Public Key Homomorphic Encryption Research Articles

Edge-Assisted Public Key Homomorphic Encryption for Preserving Privacy in Mobile Crowdsensing

Mobile crowdsensing (MCS) is becoming an increasingly important topic due to rapid proliferation of mobile apps where participants’ anonymity is a pivotal requirement with direct impacts on their safety and well being. There are two main challenges in crypto-based privacy-preserving aggregation in MCS, namely, participants joining or leaving the crowd randomly at will, and adversaries injecting fake data. The conventional approach for preserving privacy is to provide blanket anonymity to all, including adversaries, which enables the latter to cause harm without being identified. In addition, with the proliferation of edge servers, there is a need to develop edge-assisted MCS, which would be more efficient in terms of less back-haul traffic and less delay as compared to cloud-assisted-only MCS. In this paper, we present an efficient edge-assisted MCS scheme which preserves the participants’ privacy and anonymity, protects the service against adversaries, and can be used to verify that aggregation is free of anomalies. Our scheme is transparent to the join-and-leave problem; and its computational cost and communication overhead are small and fixed, i.e., it is insensitive to crowd count. We utilize group signature for source authentication to identify and block adversaries that cause harm while providing anonymity to ordinary participants.

EPMDA-FED: Efficient and Privacy-Preserving Multidimensional Data Aggregation Scheme With Fast Error Detection in Smart Grid

Smart grids bring advantages of reliabilty and high efficiency by real-time communication technologies in contrast to the traditional grids. However, smart grids also raise concerns about privacy and security for the individual fine-grained information collection. In order to guarantee privacy and securtiy in the grids, we propose an efficient and privacy-preserving multidimensional data aggregation scheme without a third trusted party and supporting fast error detection, named EPMDA-FED, in the paper. Firstly, we adopt Chinese Remainder Theorem to pack multidimensional data and encrypt the processed data using the keys generated by the negotiation among users and the control center. Secondly, our scheme is efficient for encryption without high-cost additive homomorphic public key encryption scheme, such as Paillier cryptosystem and supporting batch verification with fast error detection. Our proposed error detection algorithm is quite efficient with sublinear computation complexity. Besides, through security analysis, EPMDA-FED is semantically secure against collusion attack and the consistency of negotiated key, authenticity and data integrity of the users’ reports are guaranteed. Finally, performance evaluation shows EPMDA-FED is more efficient than existing competing approaches in terms of computation and communication overhead.

Cryptanalysis of an additively homomorphic public key encryption scheme

Based on the ElGamal cryptosystem, Bae et al. (J. Netw. Comput. Appl., vol. 59, pp. 333–344, 2016) proposed a new homomorphic encryption algorithm to reduce the network traffic and data processing time brought by their data communication and aggregation scheme. However, there is no security analysis of this encryption algorithm in their scheme. In this paper, we analyze the security of their proposed encryption algorithm and prove that it is not secure.

Privacy-Preserving Implicit Authentication Protocol Using Cosine Similarity for Internet of Things

Internet of Things provides complicated value-added services to mobile intelligent terminal users. Different sensors collect various data from the users and transmit the data to the mobile intelligent terminal for storage. Consequently, a great amount of personal and sensitive information related to these rich and colorful applications is stored in the mobile intelligent terminal. Mobile intelligent terminals have become the prominent target of network attackers. Security breach and privacy leakage severely thread the application development of the Internet of Things. We present a privacy-preserving implicit authentication framework using users' behavior features sensed by the mobile intelligent terminal based on the artificial intelligence methodology. More precisely, we first summarize the security and privacy requirements for the security authentication of the mobile intelligent terminal. Then, we present a privacy-preserving implicit authentication framework using the cosine similarity and partial homomorphic public-key encryption scheme. Finally, a performance evaluation of the proposed protocol is conducted. The result shows that the communication and computation efficiency of our protocol is more efficient than other related protocols.

Scalar Product Lattice Computation for Efficient Privacy-Preserving Systems

Privacy-preserving (PP) applications allow users to perform online daily actions without leaking sensitive information. The PP scalar product (PPSP) is one of the critical algorithms in many private applications. The state-of-the-art PPSP schemes use either computationally intensive homomorphic (public-key) encryption techniques, such as the Paillier encryption to achieve strong security (i.e., 128 b) or random masking technique to achieve high efficiency for low security. In this article, lattice structures have been exploited to develop an efficient PP system. The proposed scheme is not only efficient in computation as compared to the state-of-the-art but also provides a high degree of security against quantum attacks. Rigorous security and privacy analyses of the proposed scheme have been provided along with a concrete set of parameters to achieve 128-b and 256-b security. Performance analysis shows that the scheme is at least five orders faster than the Paillier schemes and at least twice as faster than the existing randomization technique at 128-b security. Also the proposed scheme requires six-time fewer data compared to the Paillier and randomization-based schemes for communications.

