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PADER: Paillier-based Secure Decentralized Social Recommendation

Chaochao Chen, Jiaming Qian, Fei Zheng, Yachuan Liu

TL;DR

PADER tackles privacy in recommendation systems by moving to a decentralized setting and employing Paillier Additive Homomorphic Encryption to securely train and infer a SoReg-based social recommender. It moves beyond simple bipartite decompositions by introducing secure arithmetic circuits and random-masking techniques, enabling secure evaluation of arbitrary polynomials with fixed-point real-valued data. A data-packing framework optimizes both computation and communication, and a natural-order computation approach further reduces overhead, yielding practical performance on real datasets. Experiments show comparable accuracy to plaintext training while substantially reducing communication and outperforming CKKS baselines in typical network conditions. The work provides a scalable, privacy-preserving alternative for decentralized social recommendation with open-source code.

Abstract

The prevalence of recommendation systems also brings privacy concerns to both the users and the sellers, as centralized platforms collect as much data as possible from them. To keep the data private, we propose PADER: a Paillier-based secure decentralized social recommendation system. In this system, the users and the sellers are nodes in a decentralized network. The training and inference of the recommendation model are carried out securely in a decentralized manner, without the involvement of a centralized platform. To this end, we apply the Paillier cryptosystem to the SoReg (Social Regularization) model, which exploits both user's ratings and social relations. We view the SoReg model as a two-party secure polynomial evaluation problem and observe that the simple bipartite computation may result in poor efficiency. To improve efficiency, we design secure addition and multiplication protocols to support secure computation on any arithmetic circuit, along with an optimal data packing scheme that is suitable for the polynomial computations of real values. Experiment results show that our method only takes about one second to iterate through one user with hundreds of ratings, and training with ~500K ratings for one epoch only takes <3 hours, which shows that the method is practical in real applications. The code is available at https://github.com/GarminQ/PADER.

PADER: Paillier-based Secure Decentralized Social Recommendation

TL;DR

PADER tackles privacy in recommendation systems by moving to a decentralized setting and employing Paillier Additive Homomorphic Encryption to securely train and infer a SoReg-based social recommender. It moves beyond simple bipartite decompositions by introducing secure arithmetic circuits and random-masking techniques, enabling secure evaluation of arbitrary polynomials with fixed-point real-valued data. A data-packing framework optimizes both computation and communication, and a natural-order computation approach further reduces overhead, yielding practical performance on real datasets. Experiments show comparable accuracy to plaintext training while substantially reducing communication and outperforming CKKS baselines in typical network conditions. The work provides a scalable, privacy-preserving alternative for decentralized social recommendation with open-source code.

Abstract

The prevalence of recommendation systems also brings privacy concerns to both the users and the sellers, as centralized platforms collect as much data as possible from them. To keep the data private, we propose PADER: a Paillier-based secure decentralized social recommendation system. In this system, the users and the sellers are nodes in a decentralized network. The training and inference of the recommendation model are carried out securely in a decentralized manner, without the involvement of a centralized platform. To this end, we apply the Paillier cryptosystem to the SoReg (Social Regularization) model, which exploits both user's ratings and social relations. We view the SoReg model as a two-party secure polynomial evaluation problem and observe that the simple bipartite computation may result in poor efficiency. To improve efficiency, we design secure addition and multiplication protocols to support secure computation on any arithmetic circuit, along with an optimal data packing scheme that is suitable for the polynomial computations of real values. Experiment results show that our method only takes about one second to iterate through one user with hundreds of ratings, and training with ~500K ratings for one epoch only takes <3 hours, which shows that the method is practical in real applications. The code is available at https://github.com/GarminQ/PADER.
Paper Structure (49 sections, 3 theorems, 39 equations, 8 figures, 2 tables, 2 algorithms)

This paper contains 49 sections, 3 theorems, 39 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Decentralized and Privacy-Preserving Recommendation
  4. Secure Computation
  5. Preliminaries
  6. Social Regularization Model
  7. Homomorphic Encryption
  8. Secure Computation based on AHE
  9. Fixed-Point Arithmetics
  10. Bipartite Decomposition
  11. Inefficiency of bipartite Computation
  12. Arithmetic Circuit
  13. Local Computation
  14. Level of the Variable
  15. Two-party Secure Addition and Multiplication
  16. ...and 34 more sections

Key Result

Theorem 1

Suppose that $x_1, \cdots, x_n$ are $n$ integers satisfying $P^{n} \le N$, $f(x_i, \mathbf y) < P$, and $x_i$'s degree is less than 2 in $f(x_i, \mathbf y)$, then eq:correct-pack holds.

Figures (8)

  • Figure 1: Illustration of centralized and decentralized recommendation systems.
  • Figure 2: Illustration of our packing method.
  • Figure 3: Results on different numbers of rated items, where the embedding dimension is 8 and the number of social connections is 10. The y-axis is in log-scale.
  • Figure 4: Results on different embedding dimensions, where the number of rated items is 8 and the number of social connections is 10. The y-axis is in log-scale.
  • Figure 5: Results on inference tasks.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 1
  • Example 1
  • Remark
  • Definition 2: Arithmetic circuit of a polynomial
  • Example 2
  • Theorem 1: Packed computation on integer
  • proof
  • Theorem 2
  • Proposition 1
  • proof