox{(8)}}}$$ Let Formula${\ssr CT}_{i{\ssr R}}=({\ssr C}^{i}_{{\ssr R}1},{\ssr C}^{i}_{{\ssr R}2},{\ssr C}^{i}_{{\ssr R}3,1},\ldots,{\ssr C}^{i}_{{\ssr R}3,nl},{\ssr C}^{i}_{{\ssr R}4,1},\ldots, {\ssr C}^{i}_{{\ssr R}4,nl}, {\ssr C}^{i}_{{\ssr R}5},{\ssr C}^{i}_{{\ssr R}6})$.

4) Ciphertext Deposit

Formula$U_{i}$ deposits Formula${\ssr CT}_{i{\ssr L}}$ and Formula${\ssr CT}_{i{\ssr R}}$ to the CC as: Formula TeX Source $$U_{i}\rightarrow CC:\{{\ssr CT}_{i{\ssr L}},{\ssr CT}_{i{\ssr R}},t_{2}\}.$$ The CC also adds the index Formula$Ind_{i}$ to the key ciphertext and transmits all of them to the Formula$CS_{2}$. Formula TeX Source $$CC\rightarrow CS_{2}:\{{\ssr CT}_{i{\ssr L}},{\ssr CT}_{i{\ssr R}},t_{2},Ind_{i}\}.$$

C. Range Query Phase

1) Token Generation

When S wants to query the server to retrieve the expected data, S firstly generates a range query, such as Formula$P=(a_{1}\leq{x}_{1}\leq b_{1})\wedge (a_{2}\leq{x}_{2}\leq b_{2})\cdots\wedge(a_{l}\leq {x}_{l}\leq b_{l})$. S then computes a signature Formula$\delta_{s}=Sig_{sk_{s}}(P)$.

In each querying interval Formula TeX Source $$S\rightarrow CC:\{P,ID_{S},\delta_{s}\}.$$ The CC verifies S's signature by using S's public key. If S is an authorized requester, the CC might issue query tokens to S by following steps. The CC divides Formula$P$ into two parts: Formula$P_{\geq}=({x}_{1}\geq a_{1})\wedge ({x}_{2}\geq a_{2})\cdots\wedge ({x}_{l}\geq a_{l})$ and Formula$P_{\leq}=({x}_{1}\leq b_{1})\wedge ({x}_{1}\leq b_{2})\cdots\wedge ({x}_{1}\leq b_{l})$. Let Formula$w_{\geq}=(a_{1},\ldots,a_{l})$ and Formula$w_{\leq}=(b_{1},\ldots,b_{l})$.

The CC generates two query vector Formula$\sigma_{\geq}^{\ast}({\bf w})$ and Formula$\sigma_{\leq}^{\ast}({\bf w})$ to represent Formula$P_{\geq}$ and Formula$P_{\leq}$ as (3), respectively. The wildcard ∗ in the vector Formula$\sigma_{\geq}^{\ast}({\bf w})$ means that S does not care about the attributes related to ∗. Let Formula$s(\sigma^{\ast}(w_{g}))$ be the set of Formula$k$ which satisfies Formula$\sigma_{\geq}^{\ast}(w_{k})\ne\ast$. Let Formula$s(\sigma_{\leq}^{\ast}(w))$ be the set of Formula$k^{\prime}$ which satisfies Formula$\sigma_{\leq}^{\ast}(w_{k^{\prime}})\ne\ast$. Then the CC computes a token Formula$T_{P_{\geq}}$ by using the query vector Formula$\sigma_{\geq}^{\ast}({\ssr w})$ as follows.

  1. Select a random Formula$\alpha$, Formula$\beta\in Z_{p}$, and generate Formula$\lambda_{k}$, Formula$\psi_{k}$, Formula$\gamma_{k}$, Formula$\tau_{k}\in Z_{p}$ such that Formula$\lambda_{k}y_{1}+\psi_{k}y_{2}=\alpha$, Formula$\gamma_{k}y_{1}+\tau_{k}y_{2}=\beta$ for all Formula$k\in s(\sigma_{\geq}^{\ast}(w))$.
  2. Compute a token Formula$T_{P_{\geq}}$ as Formula TeX Source $$\eqalignno{K^{s}_{{\ssr L}1}=&\, g_{1}\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{\lambda_{k}}\psi_{k}^{\gamma_{k}},\cr K^{s}_{{\ssr L}2}=&\, g_{2}\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{\varphi_{k}}\psi_{k}^{\tau_{k}},\cr K^{s}_{{\ssr L}3}=&\,g^{\alpha},\cr K^{s}_{{\ssr L}4}=&\, g^{\beta},\cr K^{s}_{{\ssr L}5}=&\, g^{-\sum_{k\in s(\sigma_{\geq}^{\ast}(w))}(v_{k}\alpha+t_{k}\beta)}.&{\hbox{(9)}}}$$

Similarly, the CC generates a token Formula$T_{P_{\leq}}$ by using the query vector Formula$\sigma_{\leq}^{\ast}({\ssr w})$ as follows.

