SLIDE 1
Multi-Party Computation (MPC) [Yao82,GMW87]
- ✁
- ✂
- ✄
- ✁☞☛
Multi-Party Computation with Hybrid Security Matthias Fitzi, Thomas - - PowerPoint PPT Presentation
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)
SLIDE 2
SLIDE 3
MPC: Adversary
- ✁
- ✂
- ✄
- ✁☞☛
- ✍
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MPC: Adversary
- Central adversary
: – corrupt up to
✁players actively – Privacy: no information about good
✄✂– Correctness:
✟ ✠ ✡- ✁☞☛
- ✍
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
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How to do Broadcast with
✁- ✁
? Construction using:
- Hardware.
SLIDE 7
How to do Broadcast with
✁- ✁
? Construction using:
- Hardware. How???
SLIDE 8
How to do Broadcast with
✁- ✁
? Construction using:
- Hardware. How???
- Signature Scheme [LSP82,DS82,PW96]
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How to do Broadcast with
✁- ✁
? Construction using:
- Hardware. How???
- Signature Scheme [LSP82,DS82,PW96]
+ Consistent PKI.
SLIDE 10
MPC with Signature Scheme
... ...
- ✁
- ✂
- ✄
- ☎
- ✝
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MPC: Compare Models Standard model: Standard Model with Signature Scheme and consistent PKI:
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- ✁
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MPC: Compare Models Standard model: Standard Model with Signature Scheme and consistent PKI:
- ✁
- ✁
Adversary can forge Signature
- r make PKI inconsistent.
SLIDE 13
Model - Idea
- ✁
- ✁
- Adversary
- can Forge Signature
- can make PKI inkonsistent
SLIDE 14
Model - Idea ?
✂ ✄ ☎ ✂ ✄ ✆Adversary
- can Forge Signature
- can make PKI inkonsistent
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Model - Idea ?
✂ ✄ ☎ ✂ ✄ ✆Adversary
- can Forge Signature
- can make PKI inkonsistent
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Hybrid Security Model A B C D
✁✁ ✁✄✂ ✁- ,
Adversary can:
- corrupt up to
players.
- if
- , forge signatures.
- if
, make the PKI inconsistent.
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
Tight Bounds for Hybrid Security
3
n n n n n
tp
n n 3
2 2 3 4
n
T tσ
- ✁
- ✁
- ✁
- ✁
- ✁
- ✁✄✂
- ✏
- ✁
- ✂
- ✏
SLIDE 19
The Protocol - Idea MPC: [RB89] / [B89]
☛ ✁- ☛
- ✁
- Broadcast
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The Protocol - Idea MPC: [RB89] / [B89]
☛ ✁- ☛
- ✁
- Broadcast: [FM00]
- ☛
- ✁
- Weak Broadcast [Dolev82]
SLIDE 21
The Protocol - Idea MPC: [RB89] / [B89]
☛ ✁- ☛
- ✁
- Broadcast: [FM00]
- ☛
- ✁
- Weak Broadcast [this paper]
- ✁☎✂
- ✏
- ✁
- ✂
- ✏
SLIDE 22
The Protocol - Idea MPC: [RB89] / [B89]
☛ ✁- ☛
- ✁
- Broadcast: [FM00]
- ☛
- ✁
- Weak Broadcast [this paper]
- ✁☎✂
- ✏
- ✁
- ✂
- ✏
Weak Broadcast:
- ✟
. . .
SLIDE 23
Weak Broadcast - Protocol
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Weak Broadcast - Protocol
SLIDE 25
Weak Broadcast - Protocol
SLIDE 26
Weak Broadcast - Protocol
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Weak Broadcast - Protocol
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Weak Broadcast - Protocol
- ✁
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- ✁
honest? Output
- , if:
- ✁✂✁✄✁✄✁✂✁✄☎
- ✟
- ✟
- ✟
and
- therwise.
SLIDE 29
Conclusion MPC with Hybrid Security: Tight Bound:
✡- ✁☎✂
- ✏
- ✁
- ✂
- ✏
- ✁
- ✁
- ✁
- ✁