Systematic overview of 3PC and 4PC frameworks. (✓) denotes availability, (◐) partial availability, (✗) unavailability. Abbreviations: O = Outsourcing, C-S = Client–Server. Additional abbreviations are defined in Table of Notation.
| Scheme | Year | 2 | 3 | 4 | HE | OT | GC | ZK | SS | Setting | Sec. | Training | Inference | Theoretical | Experimental |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ABY3 130 | 2018 | ✗ | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ | ✓ | O | SH/A | ✓ | ✓ | ◐ [T4] | ✓ |
| SecureNN 176 | 2018 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH/A | ✓ | ✓ | ✓ | ✓ |
| ASTRA 38 | 2019 | ◐ [T2] | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ | ✓ | O | SH/A/F | ✗ | ✓ | ◐ [T4] | ◐ [T3] |
| Cryptflow 104 | 2019 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH/A | ✗ | ✓ | ✓ | ✓ |
| Shen et al. 160 | 2020 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | C-S/O | SH | ✗ | ✓ | ✗ | ◐ [T3] |
| Falcon 177 | 2020 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH/A | ✓ | ✓ | ◐ [T4] | ✓ |
| BLAZE 137 | 2020 | ✗ | ✓ | ✗ | ✗ | ✓ | ✓ | ✓ | ✓ | O | F | ✓ | ✓ | ✓ | ◐ [T3] |
| pMPL 162 | 2022 | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH | ✓ | ✓ | ◐ [T5] | ✓ |
| AdamInPrivate 12 | 2022 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH/A | ✓ | ✓ | ✓ | ◐ [T3] |
| Meteor 60 | 2023 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH | ✗ | ✓ | ◐ [T5] | ✓ |
| PrivFormer 7 | 2023 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH | ✗ | ✗ | ✓ | ◐ [T3] |
| Trio 82 | 2024 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | SH | ✗ | ✓ | ◐ [T4] | ✓ |
| Brüggemann et al. 31 | 2024 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | C-S/O | A | ✗ | ✓ | ◐ [T4] | ◐ [T3] |
| Mosformer 42 | 2025 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | O | A | ✗ | ✓ | ✓ | ✓ |
| ECHO 63 | 2026 | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | ✓ | O | Cov | ✓ | ✓ | ✗ | ✓ |
| Trident 39 | 2019 | ✗ | ◐ [T2] | ✓ | ✗ | ✓ | ✓ | ✗ | ✓ | O | F | ✓ | ✓ | ✓ | ◐ [T3] |
| PrivPy 108 | 2019 | ✗ | ✗ | ✓ | ✗ | ✓ | ✗ | ✗ | ✓ | O | SH | ✓ | ✓ | ✗ | ◐ [T3] |
| FLASH 33 | 2020 | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | O | A/R | ✗ | ✓ | ✓ | ◐ [T3] |
| SWIFT 101 | 2020 | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✓ | ✓ | O | R | ◐ [T1] | ✓ | ✓ | ◐ [T3] |
| Fantastic Four 49 | 2021 | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | O | A/R | ✓ | ✓ | ◐ [T4] | ◐ [T3] |
| Tetrad 103 | 2021 | ◐ [T2] | ✗ | ✓ | ✗ | ✓ | ✓ | ✗ | ✓ | O | F/R | ✓ | ✓ | ◐ [T4] | ◐ [T3] |
| Quad 82 | 2024 | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✓ | O | A | ✗ | ✓ | ◐ [T4] | ✓ |
[T1] Training of LinReg and LogReg only. [T2] Online phase. [T3] Implementation not public. [T4] Only primitives (no ML functionalities). [T5] No costs for offline phase.
| Topic | Table(s) |
|---|---|
| 🗂️ Notation | Notation & Abbreviations |
| 📚 Related Work | Related Work Comparison |
| 🧭 Decision Graph | Decision Graph |
| ⚙️ Design & Deployment | Comprehensive MPC Design, 2PC, 3/4PC, nPC |
| 🌳 Genealogy | Genealogy |
| 🤖 ML Support | 2PC, MPC |
| 🔐 Theoretical Costs | Dot-Product, Truncation, ReLU, Softmax, Sigmoid, GELU, Normalization |
| 🧩 MPC Puzzle | MPC Puzzle |
| 📖 Bibliography | Bibliography |