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Robust Decentralized Multi-client Functional Encryption: Motivation, Definition, and Inner-Product Constructions

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14442))

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Abstract

Decentralized Multi-Client Functional Encryption (DMCFE) is a multi-user extension of Functional Encryption (FE) without relying on a trusted third party. However, a fundamental requirement for DMCFE is that the decryptor must collect the partial functional keys and the ciphertexts from all clients. If one client does not generate the partial functional key or the ciphertext, the decryptor cannot obtain any useful information. We found that this strong requirement limits the application of DMCFE in scenarios such as statistical analysis and machine learning.

In this paper, we first introduce a new primitive named Robust Decentralized Multi-Client Functional Encryption (RDMCFE), a notion generalized from DMCFE that aims to tolerate the problem of negative clients leading to nothing for the decryptor, where negative clients represent participants that are unable or unwilling to compute the partial functional key or the ciphertext. Conversely, a client is said to be a positive one if it is able and willing to compute both the partial functional key and the ciphertext. In RDMCFE scheme, the positive client set S is known by each positive client such that the generated partial functional keys help to eliminate the influence of negative clients, and the decryptor can learn the function value corresponding to the sensitive data of all positive clients when the cardinality of the set S is not less than a given threshold. We present such constructions for functionalities corresponding to the evaluation of inner products.

  1. 1.

    We provide a basic RDMCFE construction through the technique of double-masking structure, which is inspired by the work of Bonawitz et al. (CCS 2017). The storage and communication overheads of the construction are small and independent of the length of the vector. However, in the basic construction, for the security guarantee, one set of secret keys can be used to generate partial functional keys for only one function.

  2. 2.

    We show how to design the enhanced construction so that partial functional keys for different functions can be generated with the same set of secret keys, at the cost of increasing storage and communication overheads. Specifically, in the enhanced RDMCFE construction, we protect the mask through a single-input FE scheme and a threshold secret sharing scheme having the additively homomorphic property.

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Notes

  1. 1.

    This form implies that under the same threshold t and the set [n], the algorithm \({\textsf{SS}}.\textsf{Share}(\cdot ,t,[n])\) is run m times, where each time inputting a component of the vector \(\boldsymbol{r}_i\), and m shares with the same subscript are combined into a vector \(\boldsymbol{r}_{i,j}\).

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Acknowledgements

We would like to thank the anonymous reviewers for their invaluable comments. This work is supported by the National Natural Science Foundation of China (Nos. 61960206014, 62121001 and 62172434), and China 111 Project (No. B16037). Willy Susilo was partially supported by the Australian Research Council (ARC) Discovery project (DP200100144) and the Australian Laureate Fellowship (FL230100033). Fuchun Guo was partially supported by the Australian Future Fellowship (FT220100046).

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Authors and Affiliations

  1. State Key Laboratory of Integrated Service Networks (ISN), Xidian University, Xi’an, 710071, China

    Yamin Li & Xiaofeng Chen

  2. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, 450001, China

    Jianghong Wei

  3. School of Computing and Information Technology, University of Wollongong, Wollongong, NSW, 2522, Australia

    Fuchun Guo & Willy Susilo

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  1. Yamin Li
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  3. Fuchun Guo
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Correspondence to Xiaofeng Chen .

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  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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Li, Y., Wei, J., Guo, F., Susilo, W., Chen, X. (2023). Robust Decentralized Multi-client Functional Encryption: Motivation, Definition, and Inner-Product Constructions. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14442. Springer, Singapore. https://doi.org/10.1007/978-981-99-8733-7_5

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