  1. Select a random Formula$\alpha^{\prime}$, Formula$\beta^{\prime}\in Z_{p}$, and generate Formula$\lambda_{k^{\prime}}$, Formula$\psi_{k^{\prime}}$, Formula$\gamma_{k^{\prime}}$, Formula$\tau_{k^{\prime}}\in Z_{p}$ such that Formula$\lambda_{k^{\prime}}y_{1}+\psi_{k^{\prime}}y_{2}=\alpha^{\prime}$, Formula$\gamma_{k^{\prime}}y_{1}+\tau_{k^{\prime}}y_{2}=\beta^{\prime}$ for all Formula$k^{\prime}\in s(\sigma_{\leq}^{\ast}(w))$.
  2. Compute the token Formula$T_{P_{\leq}}$ as Formula TeX Source $$\eqalignno{K^{s}_{{\ssr R}1}=&\, g_{1}\prod_{k^{\prime}\in s(\sigma^{\ast}(w_{ls}))}(h_{k^{\prime}}u_{k^{\prime}}^{\sigma^{\ast}(w_{lsk^{\prime}})})^{\lambda_{k^{\prime}}}\psi_{k^{\prime}}^{\gamma_{k^{\prime}}},\cr K^{s}_{{\ssr R}2}=&\, g_{2}\prod_{k^{\prime}\in s(\sigma^{\ast}(w_{ls}))}(h_{k^{\prime}}u_{k^{\prime}}^{\sigma^{\ast}(w_{lsk^{\prime}})})^{\varphi_{k^{\prime}}}\psi_{k^{\prime}}^{\tau_{k^{\prime}}},\cr K^{s}_{{\ssr R}3}=&\,g^{\alpha^{\prime}},\cr K^{s}_{{\ssr R}4}=&\, g^{\beta^{\prime}},\cr K^{s}_{{\ssr R}5}=&\, g^{-\sum_{k^{\prime}\in s(\sigma^{\ast}(w_{ls}))}(v_{k^{\prime}}\alpha^{\prime}+t_{k^{\prime}}\beta^{\prime})}.&{\hbox{(10)}}}$$

Let Formula$T_{P_{\geq}}=(K^{s}_{{\ssr L}1},K^{s}_{{\ssr L}2},K^{s}_{{\ssr L}3},K^{s}_{{\ssr L}4},K^{s}_{{\ssr L}5})$ and Formula$T_{P_{\leq}}=(K^{s}_{{\ssr R}1}, K^{s}_{{\ssr R}2},K^{s}_{{\ssr R}3},K^{s}_{{\ssr R}4},K^{s}_{{\ssr R}5})$. Then, the CC keeps a record Formula$(ID_{s},T_{P_{\geq}}, T_{P_{\leq}})$ in its database and distributes Formula$T_{P_{\geq}}$ and Formula$T_{P_{\leq}}$ to the requester Formula$S$ as its authorized tokens: Formula TeX Source $$CC\rightarrow S:\{T_{P_{\geq}}, T_{P_{\leq}}\}.$$

2) Key and Index Query

After receiving the query tokens from the CC, the requester deposits them as well as the non-wildcard indexes sets to the cloud server Formula$CS_{2}$ as: Formula TeX Source $$S\rightarrow CS_{2}:\{T_{P_{\geq}}, T_{P_{\leq}},t_{4},s(\sigma_{\geq}^{\ast}(w)),s(\sigma_{\leq}^{\ast}(w))\}.$$ Then, the Formula$CS_{2}$ searches its database to find whether there is a key ciphertext which matches the requester's query conditions. For each key ciphertext, if its encryption vectors are satisfied with the query vectors in the query tokens, the Formula$CS_{2}$ can obtain: Formula TeX Source $$\eqalignno{ks_{i{\ssr L}}=&\,{{D_{1}.D_{2}.e(K^{s}_{{\ssr L}5},{\ssr C}^{i}_{{\ssr L}5}).{\ssr C}^{i}_{{\ssr L}6}}\over{e(K^{s}_{{\ssr L}1},{\ssr C}^{i}_{{\ssr L}1}).e(K^{s}_{{\ssr L}2},{\ssr C}^{i}_{{\ssr L}2})}},&\hbox{(11)}\cr ks_{i{\ssr R}}=&\,{{D^{\prime}_{1}.D^{\prime}_{2}.e(K^{s}_{{\ssr R}5},{\ssr C}^{i}_{{\ssr R}5}).{\ssr C}^{i}_{{\ssr R}6}}\over{e(K^{s}_{{\ssr R}1},{\ssr C}^{i}_{{\ssr R}1}).e(K^{s}_{{\ssr R}2},{\ssr C}^{i}_{{\ssr R}2})}},&{\hbox{(12)}}}$$ where Formula$D_{1}=e(K^{s}_{{\ssr L}3},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}{\ssr C}^{i}_{{\ssr L}3,k})$ and Formula$D_{2}=e(K^{s}_{{\ssr L}4}, \prod_{k\in s(\sigma_{\geq}^{\ast}(w))}{\ssr C}^{i}_{{\ssr L}4,k})$. Formula$D^{\prime}_{1}=e(K^{s}_{{\ssr R}3},\prod_{k^{\prime}\in s(\sigma_{\leq}^{\ast}(w))}{\ssr C}^{i}_{{\ssr R}3,k^{\prime}})$ and Formula$D^{\prime}_{2}=e(K^{s}_{{\ssr R}4}, \prod_{k^{\prime}\in s(\sigma_{\leq}^{\ast}(w))}{\ssr C}^{i}_{{\ssr R}4,k^{\prime}})$. Thus, the Formula$CS_{2}$ can obtain Formula$ks_{i}$ by using Formula$ks_{i{\ssr L}}$ and Formula$ks_{i{\ssr R}}$. Then, the Formula$CS_{2}$ sends this recovered key Formula$ks_{i}$ with indexes to the requester. Formula TeX Source $$CS_{2}\rightarrow S:\{(ks_{i},Ind_{i}),(ks_{i_{,}},Ind_{i^{\prime}}),\ldots\}.$$ Note that, there might be more than one session keys which are satisfied with the range query tokens. Then, the Formula$CS_{2}$ distributes all of session keys back to the requester S.

