Performance of Secure Multiparty Computation Ludwig Dickmanns - - PowerPoint PPT Presentation

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Performance of Secure Multiparty Computation Ludwig Dickmanns - - PowerPoint PPT Presentation

Dec 20, 2022 455 likes •683 views

Chair of Network Architectures and Services Department of Informatics Technical University of Munich Performance of Secure Multiparty Computation Ludwig Dickmanns Thursday 11 th October, 2018 Chair of Network Architectures and Services

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Chair of Network Architectures and Services Department of Informatics Technical University of Munich

Performance of Secure Multiparty Computation

Ludwig Dickmanns

Thursday 11th October, 2018 Chair of Network Architectures and Services Department of Informatics Technical University of Munich

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Overview

  • Introduction to SMC
  • What is SMC?
  • A.C. Yao: Millionaires’ problem
  • A.C. Yao: General approach
  • Addition with secret-sharing
  • Test Setup
  • SMC framework
  • FRESCO
  • Tested Application
  • Testbed
  • Results
  • Amount of peers
  • Transmission rate
  • Network latency
  • Practical indications
  • Conclusion
  • L. Dickmanns — Performance of SMC

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Introduction to SMC

What is SMC? [1] Secure multi-party computation (SMC):

  • Set of parties
  • Jointly calculated function
  • Input contribution by all parties
  • No input is revealed
  • No Trusted Thrid Party required
  • L. Dickmanns — Performance of SMC

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Introduction to SMC

A.C. Yao: Millionaires’ problem [2]

  • Introduced in 1982
  • Two millionaires (Alice & Bob)
  • Determine who is wealthier
  • Neither has to reveal the credit balance
  • Mathematical solution (no implementation due to lack in computational power)
  • L. Dickmanns — Performance of SMC

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Introduction to SMC

A.C. Yao: General approach [2]

  • Introduced in 1982
  • Set of m parties
  • Jointly calculated function (f(x1, ..., xm))
  • All inputs stay private
  • Cheating detection (even if m-1 parties cheat)
  • Mathematical approach (no implementation due to lack in computational power)
  • L. Dickmanns — Performance of SMC

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Introduction to SMC

SMC Example: Addition with secret-sharing [3]

  • n parties
  • Party i contributes input xi
  • Goals:
  • Calculate sum of all inputs
  • Keep inputs private
  • Protocol:
  • Input xi is split into n randomly sized shares (xi

1, ..., xi n) by party i

  • Party j receives share j of each party (x1

j , ..., xn j )

  • Party j calculates partial sum rj of received shares
  • Parties exchange partial sums
  • Complete sum can be calculated by each party
  • L. Dickmanns — Performance of SMC

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Test Setup

SMC-Framework: FRESCO [4]

  • FRamework for Efficient Secure COmputation
  • Developed by Alexandra Institute (Denmark)
  • Open source (MIT license)
  • Prototypically in usage
  • Java
  • Runnable demos
  • https://github.com/aicis/fresco
  • L. Dickmanns — Performance of SMC

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Test Setup

SMC-Framework: Tested Application

  • Adjusted FRESCO demo
  • 3-17 parties
  • Each party contributing an int array as input
  • Calculation:
  • Mean of all inputs
  • Standard deviation of all inputs
  • L. Dickmanns — Performance of SMC

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Test Setup

Testbed

  • Lab at TUM
  • High bandwidth (1 GBit/s)
  • Low network latency
  • Up to 17 physical peers
  • Star topology
  • L. Dickmanns — Performance of SMC

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Results

Evaluated parameters

  • Amount of peers:

⇒ Protocol invocations & batches ⇒ Execution time

  • Transmission rate:

⇒ Execution time

  • Network latency:

⇒ Execution time

  • L. Dickmanns — Performance of SMC

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Results

Terminology: Protocols and Batches Protocol:

  • Defined in a protocol suite
  • Base functions of protocol suites (e.g. add, OR)
  • Applications are built with protocols

Batch:

  • Contain a certain number of protocols
  • Protocols are evaluated in parallel
  • L. Dickmanns — Performance of SMC

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Results

Amount of peers: Protocol invocations and batches

  • Increase in peers:

⇒ Increase in protocols ⇒ Increase in batches

  • Both grow linearely
  • Batches slower
  • Protocols faster

3 peers 4 peers 5 peers 6 peers 7 peers 8 peers 9 peers 10 peers 11 peers 12 peers 13 peers 14 peers 15 peers 16 peers 17 peers 0.25 0.5 0.75 1 1.25 1.5 1.75 2 ·104 Protocol invocations Batches

Figure 1: The amount of native protocol invocations and the number of batches in which they have been executed depending on the number of participating peers.

