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A universal MPC machine* Drago Rotaru University of Bristol, KU - PowerPoint PPT Presentation

Jan 24, 2024 •187 likes •685 views

DIMACS Workshop 2019 A universal MPC machine* Drago Rotaru University of Bristol, KU Leuven *MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security; Joint work with Tim Wood. https://ia.cr/2019/207 Drago

  1. DIMACS Workshop 2019 A universal MPC machine* Dragoș Rotaru University of Bristol, KU Leuven *MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security; • Joint work with Tim Wood. • https://ia.cr/2019/207 Dragoș Rotaru 1 imec-Cosic, Dept. Electrical Engineering

  2. What is multiparty computation? a c b Goal : Compute F(a, b, c) Dragos Rotaru 2 Dragoș Rotaru 2 imec-Cosic, Dept. Electrical Engineering

  3. How can we achieve MPC? Secret Sharing Garbled Circuits Fast networks (LAN) Slow Networks (WAN) Arithmetic/Boolean circuits Boolean circuits Low depth, many AND gates Large depth, few AND gates Dragoș Rotaru 3 imec-Cosic, Dept. Electrical Engineering

  4. Can we switch between? A (GMW mod 2 𝑙 ) Yao GC – mod 2 B (GMW mod 2) ABY [DMZ’15] Dragoș Rotaru 4 imec-Cosic, Dept. Electrical Engineering

  5. Can we switch between? A (GMW mod 2 𝑙 ) Yao GC – mod 2 B (GMW mod 2) ABY [DMZ’15] ABY3 [MR’18] Dragoș Rotaru 5 imec-Cosic, Dept. Electrical Engineering

  6. Can we switch between? A (GMW mod 2 𝑙 ) Yao GC – mod 2 B (GMW mod 2) ABY [DMZ’15] ABY3 [MR’18] Dragoș Rotaru 6 imec-Cosic, Dept. Electrical Engineering

  7. What about dishonest majority? Dragoș Rotaru 7 imec-Cosic, Dept. Electrical Engineering

  8. What about dishonest majority? SPDZ SPDZ-BMR Dragoș Rotaru 8 imec-Cosic, Dept. Electrical Engineering

  9. What about dishonest majority? Naive >110K ANDs SPDZ SPDZ-BMR Dragoș Rotaru 9 imec-Cosic, Dept. Electrical Engineering

  10. What about dishonest majority? Naive >110K ANDs SPDZ SPDZ-BMR >110K ANDs Dragoș Rotaru 10 imec-Cosic, Dept. Electrical Engineering

  11. What about dishonest majority? Naive <1K ANDs SPDZ SPDZ-BMR 0 ANDs Dragoș Rotaru 11 imec-Cosic, Dept. Electrical Engineering

  12. How general is this? 𝐆 𝑞 SPDZ SPDZ-BMR WRK’17 𝐚 2 𝑙 HSS’17 SPDZ Dragoș Rotaru 12 imec-Cosic, Dept. Electrical Engineering

  13. How general is this? 𝐆 𝑞 SPDZ SPDZ-BMR WRK’17 𝐚 2 𝑙 HSS’17 SPDZ Dragoș Rotaru 13 imec-Cosic, Dept. Electrical Engineering

  14. How general is this? 𝐆 𝑞 SPDZ SPDZ-BMR WRK’17 𝐚 2 𝑙 HSS’17 SPDZ Dragoș Rotaru 14 imec-Cosic, Dept. Electrical Engineering

  15. How general is this? 𝐆 𝑞 SPDZ SPDZ-BMR WRK’17 𝐚 2 𝑙 HSS’17 SPDZ Any honest majority protocol Dragoș Rotaru 15 imec-Cosic, Dept. Electrical Engineering

  16. Our focus 𝐆 𝑞 SPDZ SPDZ-BMR WRK’17 𝐚 2 𝑙 HSS’17 SPDZ Dragoș Rotaru 16 imec-Cosic, Dept. Electrical Engineering

  17. Malicious MPC protocols Preprocessing Online phase phase PKC Inputs SPDZ, TinyOT, BDOZa , MASCOT, WRK’17, HSS’17, … Dragoș Rotaru 17 imec-Cosic, Dept. Electrical Engineering

  18. Let’s talk about 𝐆 𝑞 SPDZ Dragoș Rotaru 18 imec-Cosic, Dept. Electrical Engineering

  19. SPDZ online phase 𝐆 𝑞 SPDZ α 1 α 2 + α 3 + α = 𝑦 3 𝑦 1 𝑦 2 𝑦 + + = γ(𝑦) 1 γ(𝑦) 2 + + γ(𝑦) 3 α 𝑦 = Dragoș Rotaru 19 imec-Cosic, Dept. Electrical Engineering

  20. SPDZ online phase 𝐆 𝑞 SPDZ α 1 α 2 + α 3 + α = 𝑦 1 + 𝑧 1 𝑦 2 + 𝑧 2 𝑦 + 𝑧 𝑦 3 + 𝑧 3 + + = γ x 1 + γ y 1 γ x 2 + γ y 2 + γ x 3 + γ y 3 + α ( 𝑦 + 𝑧) = Dragoș Rotaru 20 imec-Cosic, Dept. Electrical Engineering

  21. SPDZ online phase 𝐆 𝑞 SPDZ ← X 𝐵 X 𝐵 Retrieve a random mask Input Dragoș Rotaru 21 imec-Cosic, Dept. Electrical Engineering

