We propose a novel end-to-end privacy-preserving framework, instantiated by three efficient protocols for different deployment scenarios, covering both input and output privacy, for the vertically split scenario in federated learning (FL), where features are split across clients and labels are not shared by all parties. We do so by distributing the role of the aggregator in FL into multiple servers and having them run secure multiparty computation (MPC) protocols to perform model and feature aggregation and apply differential privacy (DP) to the final released model. While a naive solution would have the clients delegating the entirety of training to run in MPC between the servers, our optimized solution, which supports purely global and also global-local models updates with privacy-preserving, drastically reduces the amount of computation and communication performed using multiparty computation. The experimental results also show the effectiveness of our protocols.
Figures & tables
Figure 1. Training a Global model with Frozen Local models under Gaussian Mechanism with Shuffling
Figure 2. Training a Global model with Frozen Local models under Banded Matrix Factorization Mechanism
Figure 3. Training a Global model and Local models under Banded Matrix Factorization Mechanism
Dataset
Method
Pre-ImageNet
Pre-Cifar100
CIFAR-10
Non-DP
Non-DP
Plain
90.01
91.42
DP
DP
ε=1
ε=2
ε=5
ε=8
ε=10
ε=1
ε=2
ε=5
ε=8
ε=10
G-Shuff
69.38
71.78
73.27
73.69
73.76
81.19
81.51
81.62
81.67
81.69
G-BMF (Setting 1)
69.25
70.73
71.19
71.22
71.24
77.22
77.28
77.31
77.34
77.37
Table 1. Test Accuracy ( % ) versus Different Datasets, Pre-training, and Privacy Budgets (20 epochs)
Dataset
ϵ
Method
G-Shuff
G-BMF (Setting 1)
G-BMF (Setting 2)
GL-BMF (Setting 1)
GL-BMF (Setting 2)
LDP-G
LDP-GL
CIFAR-10
1
63.71
65.14
49.14
65.97
51.32
10.29
10.56
2
69.09
70.66
55.16
71.23
56.26
11.14
11.36
5
71.93
73.63
61.47
74.09
62.29
16.69
17.14
8
72.89
74.25
64.42
74.59
65.32
23.97
24.51
10
73.88
74.41
65.85
74.78
66.61
28.16
28.89
Table 2. Test Accuracy ( % ) versus Different Privacy Budgets, LDP (100 epochs)
Dataset
ϵ
Method
G-Shuff
G-BMF
GL-BMF
ADMM
FedBCD
Split Learning
Ada-VFed
CIFAR-10
1
66.71
67.14
68.49
65.79
68.22
29.66
61.31
4
71.25
70.96
72.52
68.84
70.43
34.41
62.13
8
72.37
71.91
73.63
70.03
71.68
40.37
63.50
Table 3. Test Accuracy ( % ) versus Different Privacy Budgets, Baselines (20 epochs, γ=2 )
Dataset
Method
Plain
G-Shuff
G-BMF (Setting 1)
G-BMF (Setting 2)
GL-BMF (Setting 1)
GL-BMF (Setting 2)
CIFAR-10
0.68
0.52
0.51
0.51
0.51
0.51
Table 4. AUC Score versus Different Protocols under P-Attack (100 epochs, ϵ=8 )
Dataset
Method
Pre-ImageNet
Pre-Cifar100
Runtime (s)
Communication (MB)
Runtime (s)
Communication (MB)
CIFAR-10
G-Shuff
14.88
473.63
7.80
244.03
G-BMF
14.57
453.6
7.65
233.77
GL-BMF
132.8
6220.87
83.5
3186.62
EMNIST
G-Shuff
32.80
1228.56
18.89
632.52
G-BMF
32.00
1178.64
18.50
606.96
Table 5. Runtime and Communication cost of the MPC over LAN
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Description
W
Global model
Fi
Local model at client i
θ
Parameters of the global model W
ϕi
Parameters of local model Fi
xb,j(i)
Client i ’s local data of the j -the sample in the b -th batch
Hb,j(i)
Output of local model Fi over xb,j(i)
Appendix
Table 6. Notation Table
Dataset
Method
Pre-ImageNet
Pre-Cifar100
CIFAR-10
Non-DP
Non-DP
Plain
93.5
93.89
DP
DP
ε=1
ε=2
ε=5
ε=8
ε=10
ε=1
ε=2
ε=5
ε=8
ε=10
G-Shuff
63.71
69.09
71.93
72.89
73.88
80.16
82.11
82.85
82.98
83.02
G-BMF (Setting 1)
65.14
70.66
73.63
74.25
74.41
79.51
80.41
80.57
80.59
80.64
Appendix
Table 7. Test Accuracy ( % ) versus Different Datasets, Pre-training, and Privacy Budgets (100 epochs)
Dataset
Method
Pre-ImageNet
Pre-Cifar100
Runtime (s)
Communication (MB)
Runtime (s)
Communication (MB)
CIFAR-10
G-Shuff
83.94
473.63
44.62
244.03
G-BMF
82.60
453.6
43.92
233.77
GL-BMF
686.60
6220.87
468.19
3186.62
EMNIST
G-Shuff
194.17
1228.56
108.34
632.52
G-BMF
190.75
1178.64
106.65
606.96
Appendix
Table 8. Runtime and Communication cost of the MPC over WAN
Dataset
Method
GL-BMF
GL-Sub
ADMM
FedBCD
CIFAR-10
75.47
84.46
69.64
71.82
Appendix
