The clustering algorithm is a useful tool for analyzing medical data. For instance, the k-means clustering can be used to study precipitating factors of a disease. In order to implement the clustering algorithm efficiently, data computation is outsourced to cloud servers, which may leak the private data. Encryption is a common method for solving this problem. But cloud servers are difficult to calculate ciphertexts from multiple parties. Hence, we choose multi-key fully homomorphic encryption (FHE), which supports computations on the ciphertexts that have different secret keys, to protect the private data. In this paper, based on Chen's multi-key FHE scheme, we first propose secure squared euclidean, comparison, minimum, and average protocols. Then, we design the basic and advanced schemes for implementing the secure multi-party k-means clustering algorithm. In the basic scheme, the implementation of homomorphic multiplication includes the process of transforming ciphertexts under different keys. In order to implement homomorphic multiplication efficiently, the advanced scheme uses an improved method to transform ciphertexts. Meanwhile, almost all computations are completely outsourced to cloud servers. We prove that the proposed protocols and schemes are secure and feasible. Simulation results also show that our improved method is helpful for improving the homomorphic multiplication of Chen's multi-key FHE scheme.

As the general development trend of the automotive industry, connected and autonomous vehicles (CAVs) can be used to increase transportation safety, promote mobility choices, reduce user costs, and create new job opportunities. However, with the increasing level of connectivity and automation, malicious users are able to easily implement different kinds of attacks, which threaten the security of CAVs. Hence, this paper provides a comprehensive survey on the cyber-security in the environment of CAVs with the aim of highlighting security problems and challenges. Firstly, based on the types of communication networks and attack objects, it classifies various cyber-security risks and vulnerabilities in the environment of CAVs into in-vehicle network attacks, vehicle to everything network attacks, and other attacks. Next, it regards cyber-risk as another type of attacks in the environment of CAVs. Then, it describes and analyzes up-to-date corresponding defense strategies for securing CAVs. In addition, it concludes several available cyber-security and safety standards of CAVs, which is helpful for the practical application of CAVs. Finally, several challenges and open problems are discussed for the future research.

Digital signature is a major component of transactions on Blockchain platforms, especially in enterprise Blockchain platforms, where multiple signatures from a set of peers need to be produced to endorse a transaction. However, such process is often complex and time-consuming. Multi-signature, which can improve transaction efficiency by having a set of signers cooperate to produce a joint signature, has attracted extensive attentions. In this work, we propose two multi-signature schemes, GMS and AGMS, which are proved to be more secure and efficient than state-of-the-art multi-signature schemes. Besides, we implement the proposed schemes in a real Enterprise Blockchain platform, Fabric. Experiment results show that the proposed AGMS scheme helps achieve the goal of high transaction efficiency, low storage complexity, as well as high robustness against rogue-key attacks and $k$ -sum problem attacks.

Abstract Based on the learning with errors over rings (RLWE) assumption, a leveled fully homomorphic encryption (FHE) by the approximate eigenvector method under the same public key is proposed, which security can be reduced to the shortest vector problem on ideal lattices in the worst case. And the leveled FHE under different public keys is realized by the secret key switching without dimension reduction. Combine the public key of leveled FHE with the identity, we bring forward an efficient identity‐based leveled FHE scheme from the RLWE assumption. The security analysis shows that our identity‐based leveled FHE scheme is selective‐ID secure against chosen‐plaintext attacks in the random oracle model. And the efficiency analysis and simulation results show that the proposed identity‐based leveled FHE scheme is much more efficient than Gentry's and Wang's identity‐based cryptosystems based on the learning with errors assumption. Copyright © 2016 John Wiley & Sons, Ltd.