  22. SPDZ online phase 𝐆 𝑞 SPDZ ← X 𝐵 X 𝐵 Input Dragoș Rotaru 22 imec-Cosic, Dept. Electrical Engineering

  23. SPDZ online phase 𝐆 𝑞 SPDZ ← X 𝐵 X 𝐵 Input ← x x Open Dragoș Rotaru 23 imec-Cosic, Dept. Electrical Engineering

  24. SPDZ online phase 𝐆 𝑞 SPDZ ← X 𝐵 X 𝐵 Input ← x x Open MAC Check Dragoș Rotaru 24 imec-Cosic, Dept. Electrical Engineering

  25. SPDZ online phase 𝐆 𝑞 SPDZ ← X 𝐵 X 𝐵 Input ← x x Open  ← XOR Retrieve a Beaver triple z x y Dragoș Rotaru 25 imec-Cosic, Dept. Electrical Engineering

  26. SPDZ online phase 𝐆 𝑞 SPDZ ← X 𝐵 X 𝐵 Input ← x x Open MAC Check  ← XOR z x y Dragoș Rotaru 26 imec-Cosic, Dept. Electrical Engineering

  27. Let’s talk about 𝐆 2 SPDZ-BMR Dragoș Rotaru 27 imec-Cosic, Dept. Electrical Engineering

  28. SPDZ online phase 𝐆 2 SPDZ-BMR A B AND AND C A B C Dragoș Rotaru 28 imec-Cosic, Dept. Electrical Engineering

  29. SPDZ online phase 𝐆 2 SPDZ-BMR A B AND AND C MAC Check Λ 𝑑 ←C + λ 𝑑 Λ 𝐵 ← A + λ 𝑏 Λ 𝐶 ← B + λ 𝑐 Dragoș Rotaru 29 imec-Cosic, Dept. Electrical Engineering

  30. SPDZ online phase 𝐆 2 SPDZ-BMR A B AND AND C MAC Check Λ 𝑑 ←C + λ 𝑑 Λ 𝐵 ← A + λ 𝑏 Λ 𝐶 ← B + λ 𝑐 Inputs - cheap XOR - free Mod p arithmetic - some AND gates Dragoș Rotaru 30 imec-Cosic, Dept. Electrical Engineering

  31. Main idea: 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR x x x Dragoș Rotaru 31 imec-Cosic, Dept. Electrical Engineering

  32. Main idea: 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR x x x r Dragoș Rotaru 32 imec-Cosic, Dept. Electrical Engineering

  33. Main idea: 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR x x - x-r x r Open SPDZ – MAC Check Dragoș Rotaru 33 imec-Cosic, Dept. Electrical Engineering

  34. Main idea: 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR x x - + r x x-r x r Dragoș Rotaru 34 imec-Cosic, Dept. Electrical Engineering

  35. Introducing daBits Dragoș Rotaru 35 imec-Cosic, Dept. Electrical Engineering

  36. Introducing daBits 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR 𝒄 𝑩 𝒄 𝑪 𝒄 𝑫 Dragoș Rotaru 36 imec-Cosic, Dept. Electrical Engineering

  37. Introducing daBits 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR SPDZ Input SPDZ-BMR Input 𝒄 𝑩 𝒄 𝑪 𝒄 𝑫 Dragoș Rotaru 37 imec-Cosic, Dept. Electrical Engineering

  38. Introducing daBits 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR SPDZ Input SPDZ-BMR Input 𝒄 𝑩 𝒄 𝑩 𝒄 𝑪 𝒄 𝑪 𝒄 𝑫 𝒄 𝑫 Dragoș Rotaru 38 imec-Cosic, Dept. Electrical Engineering

  39. Introducing daBits 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR SPDZ Open SPDZ-BMR Open 𝒄 𝑩 𝒄 𝑩 𝒄 𝑪 𝒄 𝑪 𝒄 𝑫 𝒄 𝑫 Dragoș Rotaru 39 imec-Cosic, Dept. Electrical Engineering

  40. Introducing daBits 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR SPDZ XOR SPDZ-BMR XOR 𝒄 𝑩  𝒄 𝑪  𝒄 𝑫 𝒄 𝑩  𝒄 𝑪  𝒄 𝑫 Dragoș Rotaru 40 imec-Cosic, Dept. Electrical Engineering

  41. Introducing daBits 𝐆 𝑞 𝐆 2 SPDZ SPDZ-BMR SPDZ Open SPDZ-BMR Open 𝒄 𝑩  𝒄 𝑪  𝒄 𝑫 𝒄 𝑩  𝒄 𝑪  𝒄 𝑫 Dragoș Rotaru 41 imec-Cosic, Dept. Electrical Engineering

  42. daBit cost SPDZ-BMR SPDZ Dragoș Rotaru 42 imec-Cosic, Dept. Electrical Engineering

  43. Preprocessing cost per conversion Dragoș Rotaru 43 imec-Cosic, Dept. Electrical Engineering

  44. Example code in MP-SPDZ Dragoș Rotaru 44 imec-Cosic, Dept. Electrical Engineering

  45. Online cost per conversion 8X overhead than using ABY Dragoș Rotaru 45 imec-Cosic, Dept. Electrical Engineering

  46. Online cost per conversion 8X overhead than using ABY Dragoș Rotaru 46 imec-Cosic, Dept. Electrical Engineering

  47. What’s next? • SCALE- MAMBA has WRK’17. • It also has all preprocessing phases connected – ideal candidate for daBits in a more realistic system. • Moral: Stitch your work together so it would be easier to build more efficient protocols on top of them. Dragoș Rotaru 47 imec-Cosic, Dept. Electrical Engineering

  48. Thank you! Dragoș Rotaru 48 imec-Cosic, Dept. Electrical Engineering

  49. Thank you! • Questions? • https://ia.cr/2019/207 Dragoș Rotaru 49 imec-Cosic, Dept. Electrical Engineering

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