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<p>Threshold Paillier encryption scheme finds extensive application in the context of federated learning. However, the issue of client dropout frequently arises within the context of federated learning, rendering the conventional threshold Paillier encryption scheme ineffective for data decryption. To address this issue, this paper introduces a (<i>N</i>,&#xa0;<i>k</i>,&#xa0;<i>d</i>)-reparable threshold Paillier encryption scheme by combining the reparable Shamir secret-sharing scheme with the Paillier encryption scheme. The proposed scheme has demonstrated several valuable capabilities. Specifically, we initially establish the security of the secret-sharing property of this scheme, namely, any group of <i>k</i> participants can collaboratively recover the private key, while <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10640_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(k-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> or fewer participants cannot recover the private key. Moreover, we demonstrate the scheme’s ability to handle the client dropout problem, namely, any group of <i>d</i> normal participants can collectively repair the private key segments of dropout clients. Ultimately, we substantiate that the (<i>N</i>,&#xa0;<i>k</i>,&#xa0;<i>d</i>)-reparable threshold Paillier encryption scheme consistently upholds the precision of decryption processes.</p>

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Reparable threshold Paillier encryption scheme for federated learning

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Yi Zhang,
  • Kun Tian,
  • Yunfan Lu,
  • Fengxia Liu,
  • Cheng Li,
  • Zixian Gong,
  • Zhe Hu,
  • Jia Li,
  • Qun Xu

摘要

Threshold Paillier encryption scheme finds extensive application in the context of federated learning. However, the issue of client dropout frequently arises within the context of federated learning, rendering the conventional threshold Paillier encryption scheme ineffective for data decryption. To address this issue, this paper introduces a (N, k, d)-reparable threshold Paillier encryption scheme by combining the reparable Shamir secret-sharing scheme with the Paillier encryption scheme. The proposed scheme has demonstrated several valuable capabilities. Specifically, we initially establish the security of the secret-sharing property of this scheme, namely, any group of k participants can collaboratively recover the private key, while \(k-1\) k - 1 or fewer participants cannot recover the private key. Moreover, we demonstrate the scheme’s ability to handle the client dropout problem, namely, any group of d normal participants can collectively repair the private key segments of dropout clients. Ultimately, we substantiate that the (N, k, d)-reparable threshold Paillier encryption scheme consistently upholds the precision of decryption processes.