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A comparative survey of SecureMultiparty Computation Frameworks
Seminar Talk
Benjamin Assadsolimani
http://comsys.rwth-aachen.de Aachen, 15.07.2015
Outline
1 Introduction
2 Approaches to SMPC
3 Frameworks
4 Comparison
5 Conclusion
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Motivation
There is a variety of frameworks for SMPC
Developer needs to decide which one is suited best
Comparison of 4 selected frameworks regarding:
underlying assumptionsfeaturesperformance
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Secure Multiparty Computation
Secure Multiparty Computation (SMPC) allows mutuallydistrusting parties to cooperatively compute over their private data.
A B C
P1 P2 P3
F(A, B, C)
o
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Scheduling Application
Three business men want to schedule a meeting.They perform a Set Intersection (SI) of their available days
{Mo, Tue} {Tue, Thu} {Tue, Fri}
P1 P2 P3
SI({...},{...},{...})
Tue
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Outline
1 Introduction
2 Approaches to SMPC
3 Frameworks
4 Comparison
5 Conclusion
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Garbled Circuits
Represent the function by a boolean circuit
Assign random keys to each wire: k0 for 0, k1 for 1
Encrypt each gate such that one can compute the key of theoutput wire from the keys of the input wires
0 1
0 1 0 1
u v w
0 0 0
0 1 0
1 0 0
1 1 1
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Garbled Circuits
Represent the function by a boolean circuit
Assign random keys to each wire: k0 for 0, k1 for 1
Encrypt each gate such that one can compute the key of theoutput wire from the keys of the input wires
u v w
k0u k0v k0wk0u k1v k0wk1u k0v k0wk1u k1v k1w
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Secret Sharing
Produce n shares of the private variable
Use shares to compute function
Recombine shares to retrieve the result
D
D1 D2 D3
Figure : Divide a secret D into n shares D1, ...,Dn
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Protocol Flow
A
B
C
A1, B1, C1
O1
O2
Input parties comp. parties output parties
Pi1
Pi2
Pi3
Pc1
Pc2
Pc3
Po1
Po2
A2, B2, C2
A3, B3, C3
Figure : General SMPC protocol setup using secret sharing
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Adversary Models
A1, B1, C1
comp. parties
Pc1
Pc2
Pc3
A2, B2, C2
A3, B3, C3
Passive adversary:
Follows the protocolexecutionAttempts to learn privatedata from the informationavailable
Active adversary:
Behaviour may arbitrarilydeviate from the protocolspecification
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Performance Measurement
How does the runtime increase in relation to:
The number of partiesThe size of the input
Garbled Circuits
Number of gates
Depth of the circuit
Secret Sharing
Number of multiplications
Number of rounds
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Outline
1 Introduction
2 Approaches to SMPC
3 Frameworks
4 Comparison
5 Conclusion
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PICCO
Technique
Source-to-source compilerBased on secret sharing
Features
Support for floating point arithmeticParallelization of loops, arrays and user-specific code blocks
Performance Enhancement
The length of numeric data types can be specifiedReduce round time complexity as much as possible
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SEPIA
Technique
SMPC library for privacy preserving network analysisBased on secret sharing
Features
API providing a set of basic SMPC operationsOffers defence mechanisms against malicious behaviour
Performance Enhancement
Reduce number of multiplications at the expense of the roundtime complexityOptimize comparison operations by parallel execution
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FairplayMP
Technique
Generic SMPC systemBased on garbled circuits
Features
Extends the Fairplay system to the multiparty caseFunction specific optimizations can be done manually
Performance Enhancement
Protocol executes in a constant number of roundsReduced the gate’s truth table overhead
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WYSTERIA
Technique
Functional programming languageBased on garbled circuits
Features
Offers secret sharing on top of garbled circuitsAllows a dynamic number of participants
Performance Enhancement
Allows programmer to define parallel executionsSupports mixed-mode programs
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Outline
1 Introduction
2 Approaches to SMPC
3 Frameworks
4 Comparison
5 Conclusion
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Runtime Dependency
Frameworks are very similar concerning their scalability
Framework Number of parties Input size
FairplayMP close to quadratic linearWYSTERIA linear linearPICCO slightly higher than linear linearSEPIA linear linear
Table : Runtime Dependencies
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Performance Comparison
SEPIA has a slight performance edge over PICCO while bothoutperform FairplayMP
Framework Parties Input Size Hardware Setup Runtime
FairplayMP 5 32 Bit 1Gb/s LAN 1.6 Mult./s2.3 Equals/s
SEPIA 5 32 Bit 1Gb/s LAN 82730 Mult./s2070 Equals/s
PICCO 3 33 Bit 1Gb/s LAN 70250 Mult./s
Table : Performance of basic SMPC operations
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Outline
1 Introduction
2 Approaches to SMPC
3 Frameworks
4 Comparison
5 Conclusion
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Conclusion
Efficiency of a framework heavily depends on the use-casescenario:
input sizenumber of partiescomplexity of the functionmachine/ network quality
programmer has to choose the suitable framework dependingon those parameters
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