3) Data Query

Upon receiving the keys and indexes from the Formula$CS_{2}$, the requester queries the Formula$CS_{1}$ by using the received indexes to obtain the corresponding data ciphertext. Formula TeX Source $$S\rightarrow CS_{1}:\{Ind_{i}, Ind_{i^{\prime}},\ldots\}.$$ Then, the Formula$CS_{1}$ searches its database to find whether there are ciphertexts matching the requester's indexes. If so, the Formula$CS_{1}$ sends matched ciphertexts to the requester S: Formula TeX Source $$CS_{1}\rightarrow S:\{{\ssr C}_{i},{\ssr C}_{i^{\prime}},\ldots\}.$$

4) Data Decryption

After receiving the real session keys from the Formula$CS_{2}$ and ciphertexts Formula$\{{\ssr C}_{i},{\ssr C}_{i^{\prime}},\ldots\}$ from the Formula$CS_{1}$, the requester Formula$S$ can obtain the real data by using the session keys to decrypt the ciphertexts, otherwise, Formula${\ssr C}_{i}$ can be discarded. Formula TeX Source $$S:m_{i}={\ssr Dec}_{ks_{i}}({\ssr C}_{i}),\ldots$$ Formula${\ssr Dec}(\cdot)$ is the symmetric decryption algorithm corresponding to the opposite operation of Formula${\ssr Enc}(\cdot)$.

D. Enhancement With Collusion Resilience

In our system model, we assume that the adversary cannot control both CSs. Actually, in order to prevent the cloud server Formula$CS_{1}$ and Formula$CS_{2}$ in collusion to disclose the data Formula$m_{i}$, an identity based encryption scheme [24] can be used in the data encryption phase to encrypt Formula$m_{i}$. For instance, the CC has one pair of identity based public/private key Formula$(pk,sk)$. Firstly, Formula$m_{i}$ is encrypted by the CC's public key Formula$pk$. Againit is encrypted by using the session key Formula$ks_{i}$ and be outsourced to the Formula$CS_{1}$. Thus, even if the Formula$CS_{2}$ recovers the session key Formula$ks_{i}$ with the requester's query tokens, the Formula$CS_{2}$ can not decrypt the ciphertexts on the Formula$CS_{1}$ to obtain the data Formula$m_{i}$. The reason is that the Formula$CS_{2}$ cannot obtain the CC's ID-based private key Formula$sk$. When an authorized requester S asks for query tokens from the CC, the CC replies the query tokens as well as its identity based private key Formula$sk$. Accordingly, the requester can recover data Formula$m_{i}$ by using both session key Formula$ks_{i}$ from Formula$CS_{1}$ and Formula$sk$ from the CC. Note that, the requesters are high-level users, such as energy company's financial auditors, who are authorized by the CC. Therefore, they can obtain the CC's private key to decrypt their queried data. As a result, the PaRQ can remain secure even the two cloud servers are in collusion.

Furthermore, to provide forward security and prevent requesters from decrypting future encrypted data by using CC's old private key, the CC can compute different pairs of time and identity based public/private key pairs at different time intervals. Therefore, the authorized requesters can only obtain CC's private keys corresponding to their entitled intervals to decrypt their required data.

SECTION VI

SECURITY ANALYSIS

In this section, we analyze the security properties of the proposed PaRQ according to the security requirements discussed in Section III-B.

