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

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

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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

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SLIDE 1

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 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
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SLIDE 2

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 2

What is multiparty computation?

Dragos Rotaru 2

Goal: Compute F(a, b, c)

a c b

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SLIDE 3

Dragoș Rotaru 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

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SLIDE 4

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 4

Can we switch between?

ABY [DMZ’15]

Yao GC – mod 2 A (GMW mod 2𝑙 ) B (GMW mod 2)

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SLIDE 5

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 5

Can we switch between?

ABY [DMZ’15]

Yao GC – mod 2

ABY3 [MR’18]

A (GMW mod 2𝑙 ) B (GMW mod 2)

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SLIDE 6

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 6

Can we switch between?

ABY [DMZ’15]

A (GMW mod 2𝑙 ) B (GMW mod 2) Yao GC – mod 2

ABY3 [MR’18]

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SLIDE 7

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 7

What about dishonest majority?

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SLIDE 8

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 8

What about dishonest majority?

SPDZ SPDZ-BMR

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SLIDE 9

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 9

What about dishonest majority?

SPDZ SPDZ-BMR Naive

>110K ANDs

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SLIDE 10

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 10

What about dishonest majority?

SPDZ SPDZ-BMR

>110K ANDs >110K ANDs

Naive

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SLIDE 11

Dragoș Rotaru

Naive

imec-Cosic, Dept. Electrical Engineering 11

What about dishonest majority?

SPDZ SPDZ-BMR

<1K ANDs 0 ANDs

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SLIDE 12

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 12

How general is this?

SPDZ SPDZ-BMR WRK’17 HSS’17 𝐆𝑞 SPDZ 𝐚2𝑙

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SLIDE 13

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 13

How general is this?

SPDZ SPDZ-BMR WRK’17 HSS’17 𝐆𝑞 SPDZ 𝐚2𝑙

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SLIDE 14

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 14

How general is this?

SPDZ SPDZ-BMR WRK’17 HSS’17 𝐆𝑞 SPDZ 𝐚2𝑙

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SLIDE 15

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 15

How general is this?

SPDZ SPDZ-BMR WRK’17 HSS’17 𝐆𝑞 SPDZ 𝐚2𝑙 Any honest majority protocol

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SLIDE 16

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 16

Our focus

SPDZ SPDZ-BMR WRK’17 HSS’17 𝐆𝑞 SPDZ 𝐚2𝑙

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SLIDE 17

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 17

Malicious MPC protocols

Preprocessing phase Online phase

Inputs PKC SPDZ, TinyOT, BDOZa, MASCOT, WRK’17, HSS’17, …

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SLIDE 18

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 18

Let’s talk about

SPDZ 𝐆𝑞

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SLIDE 19

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 19

SPDZ online phase

𝑦1 𝑦2 𝑦3 𝑦 α𝑦 γ(𝑦)2 γ(𝑦)1 γ(𝑦)3

+ + + +

= =

α1 α2 α3 α

+ +

=

SPDZ 𝐆𝑞

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SLIDE 20

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 20

SPDZ online phase

𝑦1 + 𝑧1 𝑦2 + 𝑧2 𝑦3 + 𝑧3 𝑦 + 𝑧

α(𝑦 + 𝑧)

γ x 2 + γ y 2 γ x 1 + γ y 1

+ +

+

=

=

α1 α2 α3 α

+ +

=

+

SPDZ 𝐆𝑞

γ x 3 + γ y 3

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SLIDE 21

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 21

SPDZ online phase

SPDZ 𝐆𝑞

X𝐵

←

Input

X𝐵

Retrieve a random mask

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SLIDE 22

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 22

SPDZ online phase

SPDZ 𝐆𝑞

X𝐵

←

Input

X𝐵

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SLIDE 23

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 23

SPDZ online phase

SPDZ 𝐆𝑞

x

←

x

X𝐵

←

Open Input

X𝐵

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SLIDE 24

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 24

SPDZ online phase

SPDZ 𝐆𝑞

x

←

x

X𝐵

←

Open Input

X𝐵

MAC Check

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SLIDE 25

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 25

SPDZ online phase

SPDZ 𝐆𝑞

z x y

←

x

←

x

X𝐵

←

Open Input XOR

X𝐵

Retrieve a Beaver triple

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SLIDE 26

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 26

SPDZ online phase

SPDZ 𝐆𝑞

z x y

←

x

←

x

X𝐵

←

Open Input XOR

X𝐵

MAC Check

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SLIDE 27

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 27

Let’s talk about

SPDZ-BMR 𝐆2

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SLIDE 28

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 28

SPDZ online phase

SPDZ-BMR 𝐆2

B

AND AND

A C

A B C

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SLIDE 29

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 29

SPDZ online phase

SPDZ-BMR 𝐆2

B

AND AND

A C

Λ𝑑 ←C + λ𝑑 Λ𝐵 ← A + λ𝑏 Λ𝐶 ← B + λ𝑐

MAC Check

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SLIDE 30

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 30

SPDZ online phase

SPDZ-BMR 𝐆2

B

AND AND

A C

Λ𝑑 ←C + λ𝑑 Λ𝐵 ← A + λ𝑏 Λ𝐶 ← B + λ𝑐

MAC Check

Inputs - cheap XOR - free Mod p arithmetic - some AND gates

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SLIDE 31

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 31

Main idea:

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

x x x

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SLIDE 32

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 32

Main idea:

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

x x r x

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SLIDE 33

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 33

Main idea:

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

x x r x

  • x-r

SPDZ – MAC Check Open

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SLIDE 34

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 34

Main idea:

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

x x r x

  • x-r

+ r x

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SLIDE 35

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 35

Introducing daBits

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SLIDE 36

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 36

Introducing daBits

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

𝒄𝑩 𝒄𝑪 𝒄𝑫

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SLIDE 37

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 37

Introducing daBits

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

𝒄𝑪 𝒄𝑫

SPDZ Input SPDZ-BMR Input

𝒄𝑩

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SLIDE 38

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 38

Introducing daBits

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

𝒄𝑩

SPDZ Input SPDZ-BMR Input

𝒄𝑩 𝒄𝑪 𝒄𝑪 𝒄𝑫 𝒄𝑫

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SLIDE 39

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 39

Introducing daBits

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

𝒄𝑩

SPDZ Open SPDZ-BMR Open

𝒄𝑩 𝒄𝑪 𝒄𝑪 𝒄𝑫 𝒄𝑫

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SLIDE 40

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 40

Introducing daBits

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2 𝒄𝑩𝒄𝑪𝒄𝑫 SPDZ XOR SPDZ-BMR XOR 𝒄𝑩𝒄𝑪𝒄𝑫

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SLIDE 41

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 41

Introducing daBits

SPDZ 𝐆𝑞 SPDZ-BMR 𝐆2

𝒄𝑩𝒄𝑪𝒄𝑫

SPDZ Open SPDZ-BMR Open

𝒄𝑩𝒄𝑪𝒄𝑫

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SLIDE 42

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 42

daBit cost

SPDZ SPDZ-BMR

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SLIDE 43

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 43

Preprocessing cost per conversion

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Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 44

Example code in MP-SPDZ

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Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 45

Online cost per conversion

8X overhead than using ABY

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SLIDE 46

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 46

Online cost per conversion

8X overhead than using ABY

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SLIDE 47

Dragoș Rotaru 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.

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SLIDE 48

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 48

Thank you!

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SLIDE 49

Dragoș Rotaru imec-Cosic, Dept. Electrical Engineering 49

  • Questions?

Thank you!

  • https://ia.cr/2019/207