Privacy-preserving statistical analysis over multi-dimensional aggregated data in edge computing-based smart grid systems

Abstract

Smart grid systems enable bidirectional data communication between users and a smart grid control center (CC), by utilizing various communication infrastructures and embedded devices. To extract valuable information from users’ power consumption data efficiently, multi-dimensional data of users are required to be analyzed deeply. To protect users’ privacy, power consumption data are usually encrypted before transmission, which simultaneously makes it difficult to conduct statistical analysis. In this paper, we propose a scheme which enables privacy-preserving statistical analysis over multi-dimensional aggregated data (SA-MAD) in smart grid systems equipped with edge computing. We modify Boneh–Goh–Nissim (BGN) public key cryptosystem to a dual-message encryption mode, combining with two special superincreasing sequences to deal with multi-dimensional encrypted data aggregation. Besides, we design an identity-based aggregate signature to ensure encrypted data integrity in smart grid systems, and employ shamir secret sharing technique to support transmission fault-tolerance mechanism from smart meters to corresponding edge servers. SA-MAD enables CC to flexibly conduct privacy-preserving statistical analysis (e.g., sum, average, and variance) over aggregated data, and it could be easily extended to support covariance and linear regression computation. The performance evaluation demonstrates the feasibility of SA-MAD in edge computing-based smart grid systems.

Introduction

Traditional power grids have already no longer been satisfied with the growing demands for continuous stable electricity generation and distribution. Some related reports have indicated such trend, for instance, the electrical blackouts occurred in North America in 2003 and European in 2006 due to load imbalance and lack of effective real-time diagnosis in power grids [1], [2]. By contrast, smart grids integrate various advanced communication and information technologies, e.g., cloud computing, artificial intelligence, and other emerging techniques, to enable a cost-effective bidirectional communication between smart meters and a grid control center, which aims at making up for shortcomings in traditional power grids [3], [4].

In smart grids, a smart meter (SM) is a critical embedded device which plays an important role in the achievement of bidirectional communication mechanism. Usually, smart meters are utilized to periodically collect and send users’ power consumption data to a smart grid control center. As the collected power consumption data are closely relevant to users’ living habits and household security, an adversary in the smart grid system may intercept transmitted data and seek to extract useful information with various attacking methods, e.g., machine learning, non-intrusive load monitoring (NILM), thereby violating users’ privacy [5], [6], [7], [8], [9], [10], [11]. As such, it is indispensable to preprocess users’ data to preserve privacy against these attacks. Additionally, the integrity of power consumption data is also demanded for smart grids. This is because some malicious users may try to tamper with the data to avoid subsequent power usage billing, an external adversary may also try to tamper with or replace the data to cause system chaos or even collapse [12], [13], [14]. As smart meters are installed in the proximity of users’ houses with few protection measures, the condition always occurs that smart meter malfunctions as a result of system crash or factitious destruction [15], [16]. Consequently, a practical smart grid system should be as robust as possible and provide transmission fault-tolerance functionality for smart meters.

Data aggregation is an effective approach to preserve users’ power consumption data privacy as well as largely reduce communication overhead in various distributed environments. In smart grids, smart meters collect multi-dimensional power consumption data for process and analysis periodically, an intermediate device could be exploited as a data aggregator or communication relay between smart meters and a smart grid control center. In order to enable a control center to conduct subsequent privacy-preserving statistical analysis over those aggregated power consumption data, the homomorphic encryption technique is frequently employed to encrypt users’ data in prior to transmission. Accordingly, specific types of computations could be carried out on ciphertexts, and an encrypted result could match the result of operations performed on the plaintexts. Existing Paillier homomorphic cryptosystem [17] and BGN homomorphic cryptosystem [18] are two typical techniques in data aggregation. With various increasing big data analysis requirements in smart grids, it is necessary to introduce new techniques to construct data aggregation schemes that could support abundant privacy-preserving statistical analysis, e.g., sum, average, variance, covariance, linear regression computation.

In addition to the advantages of privacy-preserving data aggregation in statistical analysis over power consumption data, we observe that emerging edge computing technique could be introduced in the deployment of smart grids. Edge computing is a computing paradigm that has gained considerable popularity in academic and industrial areas [19], [20], [21], [22]. It brings the service and utilities of cloud computing closer to the end user and is characterized by fast processing and quick application response time. As such, it is specially suitable for delay-sensitive Internet-of-thing (IoT) applications (e.g., smart grids) which require low-latency, mobility and location awareness support. Integrating edge computing framework into smart grid systems could improve the ability of smart grids to process massive heterogeneous data and improve the real-time performance of transactions processing [23], [24], [25].

In this paper, we present a data aggregation scheme for smart grid systems based on edge computing paradigm, which enables a grid control center to conduct privacy-preserving statistical analysis over multi-dimensional aggregated data (SA-MAD). Specifically, the contributions of this work are threefold which are elaborated as follows.

• We extend the origin BGN homomorphic encryption to a BGN dual-message encryption mode, where the order of underlying bilinear map groups is constructed with four distinct primes. We design two superincreasing sequences and combine with the modified four-prime BGN encryption algorithm to enable smart meters to encrypt multi-dimensional power consumption data and corresponding square values into one ciphertext. Once all the ciphertexts from different users are aggregated to a single ciphertext, the sum of users’ multi-dimensional data and the sum of square of multi-dimensional data could be recovered by the control center with corresponding private key. Additionally, this approach could be easily extended to compute covariance and linear regression of two data types with slight modification.

