Multi-Party Computation with Hybrid Security Matthias Fitzi, Thomas - - PowerPoint PPT Presentation

multi party computation with hybrid security matthias
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Multi-Party Computation with Hybrid Security Matthias Fitzi, Thomas - - PowerPoint PPT Presentation

Multi-Party Computation with Hybrid Security Matthias Fitzi, Thomas Holenstein, and J urg Wullschleger Multi-Party Computation (MPC)


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SLIDE 1

Multi-Party Computation with Hybrid Security Matthias Fitzi, Thomas Holenstein, and J¨ urg Wullschleger

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SLIDE 2

Multi-Party Computation (MPC) [Yao82,GMW87]

✆☎ ✞✝ ✟ ✟ ✟ ✟ ✟ ✟ ✠ ✡
  • ✁☞☛
✌ ✌ ✌ ☛ ✎✍ ✏
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SLIDE 3

MPC: Adversary

✆☎ ✞✝ ✟ ✟ ✟ ✟ ✟ ✠ ✡
  • ✁☞☛
✌ ✌ ✌ ☛
slide-4
SLIDE 4

MPC: Adversary

  • Central adversary

: – corrupt up to

players actively – Privacy: no information about good

✄✂

– Correctness:

✟ ✠ ✡
  • ✁☞☛
✌ ✌ ✌ ☛
slide-5
SLIDE 5

MPC: General Achievability MPC achievable iff Standard model: Broadcast Model:

✂ ✄ ☎
✂ ✄ ✆

[BGW88,CCD88] [B89,RB89] tight [LSP82] tight [Cleve86]

x x x x x

slide-6
SLIDE 6

How to do Broadcast with

? Construction using:

  • Hardware.
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SLIDE 7

How to do Broadcast with

? Construction using:

  • Hardware. How???
slide-8
SLIDE 8

How to do Broadcast with

? Construction using:

  • Hardware. How???
  • Signature Scheme [LSP82,DS82,PW96]
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SLIDE 9

How to do Broadcast with

? Construction using:

  • Hardware. How???
  • Signature Scheme [LSP82,DS82,PW96]

+ Consistent PKI.

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SLIDE 10

MPC with Signature Scheme

... ...

✟ ✟ ✟ ✟ ✟
slide-11
SLIDE 11

MPC: Compare Models Standard model: Standard Model with Signature Scheme and consistent PKI:

✂ ✄ ☎
✂ ✄ ✆
slide-12
SLIDE 12

MPC: Compare Models Standard model: Standard Model with Signature Scheme and consistent PKI:

✂ ✄ ☎

Adversary can forge Signature

  • r make PKI inconsistent.
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SLIDE 13

Model - Idea

  • Adversary
  • can Forge Signature
  • can make PKI inkonsistent
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SLIDE 14

Model - Idea ?

✂ ✄ ☎ ✂ ✄ ✆

Adversary

  • can Forge Signature
  • can make PKI inkonsistent
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SLIDE 15

Model - Idea ?

✂ ✄ ☎ ✂ ✄ ✆

Adversary

  • can Forge Signature
  • can make PKI inkonsistent
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SLIDE 16

Hybrid Security Model A B C D

✁✁ ✁✄✂ ✁
  • ,
✁☎✂

Adversary can:

  • corrupt up to

players.

  • if
  • , forge signatures.
  • if
✁☎✂

, make the PKI inconsistent.

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SLIDE 17

Previous Results: Tight Bounds

n n

t t

n n 3 n

2

σ

n

T

3 3

n 2

p

slide-18
SLIDE 18

Tight Bounds for Hybrid Security

3

n n n n n

tp

n n 3

2 2 3 4

n

T tσ

  • ✁✄✂
✄ ✡
slide-19
SLIDE 19

The Protocol - Idea MPC: [RB89] / [B89]

☛ ✁
✁☎✂ ✂
  • Broadcast
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SLIDE 20

The Protocol - Idea MPC: [RB89] / [B89]

☛ ✁
✁☎✂ ✂
  • Broadcast: [FM00]
☛ ✁
✁☎✂ ✂
  • Weak Broadcast [Dolev82]
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SLIDE 21

The Protocol - Idea MPC: [RB89] / [B89]

☛ ✁
✁☎✂ ✂
  • Broadcast: [FM00]
☛ ✁
✁☎✂ ✂
  • Weak Broadcast [this paper]
  • ✁☎✂
✄ ✡
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SLIDE 22

The Protocol - Idea MPC: [RB89] / [B89]

☛ ✁
✁☎✂ ✂
  • Broadcast: [FM00]
☛ ✁
✁☎✂ ✂
  • Weak Broadcast [this paper]
  • ✁☎✂
✄ ✡

Weak Broadcast:

. . .

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SLIDE 23

Weak Broadcast - Protocol

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SLIDE 24

Weak Broadcast - Protocol

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SLIDE 25

Weak Broadcast - Protocol

slide-26
SLIDE 26

Weak Broadcast - Protocol

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SLIDE 27

Weak Broadcast - Protocol

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SLIDE 28

Weak Broadcast - Protocol

honest? Output

  • , if:
  • ✁✂✁✄✁✄✁✂✁✄☎
✁✂✁✄✁✂✁✄✁✄✆ ✝ ✞ ✝
✁✄✂ ✝ ✁ ✞ ✝
✁✁ ✝ ✁ ✞ ✝
✄ ✝ ✁ ✁ ✠ ✞ ✝ ✠ ✁

and

  • therwise.
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SLIDE 29

Conclusion MPC with Hybrid Security: Tight Bound:

  • ✁☎✂
✄ ✡

Trade-Off For Free! Efficient!