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Flexible Threshold Multi-client Functional Encryption for Inner Product in Federated Learning

Ruyuan Zhang, Jinguang Han, Liqun Chen

TL;DR

The paper tackles privacy in federated learning by addressing gradient leakage through multi-client functional encryption for inner products (MCFE-IP). It introduces FTMCFE-IP, a noninteractive, flexible-threshold scheme based on an asymmetric Type-III pairing that supports client dropout while enabling an authorized user to compute inner products from ciphertexts and functional keys. The authors provide formal definitions, a concrete construction, and a security proof under SXDH/DDH assumptions, complemented by an implementation and experimental evaluation. The approach offers a robust, scalable path to privacy-preserving FL with dynamic participation, reducing setup overhead and maintaining strong cryptographic guarantees for restricted data access.

Abstract

Federated learning (FL) is a distributed machine learning paradigm that enables multiple clients to collaboratively train a shared model without disclosing their local data. To address privacy issues of gradient, several privacy-preserving machine-learning schemes based on multi-client functional encryption (MCFE) have been proposed. However, existing MCFE-based schemes cannot support client dropout or flexible threshold selection, which are essential for practical FL. In this paper, we design a flexible threshold multi-client functional encryption for inner product (FTMCFE-IP) scheme, where multiple clients generate ciphertexts independently without any interaction. In the encryption phase, clients are able to choose a threshold flexibly without reinitializing the system. The decryption can be performed correctly when the number of online clients satisfies the threshold. An authorized user are allowed to compute the inner product of the vectors associated with his/her functional key and the ciphertext, respectively, but cannot learning anything else. Especially, the presented scheme supports clients drop out. Furthermore, we provide the definition and security model of our FTMCFE-IP scheme,and propose a concrete construction. The security of the designed scheme is formally proven. Finally, we implement and evaluate our FTMCFE-IP scheme.

Flexible Threshold Multi-client Functional Encryption for Inner Product in Federated Learning

TL;DR

The paper tackles privacy in federated learning by addressing gradient leakage through multi-client functional encryption for inner products (MCFE-IP). It introduces FTMCFE-IP, a noninteractive, flexible-threshold scheme based on an asymmetric Type-III pairing that supports client dropout while enabling an authorized user to compute inner products from ciphertexts and functional keys. The authors provide formal definitions, a concrete construction, and a security proof under SXDH/DDH assumptions, complemented by an implementation and experimental evaluation. The approach offers a robust, scalable path to privacy-preserving FL with dynamic participation, reducing setup overhead and maintaining strong cryptographic guarantees for restricted data access.

Abstract

Federated learning (FL) is a distributed machine learning paradigm that enables multiple clients to collaboratively train a shared model without disclosing their local data. To address privacy issues of gradient, several privacy-preserving machine-learning schemes based on multi-client functional encryption (MCFE) have been proposed. However, existing MCFE-based schemes cannot support client dropout or flexible threshold selection, which are essential for practical FL. In this paper, we design a flexible threshold multi-client functional encryption for inner product (FTMCFE-IP) scheme, where multiple clients generate ciphertexts independently without any interaction. In the encryption phase, clients are able to choose a threshold flexibly without reinitializing the system. The decryption can be performed correctly when the number of online clients satisfies the threshold. An authorized user are allowed to compute the inner product of the vectors associated with his/her functional key and the ciphertext, respectively, but cannot learning anything else. Especially, the presented scheme supports clients drop out. Furthermore, we provide the definition and security model of our FTMCFE-IP scheme,and propose a concrete construction. The security of the designed scheme is formally proven. Finally, we implement and evaluate our FTMCFE-IP scheme.
Paper Structure (18 sections, 1 theorem, 29 equations, 8 figures, 2 tables)

This paper contains 18 sections, 1 theorem, 29 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Functional Encryption
  4. FE for Federated Learning
  5. Our Contributions
  6. Organization
  7. Preliminaries
  8. Bilinear Groups
  9. Complexity Assumptions
  10. System Model
  11. Formal Definition
  12. Security Model
  13. Concrete Construction of Our FTMCFE-IP scheme
  14. Degree-check Technique
  15. Main Construction
  16. ...and 3 more sections

Key Result

Theorem 1

The above FTMCFE-IP scheme is sta-IND secure in the random oracle model if the SXDH assumption holds on $\left( G,\hat{G},G_T,e,p \right)$. For any PPT adversary $\mathcal{A}$ with running time $t$, we have where $Q_1 \text{ and } Q_2$ denote the number of queries to hash oracles $H_1$ and $H_2$, respectively. $t_{G}$ and $t_{\hat{G}}$ represent the computational time for performing an exponentia

Figures (8)

  • Figure 1: The framework of our FTMCFE-IP scheme.
  • Figure 2: Security model of our FTMCFE-IP scheme.
  • Figure 3: The $\mathbf{Setup}$ algorithm of our FTMCFE-IP scheme
  • Figure 4: The $\mathbf{PKeyGen}$ algorithm of our FTMCFE-IP scheme
  • Figure 5: The $\mathbf{Enc}$ algorithm of our FTMCFE-IP scheme
  • ...and 3 more figures

Theorems & Definitions (7)

  • Definition 1: Bilinear Groups IBE
  • Definition 2: Decisional Diffie-Hellman Assumption (DDH) DDMCFE2020
  • Definition 3: Multi-DDH DMCFE2018
  • Definition 4: Symmetric eXternal Diffie-Hellman Assumption (SXDH) DDFE2025
  • Definition 5: Flexible Threshold Multi-client Functional Encryption for Inner Product (FTMCFE-IP)
  • Definition 6
  • Theorem 1: sta-IND-Security