• To improve system robustness and support transmission fault tolerance mechanism, we exploit shamir secret sharing technique to split a preset parameter into $\ell$ slices, where $\ell$ is the number of smart meters in a single grid area. Each smart meter utilizes this slice to further obfuscate the ciphertext such that even if the decryption private keys of the control center are leaked to an adversary, the confidentiality of each user’s power consumption data is still preserved. As long as the number of smart meters in the grid area is greater than or equal to the threshold value, the obfuscation factor in the ciphertext could be canceled by corresponding edge server during data aggregation process. Accordingly, the subsequent data aggregation and statistical analysis functionalities could also be achieved. Besides, we design a new identity-based aggregate signature algorithm to ensures the data integrity of multi-dimensional power consumption data in the whole smart grid systems equipped with edge computing.

• We strictly demonstrate the correctness of SA-MAD, including average, variance, covariance and linear regression with the help of modified four-prime encryption and superincreasing sequences. We prove that the modified four-prime BGN encryption algorithm achieves ciphertext indistinguishability under the composite order subgroup decision assumption, and also prove that SA-MAD achieves fault-tolerance and preserves the integrity of encrypted data. We finally conduct comprehensive performance evaluation to demonstrate its feasibility and outstanding advantages in the deployment of edge computing-based smart grids.

Homomorphic encryption is a common technique used by existing data aggregation schemes [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36]. By utilizing the homomorphic properties of encryption algorithms, data aggregation enables a control center of smart grids to compute some statistical results directly over aggregated ciphertext without decrypting each ciphertext from different smart meters, thereby protecting users’ privacy. In 2012, Lu et al. [26] exploited Paillier homomorphic cryptosystem [17] to design a privacy preserving aggregation scheme for secure smart grids. Their scheme supports sum computation for the control center due to the additive homomorphic property of Paillier cryptosystem, but does not support variance and other more complex statistical computations. Li et al. [27] also employed Paillier homomorphic cryptosystem and combine it with superincreasing sequences to propose a privacy preserving multi-subset aggregation scheme for smart grids. Their scheme can achieve the computation of total usage of power consumption in different ranges, and the computation of total users in corresponding range. However, the data integrity preservation is not considered in their scheme, which is also a critical security requirement. Wang et al. [28] extended the methods in [27] and added a procedure to update the blinding factors used by smart meters to achieve stronger security. Besides, their scheme also achieves fault tolerance to solve the situation that device malfunction or battery exhaustion. Wang et al. [37] proposed an identity-based data aggregation scheme for smart grids, they presented a new definition of an identity-based encryption and signature scheme, in which an identity-based encryption scheme and an identity-based signature scheme are combined into a single scheme that could share the same private and public parameters. The identity-based additive homomorphic encryption scheme in [29] is utilized in their scheme to be a basic component to encrypt and aggregate users’ data. Merad-Boudia et al. [30] proposed an efficient and secure multi-dimensional data aggregation scheme for fog computing-based smart grids. They also used Paillier cryptosystem to encrypt users’ power consumption data, and a binary encoding algorithm is integrated to aggregate multi-dimensional data. Liu et al. [31] proposed a privacy preserving aggregation scheme based on a double trapdoor decryption cryptosystem proposed in [38] and arithmetic circuit technique. In their scheme, the encrypted power data consumption can be outsourced to clouds while being efficiently aggregated by fog nodes. With the encrypted data, their scheme allows a requester (the control center or a service provider) to launch function query for its particular applications. Alsharif et al. [39] utilized masking technique to propose a privacy-preserving multi-dimensional and multi-subset data aggregation scheme. Their scheme can simultaneously achieve multi-dimensional data aggregation with multi-subset for each dimension. Chen et al. [32] proposed a data aggregation scheme for electric vehicle networks by designing an identity-based sequential aggregate signed data based on factoring and a threshold Paillier homomorphic encryption scheme. Lyu et al. [33] utilized the differential privacy and homomorphic encryption techniques to present a data aggregation scheme for smart grids with the aid of fog computing architecture. They used the Gaussian mechanism to distribute noise generation among parties to offer provable differential privacy guarantees of the aggregate statistic on both fog level and cloud level. Ding et al. [40] constructed an identity-based metering data aggregation scheme to achieve more efficient data integrity batch verification by a collector and the power service provider. Zhao et al. [34] introduced a somewhat homomorphic encryption scheme into the fog computing-based smart grids to present a data aggregation scheme with smart pricing and packing method. In recent, Zhang et al. [35] proposed an encrypted data aggregation scheme with lightweight verification in fog-assisted smart grids, which could address key-leakage resilient issue.

The remainder of the paper is organized as follows. Section 2 gives necessary preliminaries. Section 3 introduces the system framework and design goals. Section 4 gives modified four-prime BGN encryption algorithm and detailed construction of SA-MAD. In Section 5, we provide detailed security analysis, including privacy-preserving property and data integrity guarantee. In Section 6, we further provide the extension of SA-MAD. Section 7 gives a functionality comparison and comprehensive performance evaluation compared with existing schemes. Finally, in Section 8, we conclude our work.