As an important cryptographic primitive in cloud computing and outsourced computing, fully homomorphic encryption (FHE) is an animated area in modern cryptography. However, the efficiency of FHE has been a bottleneck that impeding its application. According to Gentry's blueprint, bootstrapping, which is used to control the noise propagation in ciphertexts, is the most important process in FHE. However, bootstrapping is also the most expensive process that affects the scheme's efficiency. This paper has made three improvements to accelerate the bootstrapping. Firstly, as hundreds of serial homomorphic additions take most of the time of bootstrapping, we constructed the logical expression using truth table to reduce the amount of serial homomorphic additions by two-thirds and thus proposed an efficient FHE scheme with bootstrapping within 10 ms. Secondly, the most expensive parts in our bootstrapping, enhanced homomorphic constant multiplication and homomorphic addition, can be implemented in parallel, which may accelerate the bootstrapping. At last, we proposed a set of more efficient combinations of parameters. Analysis shows that our scheme's security level is 128 bits and the correctness is improved compared with CGGI16 scheme in ASIACRYPT 2016. Experiments show that the running time of bootstrapping in this paper is within 10 ms, which is only 52% of CGGI16, and is less than CGGI17 in ASIACRYPT 2017.

To ensure no private information is leaked in the aggregation phase in federated learning (FL), many frameworks use homomorphic encryption (HE) to mask local model updates. However, the heavy overheads of these frameworks make them unsuitable for cross-device FL, where the clients are a huge number of mobile and edge devices with limited computing resources. Even worse, some of them also fail to manage the dynamic changes of clients. To overcome these shortcomings, we propose a threshold multi-key HE scheme tMK-CKKS and design an efficient and robust privacy-preserving FL framework. Robustness means that our framework allows clients to join in or drop out during the training process. Besides, because our tMK-CKKS scheme can pack multiple messages in a single ciphertext, our framework significantly reduces the computation and communication overhead. Moreover, the threshold mechanism in tMK-CKKS ensures that our framework can resist collusion attacks between the server and no more than t (threshold value) curious internal clients. Finally, we implement our framework in FedML and conduct extensive experiments to evaluate our framework. Utility evaluations on 6 benchmark datasets show that our framework can protect privacy without sacrificing the model accuracy. Efficiency evaluations on 4 typical deep learning models demonstrate that: our framework can speed up the computation by at least 1.21 $$\times $$× over xMK-CKKS-based framework, 15.84 $$\times $$× over Batchcrypt-based framework, and 20.30 $$\times $$× over CRT-Paillier-based framework. Our framework can reduce the communication burden by at least 8.61 MB over Batchcrypt-based framework, 35.36 MB over xMK-CKKS-based framework and 42.58 MB over CRT-Paillier-based framework. The advantages in both computation and communication expand with the size of deep learning models.

Privacy-preserving multidimensional data aggregation (MDA) aggregates the data of all different users into a single value, preventing the leakage of personal data while ensuring its availability. However, most current MDA schemes only consider sum operations, i.e., the message of each dimension in the aggregation result is the sum of the corresponding dimensional messages of all individual message vectors. We propose an MDA scheme with fine-grained linear homomorphism, called MDA-FLH. First, we construct a fine-grained linear homomorphic encryption scheme which can assign different weights to each dimension of user’s data and maintain the linear homomorphic property in each dimension. We combine the Chinese remainder theorem (CRT) and Paillier encryption to encode the multidimensional data with CRT and assign different weights to each dimension of user’s data in the Paillier ciphertext. Second, our scheme has the property of fault tolerance. In conjunction with the extended Shamir’s threshold secret-sharing scheme, a security-enhanced and fault-tolerant data aggregation method has been designed so that it is resistant to internal attacks such as the control center (CC) access to individual private data if given the corresponding ciphertext. Finally, two practical schemes are designed based on MDA-FLH: 1) fine-grained electricity price statistics scheme and 2) multistep electricity price statistics scheme. Security analysis shows that our scheme can achieve privacy, confidentiality, integrity, and source authentication. Performance analysis shows that our scheme is efficient, especially that smart meters (SMs) are computationally economic, which makes our scheme more suitable for resource-constrained SM. Also, our scheme can provide linear homomorphism operations on each dimension, which further expands its applications.

This article focuses on the distributed cooperative compound tracking issue of the vehicular platoon. First, a definition, called compound tracking control, is proposed, which means that the practical finite-time stability and asymptotical convergence can be simultaneously satisfied. Then, a modified performance function, named finite-time performance function, is designed, which possesses the faster convergence rate compared to the existing ones. Moreover, the adaptive neural network (NN), prescribed performance technique, and backstepping method are utilized to design a distributed cooperative regulation protocol. It is worth noting that the convergence time of the proposed algorithm does not depend on the initial values and design parameters. Finally, simulation experiments are given to further verify the effectiveness of the presented theoretical findings.

Multi-Key Full Homomorphic Encryption (MKFHE) can perform arbitrary operations on encrypted data under different public keys (users), and the final ciphertext can be jointly decrypted by all involved users. Therefore, MKFHE has natural advantages and application value in security multi-party computation (MPC). The MKFHE scheme based on Brakerski-Gentry-Vaikuntanathan (BGV) inherits the advantages of BGV FHE scheme in aspects of encrypting a ring element, the ciphertext/plaintext ratio, and supporting the Chinese Remainder Theorem (CRT)-based ciphertexts packing technique. However some weaknesses also exist such as large ciphertexts and keys, and complicated process of generating evaluation keys. In this paper, we present an efficient BGV-type MKFHE scheme. Firstly, we construct a nested ciphertext extension for BGV and separable ciphertext extension for Gentry-Sahai-Waters (GSW), which can reduce the size of the extended ciphertexts about a half. Secondly, we apply the hybrid homomorphic multiplication between RBGV ciphertext and RGSW ciphertext to the generation process of evaluation keys, which can significantly reduce the amount of input/output ciphertexts and improve the efficiency. Finally, we construct a directed decryption protocol which allows the evaluated ciphertext to be decrypted by any target user, thereby enhancing the ability of data owner to control their own plaintext, and abolish the limitation in current MKFHE schemes that the evaluated ciphertext can only be decrypted by users involved in homomorphic evaluation.

Combining multi-key fully homomorphic encryption (MKFHE) and identity-based encryption (IBE) to construct multi-identity based fully homomorphic encryption (MIBFHE) scheme can not only realize homomorphic operations and flexible access control on identity ciphertexts but also reduce the burden of public key certification management. However, MKFHE schemes used to construct MIBFHE usually have complex construction and large computational complexity, which also causes the same problem for MIBFHE schemes. To solve this problem, we construct a concise and efficient MIBFHE scheme based on the learning with errors (LWE) problem. Firstly, we construct an MKFHE scheme using a new method called “the decomposition method”. Secondly, we make an appropriate deformation of the current IBE scheme. Finally, we combine the above MKFHE scheme with IBE scheme to construct our MIBFHE scheme and prove its IND-sID-CPA security under the LWE assumption in the random oracle model. The analysis results show that our MIBFHE scheme can generate the extended ciphertext directly from the encryption algorithm, without generating fresh ciphertext in advance. In addition, the noise expansion rate is reduced from the polynomial of lattice dimension n and modulus q to the constant K of the maximum number of users. The scale of introduced auxiliary ciphertexts is reduced from Õ( n ⁴ L ⁴ ) to Õ( n ² L ⁴ ) when generating the extended ciphertext.