  • The individual residential users' data confidentiality can be achieved. In the PaRQ, the residential user's data Formula$m_{i}$ is encrypted by its session key Formula$ks_{i}$. For the eavesdroppers and the Formula$CS_{2}$, they cannot obtain anything from the ciphertext Formula${\ssr C}_{i}$ because they lack of the secret key Formula$ks_{i}$. Although the Formula$CS_{2}$ can recover Formula$ks_{i}$ from the requester's query tokens, the Formula$CS_{2}$ cannot extract the ciphertexts from the Formula$CS_{1}$ if they are not in collusion. Our enhancement introduced in Section V-D can be resilient to the collusion attack even if the Formula$CS_{1}$ is in collusion with the Formula$CS_{2}$. Accordingly, the individual residential users data confidentiality is achieved in the proposed PaRQ scheme.
  • The individual residential users' data privacy can be preserved. In our PaRQ, Formula$ks_{i}$ and the searchable attributes are hid in two ciphertexts Formula$\{{\ssr CT}_{i{\ssr L}},{\ssr CT}_{i{\ssr R}}\}$. Other requesters cannot obtain Formula$ks_{i}$ from the Formula$CS_{2}$ if they cannot obtain the authorized query tokens Formula$\{T_{P_{\geq}}, T_{P_{\leq}}\}$ from the CC or their query vectors in the query tokens are not satisfied with the encryption vectors on the ciphertexts. Accordingly, they cannot pry into the session keys and decrypt the encrypted metering data. The range query correctness can be demonstrated as follows. In (11), the numerator equals: Formula TeX Source $$\eqalignno{& D_{1}\cdot D_{2}\cdot e(K^{s}_{{\ssr L}5},{\ssr C}^{i}_{{\ssr L}5})\cdot{\ssr C}^{i}_{{\ssr R}6}\cr &\quad=e\left(g^{\alpha},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}(x_{ik})})^{r_{i1}}g^{v_{k}r_{i2}}\right)\cr &\qquad\cdot e\left(g^{\beta},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}\psi_{1}^{r_{i1}}g^{t_{1}r_{i2}}\right)\cr &\qquad\cdot e\left(g^{-\sum_{k\in s(\sigma_{\geq}^{\ast}(w))}(v_{k}\alpha+t_{k}\beta)},g^{r_{i2}}\right)\cdot\Gamma^{r_{i1}}ks_{i{\ssr L}}\cr &\quad=e\left(g^{\alpha},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}(x_{ik})})^{r_{i1}}\right)\cr &\qquad\cdot e\left(g^{\beta},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}\psi_{k}^{r_{i1}}\right)\cr &\qquad\cdot e\left(g^{r_{i2}},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}g^{v_{k}\alpha+t_{k}\beta}\right)\cr &\qquad\cdot e\left(g^{-\sum_{k\in s(\sigma_{\geq}^{\ast}(w))}(v_{k}\alpha+t_{k}\beta)},g^{r_{i2}}\right)\cdot\Gamma^{r_{i1}}ks_{i{\ssr L}}\cr &\quad=e\left(g^{\alpha},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}(x_{ik})})^{r_{i1}}\right)\cr &\qquad\cdot e\left(g^{\beta},\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}\psi_{k}^{r_{i1}}\right)\cdot\Gamma^{r_{i1}}ks_{i{\ssr L}}.&{\hbox{(13)}}}$$
  • while the denominator equals: Formula TeX Source $$\eqalignno{& e(K^{s}_{{\ssr L}1},{\ssr C}^{i}_{{\ssr L}1}).e(K^{s}_{{\ssr L}2},{\ssr C}^{i}_{{\ssr L}2})\cr &\quad=e\left(g_{1}\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{\lambda_{k}}\psi_{k}^{\gamma_{k}},g^{y_{1}r_{i1}}\right)\cr &\qquad\cdot e\left(g_{2}\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{\varphi_{k}}\psi_{k}^{\tau_{k}},g^{y_{2}r_{i1}}\right)\cr &\quad=\Gamma^{r_{i1}}\cdot\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}[e((h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{\lambda_{k}},g^{y_{1}r_{i1}})\cr &\hskip10em\cdot e((h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{\varphi_{k}},g^{y_{2}r_{i1}})]\cr &\qquad\cdot\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}[e(\psi_{k}^{\gamma_{k}},g^{y_{1}r_{i1}})\cdot e(\psi_{k}^{\tau_{k}},g^{y_{2}r_{i1}})]\cr &\quad=\Gamma^{r_{i1}}\cdot\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}e((h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{r_{i1}},g^{\lambda_{k}y_{1}+\psi_{k}y_{2}})\cr &\qquad\cdot\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}e(\psi_{k}^{r_{i1}},g^{\gamma_{k}y_{1}+\tau_{k}y_{2}})\cr &\quad=\Gamma^{r_{i1}}\cdot e\left(\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{r_{i1}},g^{\alpha}\right)\cr &\qquad\cdot e\left(\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}\psi_{k}^{r_{i1}},g^{\beta}\right).&{\hbox{(14)}}}$$

Let Formula$\Theta$ be the set of indexes Formula$i\in s(\sigma_{\geq}^{\ast}(w))$ where Formula$\sigma_{\geq}^{\ast}(w_{k})\ne\sigma_{\geq}(x_{ik})$. The (11) outputs follows Formula TeX Source $$\eqalignno{&{{D_{1}\cdot D_{2}\cdot e(K_{s50},C_{i50})\cdot C_{i60}}\over{e(K_{s10},C_{i10})\cdot e(K_{s20},C_{i20})}}\cr &\quad=e(g^{\alpha},\prod_{k\in\Theta}(u_{k}^{\sigma_{\geq}(x_{ik})-\sigma_{\geq}^{\ast}(w_{k})})^{r_{i1}})\cdot ks_{iL}\cr &\quad=e(g,g)^{\alpha r_{i1}\Sigma_{k\in\Theta}(log_{g}(u_{k}))(\sigma_{g}(x_{ik})-\sigma_{\geq}^{\ast}(w_{k}))}.&{\hbox{(15)}}}$$ If Formula$\sigma_{\geq}^{\ast}(w_{k})$ equals Formula$\sigma_{\geq}(x_{ik})$ for all Formula$k\in s(\sigma_{\geq}^{\ast}(w))$, Formula$ks_{i{\ssr L}}$ can be recovered; otherwise, the unauthorized requesters cannot obtain Formula$ks_{i{\ssr L}}$ according to (11).

Similarly, the unauthorized requesters cannot obtain Formula$ks_{i{\ssr R}}$ from (12). Therefore, only the authorized requester can obtain the query results and the users' data privacy is preserved.

  • The requester's query privacy can be preserved. In our PaRQ, a requester's query is divided into two parts: Formula$P_{\geq}$ and Formula$P_{\leq}$, by the Formula$CC$. Both of them are translated into tokens Formula$T_{P_{\geq}}$ and Formula$T_{P_{\leq}}$ in the form of Formula$\prod_{k\in s(\sigma_{\geq}^{\ast}(w))}(h_{k}u_{k}^{\sigma_{\geq}^{\ast}(w_{k})})^{\lambda_{k}}\psi_{k}^{\gamma_{k}}$ and Formula$\prod_{k^{\prime}\in s(\sigma_{\leq}^{\ast}(w))} (h_{k^{\prime}}u_{k^{\prime}}^{\sigma_{\leq}^{\ast}(w_{k^{\prime}})})^{\varphi_{k^{\prime}}}\psi_{k^{\prime}}^{\tau_{k^{\prime}}}$, respectively. For the eavesdroppers, they can learn nothing about the query Formula$P$ only with the tokens Formula$T_{P_{\geq}}$ and Formula$T_{P_{\leq}}$ because they have no idea about the index sets and encryption parameters Formula$\lambda_{k}$, Formula$\psi_{k}$, Formula$\gamma_{k}$, Formula$\tau_{k}$. Since the Formula$CS_{2}$ still does not know the encryption parameters Formula$\lambda_{k}$, Formula$\psi_{k}$, Formula$\gamma_{k}$, Formula$\tau_{k}$, it also cannot obtain the real value of Formula$P$ even with the tokens and the index sets Formula$s(\sigma_{\geq}^{\ast}(w))$ and Formula$s(\sigma_{\leq}^{\ast}(w))$. Therefore, the requester's query privacy is preserved in the proposed PaRQ scheme.

