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Verifiable privacy-preserving cox regression from multi-key fully homomorphic encryption

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Abstract

While it is well known that privacy-preserving cox regression generally consists of a semi-honest cloud service provider (CSP) who performs curious-but-honest computations on ciphertexts to train the cox model. No one can verify the behaviors of CSP when he performs computations dishonestly in reality. Focusing on this problem, we propose a verifiable privacy-preserving cox regression algorithm tailored with the semi-malicious CSP, where all his behaviors are recorded on a witness tape fulfilling the requirement of transparency. To be specific, a multi-key fully homomorphic encryption (FHE) is used to protect the information of different data owners. The verifiability of our proposed multi-key homomorphic message authenticator (HMAC) ensures CSP sends correct results back to data owners. Furthermore, the compactness of FHE and succinctness of HMAC both under multi keys make the cox regression scheme more feasible. The efficiency of our proposed cox regression scheme is also proved by both theoretical analyses and experimental evaluations. After 21 iterations, it costs no more than 10 min to evaluate our cox regression scheme.

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Data Availability

No new data were generated or analysed in support of this research.

Notes

  1. When level \(D_i=D\), ignore the subscript of \(pk=(\varvec{b}_{D_i}^T, \varvec{a}_{D_i}^T)\), and denote the public key with \(pk=(\varvec{b}^T, \varvec{a}^T)\) for simplicity.

  2. For simplicity, we just take multilinear map \(\mathfrak {e}\) ignoring the subscripts, since the subscripts seem to have no effect on the function of multilinear maps.

  3. Any two authenticators \(\widehat{\varvec{\sigma }_1}, \widehat{\varvec{\sigma }_2}\) can be changed into same space \(\mathbb {R}_p\times \mathbb {G}_i\times \mathbb {G}_i\): by multiplying the authenticator with underlying message 1, i.e. \(\sigma _U\). Moreover, the i-level encoding is \(\varPhi _i=\mathfrak {e}(\varPhi _{i-1}, g_1^a)\) for integer \(i\ge 2\).

  4. In order to highlight the number of modular products, some numbers are outside the \(O(\cdot )\).

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Funding

This research was funded by Sichuan Science and Technology Program under Grant No.2023NSFSC1396, and Stability Program of National Key Laboratory of Security Communication(2023) under Grant No.M3023Y327.

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Authors and Affiliations

  1. National Key Laboratory of Security Communication, Chengdu, 610041, China

    Wenju Xu, Xin Li & Wei Zhao

  2. Engineering University of People’s Armed Police, Xi’an, 710086, China

    Yunxuan Su

  3. The State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    Baocang Wang

Authors
  1. Wenju Xu
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  2. Xin Li
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  3. Yunxuan Su
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  4. Baocang Wang
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Contributions

Wenju Xu: Validation, Formal analysis, Writing-original draft. Xin Li: Software. Yunxuan Su: Software. Baocang Wang: Conceptualization, Methodology, Supervision. Wei Zhao: Writing-review & editing.

Corresponding author

Correspondence to Wenju Xu.

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This article is part of the Topical Collection: Special Issue on 2 - Track on Security and Privacy

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Xu, W., Li, X., Su, Y. et al. Verifiable privacy-preserving cox regression from multi-key fully homomorphic encryption. Peer-to-Peer Netw. Appl. 17, 3182–3199 (2024). https://doi.org/10.1007/s12083-024-01740-9

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