An Efficient NIZK Scheme for Privacy-Preserving Transactions Over Account-Model Blockchain

We introduce the abstract framework of decentralized smart contracts system with balance and transaction amount hiding property over account-model blockchain. To build a concrete system with such properties, we utilize a homomorphic public-key encryption scheme and construct a highly efficient non-interactive zero knowledge (NIZK) argument based upon the encryption scheme to ensure the validity of the transactions. Our NIZK scheme is perfect zero knowledge in the common reference string model, while its soundness holds in the random oracle model. Compared to previous similar constructions, our proposed NIZK argument dramatically improves the time efficiency in generating a proof, at the cost of relatively longer proof size.

Secure Edge Electricity Data Aggregation Scheme for Low Voltage Transformer Areas

The smart grid system is the physical power infrastructure integrated with many intelligent electronic devices. It supports the two-way flow of energy as well as information. The smart meters are important intelligent devices, which account for the largest portion among all terminals in the smart grid. In many application scenarios, the master station need high frequency total electricity consumption information of each low voltage transformer area. It requires frequent data interchange between smart meters and master station. However, the electric communication network cannot provide enough bandwidth resource to support such high frequency data interchange. Edge Computing Nodes (ECNs), which can be deployed at different low voltage transformer areas, can achieve the electricity data aggregation at the edge side. The communication resource can be saved since only aggregated electricity data will be uploaded to the master station. Traditional data aggregation scheme requires the plaintext from smart meters. From the viewpoint of security and privacy-preserving, it is not safe to implement the data decryption operation at edge side. Therefore, the data aggregation scheme with ciphertext is required at the edge side. In this paper, we propose a secure edge electricity data aggregation scheme based on homomorphic public key encryption techniques. The ECNs will implement the electricity data aggregation with the ciphertext from different smart meters, and the aggregated data will be transmitted to the master station through communication network. The mater station can use its public key to obtain the total electricity consumption of each low voltage transformer area.

Reversible Data Hiding Scheme in Homomorphic Encrypted Image Based on EC-EG

To combine homomorphic public key encryption with reversible data hiding, a reversible data hiding scheme in homomorphic encrypted image based on EC-EG is proposed. Firstly, the cover image is segmented. The square grid pixel group randomly selected by the image owner has one reference pixel and eight target pixels. The n least significant bits (LSBs) of the reference pixel and all bits of target pixel are self-embedded into other parts of the image by a method of predictive error expansion (PEE). To avoid overflowing when embedding data, the n LSBs of the reference pixel are reset to zero before encryption. Then, the pixel values of the image are encrypted after being encoded onto the points of the elliptic curve. The encrypted reference pixel replaces the encrypted target pixels surrounding it, thereby constructing the mirroring central ciphertext (MCC). In a set of MCC, the data hider embeds the encrypted additional data into the n LSBs of the target pixels by homomorphic addition in ciphertexts, while the reference pixel remains unchanged. The receiver can directly extract additional data by homomorphic subtraction in ciphertexts between the target pixels and the corresponding reference pixel; extract the additional data by subtraction in plaintexts with the directly decrypted image; and restore the cover image without loss. The experimental results show that the proposed scheme has higher security than the similar algorithms, and the average embedding rate of the scheme is 0.25 bpp under the premise of ensuring the quality of the directly decrypted image.

Fully Homomorphic Public-Key Encryption Against Ciphertext Square Attack with Two Ciphertexts

A fully homomorphic public-key encryption (FHPKE) is the important cryptosystem as the basic scheme for the cloud computing. Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, some fully homomorphic encryption schemes were proposed. In the systems proposed until now the bootstrapping process is the main bottleneck and the large complexity for computing the ciphertext is required. The existence of an efficient fully homomorphic cryptosystem would have great practical implications in the outsourcing of private computations, for instance, in the context of cloud computing. In recent year Yagisawa proposed fully homomorphic encryptions without bootstrapping which have the weak point in the enciphering function or not immune from “ciphertext square attack” which is the attack proposed in this article. In this article, a new FHPKE against “ciphertext square attack” is proposed which does not need the bootstrapping and does not require the large complexity for enciphering. The scheme has the following features; (a) its security bases on computational difficulty to solve the multivariate algebraic equations of high degrees; (b) it requires two ciphertexts corresponding to a plaintext. We describe concretely how to construct the proposed system over octonion ring. It is shown that proposed system is immune from “ciphertext square attack”, “m and -m attack” and the Gröbner basis attacks and the complexity to encipher and decipher is not large.