From the above security analysis and comparison in Table II, our PaRQ can achieve all of the data confidentiality and privacy and query privacy, compared with order-preserving encryption (OPE) [16] based technique and bucketization (Buket) based technique [18].

Table 2
TABLE II COMPARISON OF SECURITY PROPERTIES.
SECTION VII

PERFORMANCE EVALUATION

In this section, we evaluate the performance of the proposed PaRQ scheme in terms of the communication overhead, computation complexity and response time of the system.

A. Communication Overhead

We numerically analyze the communication overhead of our PaRQ, compared with the MRQED [23], in terms of the public key size, ciphertexts size and token size. Since the functionality of the decryption key computation phase in determining the query results in MRQED is similar to that of query tokens in the PaRQ, therefore, we take their size in comparison. “Tok/Dek” in Tables II and III represents Token or Decryption key. Since most pairing-based cryptosystems need to work in a subgroup of the elliptic curve Formula$E(F_{q})$, by representing elliptic curve points using point compression, the lengths of the elements in Formula$G_{1}$ and Formula$G_{2}$ are roughly 161-bit (using point compression) and 1,024-bit, respectively. In the following, Formula$l$ is the number of data dimensions and Formula$N$ is domain of attribute values.

Table 3
TABLE III COMPARISON OF COMMUNICATION COMPLEXITY (BIT).

In the key generation phase, the public key includes Formula$(5Nl+3) G_{1}$ elements. If we choose AES ciphertext with 256-bit, the data ciphertext Formula${\ssr C}_{i}$ is only of 256 bits. In addition, session key's ciphertext includes two parts: Formula${\ssr CT}_{i{\ssr L}}$ and Formula${\ssr CT}_{i{\ssr R}}$, each of which includes Formula$(2Nl+3) G_{1}$ elements and a Formula$G_{2}$ element, thus the size of each session key's ciphertext is Formula$(4Nl+6)\times 161+2048 {\rm bits}$. Since each query token includes 5 Formula$G_{1}$ elements, the size of the two query tokens Formula$\{T_{P_{\geq}}, T_{P_{\leq}}\}$ is Formula$161\times 10=1610 {\rm bits}$.

In comparison, the public key in the MRQED [23] includes Formula$8Nl G_{1}$ elements and a Formula$G_{2}$ element. The decryption keys include Formula$5Nl G_{1}$ elements. In addition, there are Formula$(4Nl+1) G_{1}$ elements and a Formula$G_{2}$ element in the ciphertexts. Table III shows that compared with the MRQED, our PaRQ consumes less communication overhead. Especially, our PaRQ significantly reduces the tokens transmission overhead, which is a constant, i.e., 1600 bits; in the MRQED the transmission overhead of the decryption keys may increase with both Formula$l$ and Formula$N$. The total communication overhead comparison is depicted in Fig. 5. It further indicates that our PaRQ costs less communication overhead than the MRQED.

Figure 5
Fig. 5. Comparison of communication overhead between PaRQ and MRQED schemes.

B. Computation Overhead

In our PaRQ, the computation tasks include pairing operations and exponentiation operations. For simplicity of description, the pairing operation and exponentiation operation are denoted as Formula$C_{p}$ and Formula$C_{e}$, respectively. Since the AES encryption/decryption and multiplication are much faster than the pairing operations, we do not analyze the AES encryption/decryption and multiplication in this subsection.

For the PaRQ, the symmetric encryption of Formula${\ssr C}_{i}$ is very fast. Meanwhile, the corresponding session key is encrypted into key ciphertexts Formula$\{{\ssr CT}_{i0},{\ssr CT}_{i1}\}$ by using its encryption vectors. The computation overhead of Formula$\{{\ssr CT}_{i0},{\ssr CT}_{i1}\}$ is Formula$(10Nl+8)C_{e}$ because each part requires Formula$(5Nl+4)$ exponentiation operations. In the token generation phase, the computation cost of Formula$\{T_{P_{\geq}}, T_{P_{\leq}}\}$ is Formula$(12l+2)C_{e}$, because each query token in Formula$\{T_{P_{\geq}}, T_{P_{\leq}}\}$ needs Formula$6l+3$ exponentiation operations. After receiving the tokens, the Formula$CS_{2}$ needs to compute 10 pairings to recover the session key Formula$\{ks_{i{\ssr L}},ks_{i{\ssr R}}\}$, i.e., Formula$10C_{p}$.

On the other hand, the MRQED [23] needs Formula$(8Nl+3)$ exponentiation operations to encrypt a message, another Formula$8Nl$ exponentiation operations to derive the decryption keys and Formula$5l\cdot l_{og}N$ pairing operations to search the correct results. From Table IV, we can see that the encryption overhead in both PaRQ and MRQED increase with Formula$l$ and Formula$N$. The computation overhead of token generation in the PaRQ only increases wtih Formula$l$, whereas, the overhead of decryption key generation in MRQED increases with both Formula$l$ and Formula$N$. When a query is executed in a database, the overhead in our PaRQ is a constant Formula$(10C_{p})$; the overhead in the MRQED still increases with both Formula$l$ and Formula$N$. Hence, our PaRQ is much more efficient than the MRQED. Further comparison of their range query response time is analyzed in Section VII-C.

Table 4
TABLE IV COMPARISON OF COMPUTATION COMPLEXITY.