  • L. Dickmanns — Performance of SMC

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Results

Amount of peers: Execution time

  • Increase in peers:

⇒ Increase in execution time

  • Grows linearely

5 10 15 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Figure 2: The execution time depending on the number of participating peers.

  • L. Dickmanns — Performance of SMC

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Results

Transmission rate: Execution time

  • 1000 MBit/s to 100 MBit/s:

⇒ No significant change

  • 100 MBit/s to 10 MBit/s:

⇒ Small increase (~factor 2)

  • 10 MBit/s to 1 MBit/s:

⇒ Significant change (up to ~factor 6) Problematic combination:

  • Low Bandwidth
  • High number of peers

100 101 102 103 10 20 30 40 50 60 Transmission rate [MBit] Execution time [s] 3 peers 4 peers 5 peers 6 peers 7 peers 8 peers 9 peers 10 peers 11 peers 12 peers 13 peers 14 peers 15 peers 16 peers 17 peers

Figure 3: The execution time of the secure computation depending on the transmission rate. The shown case has no additional network latency.

  • L. Dickmanns — Performance of SMC

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Results

Network latency: Execution time

  • Default link latency of 0.18ms
  • Added delays: 0ms, 10ms, 25ms, 50ms
  • Behavior: Root function
  • Greatest absolute increase in execution

time Problematic combination:

  • High network latency
  • High number of peers

20 40 25 50 75 100 125 150 175 200 Network latency [ms] Execution time [s] 3 peers 4 peers 5 peers 6 peers 7 peers 8 peers 9 peers 10 peers 11 peers 12 peers 13 peers 14 peers 15 peers 16 peers 17 peers

Figure 4: The execution time of the secure computation depending on the number of peers and on the network latency of the network. The latency highly influences computation time irrespective of the available transmission rate.

  • L. Dickmanns — Performance of SMC

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Parctical Indications

Disadvantageous circumstances High number of peers:

  • Increase in protocol invocations & batches
  • Increase in execution time

Low bandwidth (<10MBit/s):

  • Increase in execution time
  • Combination with high number of peers

High network latency:

  • Increase in execution time
  • Combination with high number of peers

Example: Large scale mobile application

  • Large amount of peers
  • Possibly low bandwidth
  • EDGE: 384 KBit/s [5]
  • 3G: 7.2 MBit/s (HSPA) [5]
  • Possibly high network latency
  • EDGE: 200-450ms [6]
  • 3G: 100-350ms [7]
  • L. Dickmanns — Performance of SMC

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Parctical Indications

Advantageous circumstances Limited number of peers:

  • Limited protocol invocations & batches
  • Lower in execution time

High bandwidth (>10MBit/s):

  • Lower in execution time
  • Combination with limited number of peers

Low network latency:

  • Lower in execution time
  • Combination with limited number of peers

Example: Evaluation Testbed

  • Limited amount of peers (17)
  • High bandwidth (1 GBit/s)
  • Low network latency (0.18ms)
  • L. Dickmanns — Performance of SMC

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Conclusion

Summary - Feasibility of use-cases Possibly already feasible:

  • Intranet applications
  • Limited peers
  • High bandwidth
  • Low latency
  • Internet application
  • Limited peers (close to each other)
  • High bandwidth
  • Low latency

Problematic at the moment:

  • Internet application
  • Many peers
  • Medium bandwidth
  • Medium latency
  • Mobile application
  • Many peers
  • Low bandwidth
  • High latency
  • L. Dickmanns — Performance of SMC

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Conclusion

Outlook Factors increasing feasibility by use-case:

  • Mobile application:
  • Limit allowed number of peers
  • Higher 3G+/4G network coverage

⇒ Increase in bandwidth ⇒ Decrease in latency

  • Internet application:
  • Limit allowed number of peers
  • Higher high-speed optical fiber coverage

⇒ Increase in bandwidth ⇒ Decrease in latency

General factors:

  • Faster network infrastructure
  • New technologies
  • L. Dickmanns — Performance of SMC

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Bibliography

[1] Secure multi-party computation. https://en.wikipedia.org/wiki/Secure_multi-party_computation. [2] A.C. Yao. Protocols for secure computations. https://research.cs.wisc.edu/areas/sec/yao1982-ocr.pdf, 1982. [3] What is spdz? https://bristolcrypto.blogspot.com/2016/10/what-is-spdz-part-1-mpc-circuit.html. [4] FRamework for Efficient Secure COmputation (fresco). https://github.com/aicis/fresco. [5] Mobiles internet. https://de.wikipedia.org/wiki/Mobiles_Internet. [6] Alles zum thema edge. https://www.onlinekosten.de/mobiles-internet/edge/. [7] 3g/4g ping/latency. https://www.evdoinfo.com/content/view/4818/64/.

  • L. Dickmanns — Performance of SMC

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