An experimental study of encrypted polynomial arithmetics for private set operations

Recent studies on the performance of private set operations have examined the use of homomorphic public-key encryption and the technique of representing sets as polynomials in a cryptographic model. These polynomial-based solutions require intensive polynomial arithmetic that exhibit quadratic computational complexity. In an effort to develop practical algorithms for private set operations, various well-known techniques such as Karatsuba’s algorithm or the fast Fourier transform (FFT) can be used to reduce the complexity of polynomial computations. The FFT appears to be the obvious best choice; however, the use of FFTs in the implementation of polynomial-based set operations may lead to certain subtle technical problems. These problems become particularly serious when the cardinality of the sets is dynamic. Furthermore, our experiment shows that Karatsuba’s algorithm delivers higher performance than the FFT in our application, provided that a reasonable response time is important. In addition, our experimental implementation demonstrates the heuristic bound on cardinality for which Karatsuba’s algorithm outperforms the FFT. This value can be used to determine the superior optimization techniques and settings in the deployment of private set operation schemes.

A Secure Cloud Storage using ECC-Based Homomorphic Encryption

This paper presents a new homomorphic public-key encryption scheme based on the elliptic curve cryptography (HPKE-ECC). This HPKE-ECC scheme allows public computation on encrypted data stored on a cloud in such a manner that the output of this computation gives a valid encryption of some operations (addition/multiplication) on original data. The cloud system (server) has only access to the encrypted files of an authenticated end-user stored in it and can only do computation on these stored files according to the request of an end-user (client). The implementation of proposed HPKE-ECC protocol uses the properties of elliptic curve operations as well as bilinear pairing property on groups and the implementation is done by Weil and Tate pairing. The security of proposed encryption technique depends on the hardness of ECDLP and BDHP.

Security and Privacy for Cloud-Based IoT: Challenges

The Internet of Things is increasingly becoming a ubiquitous computing service, requiring huge volumes of data storage and processing. Unfortunately, due to the unique characteristics of resource constraints, self-organization, and shortrange communication in IoT, it always resorts to the cloud for outsourced storage and computation, which has brought about a series of new challenging security and privacy threats. In this article, we introduce the architecture and unique security and privacy requirements for the next generation mobile technologies on cloud-based IoT, identify the inappropriateness of most existing work, and address the challenging issues of secure packet forwarding and efficient privacy preserving authentication by proposing new efficient privacy preserving data aggregation without public key homomorphic encryption. Finally, several interesting open problems are suggested with promising ideas to trigger more research efforts in this emerging area.

Blinded additively homomorphic encryption schemes for self-tallying voting

In this paper, we propose a self-tallying election protocol based public key homomorphic encryption. The additive homomorphism allows a set of participants (voters) to publish an encrypted value (ballot) and to compute the encrypted sum of all these values based on their ciphertexts. Our scheme has the particularity that anyone can decrypt the sum, but only once all participants have contributed to its computation. More precisely, the sum can be decrypted at all times, but remains blinded until all participants have contributed their vote, which contains a share of the unblinding key. Additionally, we propose an adaptation of Helios in order to provide self-tallying.

Fully homomorphic SIMD operations

At PKC 2010 Smart and Vercauteren presented a variant of Gentry's fully homomorphic public key encryption scheme and mentioned that the scheme could support SIMD style operations. The slow key generation process of the Smart---Vercauteren system was then addressed in a paper by Gentry and Halevi, but their key generation method appears to exclude the SIMD style operation alluded to by Smart and Vercauteren. In this paper, we show how to select parameters to enable such SIMD operations. As such, we obtain a somewhat homomorphic scheme supporting both SIMD operations and operations on large finite fields of characteristic two. This somewhat homomorphic scheme can be made fully homomorphic in a naive way by recrypting all data elements separately. However, we show that the SIMD operations can be used to perform the recrypt procedure in parallel, resulting in a substantial speed-up. Finally, we demonstrate how such SIMD operations can be used to perform various tasks by studying two use cases: implementing AES homomorphically and encrypted database lookup.

Homomorphic Encryption and Its Security Application

Homomorphic encryption scheme allows one to directly operate ciphertext without being able to decrypt and it has a wide application prospect. In this article we describe the typical encryption schemes including single-key homomorphic encryption scheme and public key homomorphic encryption scheme and then elaborate its application in the field of security, including the applications in database security, secure multi-party computation and the Internet of things. Finally, we discuss the research direction of homomorphic encryption.

A security framework for privacy-preserving data aggregation in wireless sensor networks

A formal treatment to the security of Concealed Data Aggregation (CDA) and the more general Private Data Aggregation (PDA) is given. While there exist a handful of constructions, rigorous security models and analyses for CDA or PDA are still lacking. Standard security notions for public key encryption, including semantic security and indistinguishability against chosen ciphertext attacks, are refined to cover the multisender nature and aggregation functionality of CDA and PDA in the security model. The proposed security model is sufficiently general to cover most application scenarios and constructions of privacy-preserving data aggregation. An impossibility result on achieving security against adaptive chosen ciphertext attacks in CDA/PDA is shown. A generic CDA construction based on public key homomorphic encryption is given, along with a proof of its security in the proposed model. The security of a number of existing schemes is analyzed in the proposed model.