C. Response Time

To provide good services to requesters, the response time of a range query is an important metric. For example, it would be useful for the requesters to know how long they exactly need to wait for a range query result so that they can efficiently schedule their tasks. Actually, response time varies according to many factors, such as communication latency etc. We analyze the response time of our PaRQ with or without considering the network communication latency Formula$\Delta$. The other factors are not being included in this calculation of the response time.

In the PaRQ, a range query is processed by the CC, Formula$CS_{1}$ and Formula$CS_{2}$. We model our range query process as a tandem model of network queues [27], as shown in Fig. 6. We assume that the range query arrives the system according to a poisson process with rate Formula$\lambda$, and uses the CC for token generation in an exponentially distributed time interval with mean Formula$1/\mu$ (as an Formula$M/M/1$ queue). Upon exiting the CC, the requester continue accesses the Formula$CS_{2}$ with rate Formula$\lambda_{2}$ for a time which is deterministic Formula$1/\mu_{2}$ (as an Formula$M/D/1$ queue). Finally, the requester accesses server Formula$CS_{1}$ with rate Formula$\lambda_{1}$ for a time which is exponentially distributed with mean Formula$1/\mu_{1}$ (as an Formula$M/M/1$ queue). Let Formula TeX Source $$\rho={{\lambda}\over{\mu}};\rho_{1}={{\lambda_{1}}\over{\mu_{1}}};\rho_{2}={{\lambda_{2}}\over{\mu_{2}}}.$$ If all the network states are in the set of Formula$n=\{n_{0},n_{1},n_{2}\}$, according to Jackson's Theorem [28], the steady-state probability distribution of the system is given as: Formula TeX Source $$P(n_{1},n_{2},n_{3})=\rho^{n_{0}}(1-\rho)\rho_{1}^{n_{1}}(1-\rho_{1})\rho_{2}^{n_{2}}(1-\rho_{2}).$$ Let Formula$T$, Formula$T_{1}$ and Formula$T_{2}$ be the average queuing delay of the CC, Formula$CS_{1}$ and Formula$CS_{2}$, respectively. They can be calculated as: Formula TeX Source $$\eqalignno{T=&\,{{1}\over{\mu-\lambda}}={{1}\over{\mu (1-\rho)}};\cr T_{1}=&\,{{1}\over{\mu_{1}-\lambda_{1}}}={{1}\over{\mu_{1}(1-\rho_{1})}};\cr T_{2}=&\,{{1}\over{\mu_{2}}}{{2-\rho_{2}}\over{2-2\rho_{2}}}.}$$ Then, the total delay of the range query in the PaRQ is: Formula TeX Source $$T_{tol}={{1}\over{\mu (1-\rho)}}+{{1}\over{\mu_{1}(1-\rho_{1})}}+{{1}\over{\mu_{2}}}{{2-\rho_{2}}\over{2-2\rho_{2}}}.$$ In this section, the response time of a range query is the total queuing delay on all the servers.

Figure 6
Fig. 6. Tandem model [27] of a range query process.

Detailed experiments are conducted on a Pentium IV 3-GHz system to study the execution time [29]. For Formula$G_{1}$ over the Freeman–Scott–Teske (FST) curve, a single exponentiation operation in Formula$G_{1}$ with 161 bits costs 1.1 ms, and the corresponding pairing operation costs 3.1 ms. Without loss of generality, let Formula$N=20$, Formula$l=5$. According to Table IV, the processing time of the CC is the tokens generation time, i.e., Formula$1/\mu=(12l+6)\times 1.1=72.6 {\rm ms} \approx0.073 {\rm s}$. If range query length is exponentially distributed with mean 2 Kbits and arrives according to a poisson process with rate 1query/10minute, i.e., Formula$\lambda=1/600$, and the queuing delay Formula$T={{1}\over{\mu-\lambda}}=0.073 {\rm s}$ and average queue length Formula$L={{\lambda}\over{\mu-\lambda}}=0.0012$.

Next, the processing time of the Formula$CS_{2}$ depends on the query tokens verification and the searching time in Formula$CS_{2}$'s database. The computation time of a query token verification over one record is Formula$10\times 3.1=31 {\rm ms}$. If the number of records in Formula$CS_{2}$'s database is Formula$M=100$, the Formula$CS_{2}$'s processing delay is 3.1 s, i.e., Formula$1/\mu_{2}=3.1 {\rm s}$. At last, querying indexed ciphertexts on the Formula$CS_{1}$ is typically processed very fast, the processing time is only several milliseconds (e.g Formula$1/\mu_{1}=10 {\rm ms}$). Since Formula$\mu_{2}=max(\lambda_{1})$, considering the extreme case Formula$\lambda_{1}=\mu_{2}$, then, Formula$T_{1}=0.01 {\rm s}$ and Formula$L_{1}\approx 0$. Therefore, Formula$T$, Formula$L$, Formula$T_{1}$, Formula$L_{1}$ are very small, and few rang query tasks can be buffered in the queue Formula$CS_{1}$ and CC. As a result, their queuing delay can be neglected.

