Abstract

As the world grapples with the COVID-19 and its variants, multi-user collaboration by means of cloud computing is ubiquitous. How to make better use of cloud resources while preventing user privacy leakage has become particularly important. Multi-key homomorphic encryption(MKHE) can effectively deal with the privacy disclosure issue during the multi-user collaboration in the cloud computing setting. Firstly, we improve the DGHV homomorphic scheme by modifying the selection of key and the coefficients in encryption, so as to eliminate the restriction on the parity of the ciphertext modulus in the public key. On this basis, we further propose a DGHV-type MKHE scheme based on the number theory. In our scheme, an extended key is introduced for ciphertext extension, and we prove that it is efficient in performance analysis. The semantic security of our schemes is proved under the assumption of error-free approximate greatest common divisor and the difficulty of large integer factorization. Furthermore, the simulation experiments show the availability and computational efficiency of our MKHE scheme. Therefore, our scheme is suitable for the multi-user scenario in cloud environment.

Introduction

In the post-pandemic era, telecommuting has become an indispensable working mode, and emerging technologies such as cloud computing have played an important role in epidemic monitoring, prevention and control and medical assistance, showing broader application prospects and growth potential [1], [2]. According to Gartner, from 2015 to 2020, the penetration rate of global cloud computing market represented by IaaS, PaaS and SaaS increased year by year from 4.3% to 13.1%, and will rise to 15.3% in the next year. The market size is 208.3 billion dollars in 2020 and will exceed 600 billion dollars in 2025 [3].

Cloud services can eliminate the storage space constraints of personal devices and reduce local computing overhead. In practice, different companies or organizations store data in the cloud and use the cloud to share data with other members. Designing a one-to-many data sharing scheme based on attribute-based encryption(ABE) [4], [5] can achieve effective access control, but ABE is not suitable for collaborative computing between multiple members in a cloud environment. At the same time, multiple clients want to use the computing power of the cloud server to perform machine learning and data mining, collaboratively solve optimization problems and obtain optimal results. However, uploading user data to the server and training the model on the server may lead to serious user privacy disclosure. For example, in 2021, the registration information of Alibaba Cloud users was leaked, in 2022, 37 GB source code of Microsoft was leaked, and 170 million data of super star learning APP was illegally sold. The losses caused by global cybercrime more than 6 trillion in 2021, about six times as much as in 2020. With frequent privacy disclosure, the public pays more attention to privacy protection. In order to make better use of cloud services, we need a method to process data safely in the cloud environment.

Conclusion

Considering the diversity of users in the cloud computing environment, MKHE supports information storage and sharing and secure homomorphic calculation from different users. It is more suitable to solve privacy and security issues in the cloud computing, which is of great practical significance. However, the existing MKHE schemes weaken the functionality of MKHE in the expansion of ciphertext dimension and computational complexity. In this paper, we first improve the DGHV scheme [11] and propose a DGHV-type MKHE scheme. Compared with the original DGHV scheme, on the premise of ensuring security, an extended key is introduced to expand the function of the scheme. Compared with other MKHE schemes, our scheme is easier to understand in ciphertext composition and calculation form. In addition, in the experiment, the cubic form is used to reduce the public key size of the scheme to ?(? 3 ). Through experiments, we evaluate the generation time of the keys, storage capacity, expansion and homomorphic operation. However, introducing a trusted KGC when generating joint key may be difficult to meet in some practical applications. Whether to cancel the setting of KGC in joint key distribution is an important research content. We should also strive to make MKHE better applicable to the cloud environment.