Table 9. Test Accuracy (%) versus Different Baselines (100 epochs, ϵ=4 , γ=2 )
This article presents DDP-SA, a scalable privacy-preserving federated learning framework that jointly leverages client-side local differential privacy (LDP) and full-threshold additive secret sharing (ASS) for secure aggregation. Unlike existing methods that rely solely on differential privacy or on secure multi-party computation (MPC), DDP-SA integrates both techniques to deliver stronger end-to-end privacy guarantees while remaining computationally practical. The framework introduces a two-stage protection mechanism: clients first perturb their local gradients with calibrated Laplace noise, then decompose the noisy gradients into additive secret shares that are distributed across multiple intermediate servers. This design ensures that (i) no single compromised server or communication channel can reveal any information about individual client updates, and (ii) the parameter server reconstructs only the aggregated noisy gradient, never any client-specific contribution. Extensive experiments show that DDP-SA achieves substantially higher model accuracy than standalone LDP while providing stronger privacy protection than MPC-only approaches. The proposed framework scales linearly with the number of participants and offers a practical, privacy-preserving solution for federated learning applications with controllable computational and communication overhead.
Federated learning enables multiple clients to collaboratively train models without sharing their private data. However, the lack of visibility into local training makes it difficult to verify whether clients follow the prescribed training procedure or submit malicious updates, such as model poisoning. A natural approach is to replay client training for verification. However, privacy-preserving replay produces numerical results that cannot be directly matched with local client execution because the two run in different environments. We present OPFL, an optimistic verification framework for privacy-preserving federated learning. To protect data privacy, OPFL performs replay inside secure multi-party computation (MPC). Although gradients computed on MPC and local GPUs are not bitwise identical, we observe that their absolute differences are stable and bounded. OPFL therefore calibrates an empirical boundary offline and uses it to distinguish benign numerical deviations from malicious manipulation. To reduce the cost of expensive MPC replay, OPFL adopts optimistic verification by post auditing only sampled training steps. Experiments on LeNet, BERT, and Qwen show that the boundary generalizes across datasets, input lengths, and GPUs, while achieving 0% ASR against model poisoning and PGD-based attacks. On a LeNet workload, at p=0.01, OPFL is approximately 98.6× faster than full MPC-based FL and 625.5× faster than ZK-based approach.
Federated learning enables collaborative model training across distributed clients, yet vanilla FL exposes client updates to the central server. Secure-aggregation schemes protect privacy against an honest-but-curious server, but existing approaches often suffer from many communication rounds, heavy public-key operations, or difficulty handling client dropouts. Recent methods like One-Shot Private Aggregation (OPA) cut rounds to a single server interaction per FL iteration, yet they impose substantial cryptographic and computational overhead on both server and clients. We propose a new protocol called DisAgg that leverages a small committee of clients called Aggregators to perform the aggregation itself: each client secret-shares its update vector to Aggregators, which locally compute partial sums and return only aggregated shares for server-side reconstruction. This design eliminates local masking and expensive homomorphic encryption, reducing endpoint computation while preserving privacy against a curious server and a limited fraction of colluding clients. By leveraging optimal trade-offs between communication and computation costs, DisAgg processes 100k-dimensional update vectors from 100k 5G clients with a 4.6x speedup compared to OPA, the previous best protocol.