From the above analysis, the processing time on the CC is much faster than the query arriving interval. Thus, Formula$\lambda=\lambda_{2}=1/600$. Moreover, compared with the Formula$CS_{2}$ queue, the service rate of the Formula$CS_{1}$ and CC is much faster, i.e., Formula$\mu_{1}\gg\mu\gg\mu_{2}$. Therefore, a range query's average response time is mainly determined by the processing time of the Formula$CS_{2}$. Consequently, the whole range query response time is distributed approximately as in the Formula$CS_{2}$ queue, that is, as in an Formula$M/D/1$ queue with poisson rate Formula$\lambda_{2}$ and service rate Formula$1/\mu_{2}$. Hence, the response time of a range query can be represented by Formula$T^{,}_{tol}$. Formula TeX Source $$T^{,}_{tol}={{1}\over{\mu_{2}}}{{2-\rho_{2}}\over{2-2\rho_{2}}}.$$ If the total communication latency Formula$\Delta$ among all network links is not negligible, the formula Formula$T^{,}_{tol}$ should be adjusted to Formula TeX Source $$T^{,}_{tol}={{1}\over{\mu_{2}}}{{2-\rho_{2}}\over{2-2\rho_{2}}}+\Delta.$$ In fact, the smart grid usually uses 3G (3rd Generation) or 4G (4th Generation) cellular network topology for cells data transmission. Data transmission rate is 60–240 Kbps, and distance converge depends upon the availability of cellular service [30]. Hence, the communications rate among the requesters, the CC and the CSs in our PaRQ scheme is assumed to be 240 Kbps. Here, Formula$\lambda_{2}=1/600$ and Formula$1/\mu_{2}=3.1 {\rm s}$.

  1. If the communication latency Formula$\Delta$ is negligible, i.e., Formula$\Delta\approx 0$, we can see from Fig. 7 that the response time of a range query is increased with the number of the database records. Comparing the total response time of a range query with or without considering the queuing delay of the CC and Formula$CS_{1}$ by using Formula$T_{tol}$ and Formula$T^{,}_{tol}$, respectively, Fig. 7 also shows that they are almost the same, which means that the queuing delay of the Formula$CS_{1}$ and CC really can be neglected in response time calculation.
  2. If the communication latency Formula$\Delta$ is not negligible, we should consider the communication overhead during the range query process. From the above analysis, if S sends a 2K-bit range query to the CC, the CC replies with two 1610-bit tokens. Then, S forwards these two tokens to the Formula$CS_{2}$, and the Formula$CS_{2}$ replies the satisfactory keys and indexes. If Formula$t$ is the average number of matched results and the size of the keys and indexes are 80 bits each, thus, their communication overhead is 160t bits. Finally, when S accesses the Formula$CS_{1}$, the Formula$CS_{1}$ replies the correct indexed ciphertexts. Usually, the size of the ciphertext is large. Let it be 1 Mbits/packet. The communication overhead of the ciphertexts is 1 tM bits. Hence, the system communication latency Formula$\Delta\approx 0.022+4.26t$. Formula TeX Source $$T^{,}_{tol}={{1}\over{\mu_{2}}}{{2-\rho_{2}}\over{2-2\rho_{2}}}+0.022+4.26t.$$
    Fig. 8 illustrates that both the number of data records in the Formula$CS_{2}$'s database and the number of replied ciphertexts from the Formula$CS_{1}$ can augment the system response time.
  3. Compared with the MRQED, Table II shows that the MRQED needs Formula$5l\cdot l_{og}NC_{p}$ to verify a query on a ciphertext. In a database with the number of data records Formula$M=100$, the processing time in the database is Formula$5l\cdot l_{og}N\times 3.1 {\rm s}$. Similarly, in the MRQED, the encryption and decryption key generation time is much shorter than the processing time of data query in the database. Therefore, the range query response time of the MRQED is mainly determined by the query in database. Thus, the range query service in the MRQED can also be modeled by using an Formula$M/D/1$ queue with poisson rate Formula$\lambda^{\prime}_{2}=1/600$ and service rate Formula$1/\mu^{\prime}_{2}=5l\cdot l_{og}N\times 3.1$. Fig. 9 illustrates the response time comparison between the PaRQ and the MRQED without communication delay, the range query arrival rates are Formula$\lambda_{2}=\lambda^{\prime}_{2}=1/600$. From Table IIand Fig. 9, we can observe that in the MRQED, if the number of data records in the database is a constant, the response time of a range query increases with the domain Formula$N$ and the number of dimensions Formula$l$, while the service time in our PaRQ is Formula$1/\mu_{2}=3.1 {\rm s}$. Thus, no matter how many dimensions of the data and how large the domain is, a single range query process time in the PaRQ remains Formula${{1}\over{\mu_{2}}}{{2-\rho_{2}}\over{2-2\rho_{2}}}=3.1 {\rm s}$, which is much less than that of the MRQED.
Figure 7
Fig. 7. Response time in PaRQ scheme, Formula$\Delta=0$.
Figure 8
Fig. 8. Response time in PaRQ scheme, Formula$\Delta=0.022+4.26t.{\rm c}$.
Figure 9
Fig. 9. Comparison of the number of matched residential users. (a) Formula$\lambda_{2}=\lambda^{\prime}_{2}=1/600$, Formula$1/\mu_{2}=3.1 {\rm s}$, Formula$1/\mu^{\prime}_{2}=0.6699 {\rm l}$. (b) Formula$\lambda_{2}=\lambda^{\prime}_{2}=1/600$, Formula$1/\mu_{2}=3.1 {\rm s}$, Formula$1/\mu^{\prime}_{2}=0.775\times\log_{2}(N)$.
SECTION VIII

CONCLUSION

In this paper, we have proposed a privacy-preserving range query scheme, named PaRQ, for smart grid. An HVE based range query predicate is constructed to realize the range query on encrypted metering data. The PaRQ allows users to store their data on cloud servers in encrypted form, and range queries can be executed by using cloud server's computational capabilities. A requester with authorized query tokens can obtain the correct session keys to retrieve the metering data within specific query ranges. Security analysis demonstrates that the PaRQ can achieve data confidentiality and privacy and preserve query privacy. Performance evaluation shows that the PaRQ can significantly reduce computation and communication overhead, as well as response time. For our future work, we intend to enhance our PaRQ to support ranked range query with security and privacy preservation.

Footnotes

This work was supported by the National Natural Science Foundation of China under Grants 61073189, 61272437, and 61202369, NSERC, Canada, the Innovation Program of Shanghai Municipal Education Commission under Grant 13ZZ131, the Foundation Key Project of Shanghai Science and Technology Committee under Grant 12JC1404500, and the Project of Shanghai Science and Technology Committee under Grant 12510500700.

M. Wen, is with the College of Computer Science and Technology, Shanghai University of Electric Power, Shanghai 201101, China and also with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada CORRESPONDING AUTHOR: M. WEN (wenmi2222@gmail.com)

J. Lei is with the College of Computer Science and Technology, Shanghai University of Electric Power, Shanghai 201101, China

K. Zhang, X. Liang, and X. Shen are with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada

R. Lu is with the School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore 639798

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

References

No Data Available

Authors

Mi Wen

Mi Wen

Mi Wen (M'10) received the Ph.D. degree in computer science from Shanghai Jiao Tong University, Shanghai, China, in 2008. She is currently an Associate Professor with the College of Computer Science and Technology, Shanghai University of Electric Power, Shanghai. Her current research interests include security in wireless sensor network and privacy preserving in smart grid.

Rongxing Lu

Rongxing Lu

Rongxing Lu (S'09–M'11) received the Ph.D. degree in computer science from Shanghai Jiao Tong University, Shanghai, China, in 2006, and the Ph.D. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2012. He is currently an Assistant Professor with the School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore. His current research interests include wireless network security, applied cryptography, and trusted computing.

Kuan Zhang

Kuan Zhang

Kuan Zhang received the B.Sc. degree in electrical and computer engineering and the M.Sc. degree in computer science from Northeastern University, Shenyang, China, in 2009 and 2011, respectively. He is currently pursuing the Ph.D. degree with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada. His current research interests include packet forwarding, and security and privacy for mobile social networks.

Jingsheng Lei

Jingsheng Lei

Jingsheng Lei is a Professor and the Dean of the College of Computer Science and Technology, Shanghai University of Electronic Power, Shanghai China. He received the B.S. degree in mathematics from Shanxi Normal University, Xian, China, in 1987, and the M.S. and Ph.D. degrees in computer science from Xinjiang University, Xinjiang, China, in 2000 and 2003, respectively. His current research interests include machine learning, data mining, pattern recognition and cloud computing. He has published more than 80 papers in international journals or conferences. He serves as an Editor-in-Chief of the Journal of Computational Information Systems. He is the member of the Artificial Intelligence and Pattern Recognition Technical Committee of the China Computer Federation and the Machine Learning Technical Committee of the Chinese Association of Artificial Intelligence.

Xiaohui Liang

Xiaohui Liang

Xiaohui Liang (S'10) received the B.Sc. degree in computer science and engineering and the M.Sc. degree in computer software and theory from Shanghai Jiao Tong University, Shanghai, China, in 2006 and 2009, respectively. He is currently pursuing the Ph.D. degree with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada. His current research interests include applied cryptography, and security and privacy issues for e-healthcare system, cloud computing, mobile social networks, and smart grid.

Xuemin Shen

Xuemin Shen

Xuemin Shen (M'97–SM'02–F'09) received the B.Sc. degree from Dalian Maritime University, Dalian, China, and the M.Sc. and Ph.D. degrees from Rutgers University, NJ, USA, in 1982, 1987, and 1990, respectively, all in electrical engineering. He is a Professor and University Research Chair with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada. He was the Associate Chair for Graduate Studies from 2004 to 2008. His current research interests include resource management in interconnected wireless/wired networks, wireless network security, wireless body area networks, vehicular ad hoc, and sensor networks. He is the co-author or editor of six books, and has published more than 600 papers, and book chapters in wireless communications and networks, control, and filtering. He served as the Technical Program Committee Chair for IEEE VTC in 2010, the Symposia Chair for IEEE ICC in 2010, the Tutorial Chair for IEEE VTC in 2011, and IEEE ICC in 2008, the Technical Program Committee Chair for IEEE Globecom in 2007, the General Co-Chair for Chinacom in 2007 and QShine in 2006, the Chair for IEEE Communications Society Technical Committee on Wireless Communications, and P2P Communications and Networking. He serves/served as the Editor-in-Chief for the IEEE Network, Peer-to-Peer Networking and Application, and IET Communications, a Founding Area Editor for the IEEE Transactions on Wireless Communications, an Associate Editor for the IEEE Transactions on Vehicular Technology, Computer Networks, and ACM/Wireless Networks, and the Guest Editor for the IEEE JSAC, IEEE Wireless Communications, the IEEE Communications Magazine, and ACM Mobile Networks and Applications. He received the Excellent Graduate Supervision Award in 2006, and the Outstanding Performance Award from the University of Waterloo in 2004, 2007, and 2010, the Premiers Research Excellence Award from the Province of Ontario, Canada, in 2003, and the Distinguished Performance Award from the Faculty of Engineering, University of Waterloo, in 2002 and 2007. He is a registered Professional Engineer of Ontario, Canada. He is a fellow of the Engineering Institute of Canada and the Canadian Academy of Engineering. He is a Distinguished Lecturer of IEEE Vehicular Technology Society and Communications Society. He has been a Guest Professor of Tsinghua University, Shanghai Jiao Tong University, Zhejiang University, Beijing Jiao Tong University, Northeast University.

Cited By

No Data Available

Keywords

Corrections

None

Multimedia

No Data Available
This paper appears in:
No Data Available
Issue Date:
No Data Available
On page(s):
No Data Available
ISSN:
None
INSPEC Accession Number:
None
Digital Object Identifier:
None
Date of Current Version:
No Data Available
Date of Original Publication:
No Data Available

Text Size