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Secure Multiparty RAM Computation in Constant Rounds
Sanjam Garg Divya Gupta Peihan Miao Omkant Pandey
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π· 1 π· 2 π· 3 π· π π π· (π₯) π π· (π₯) π π· (π₯) π₯ 1 π₯ 3 π₯ 2
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Our goal: MPC for RAM How about MPC + RAM ?
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MPC + RAM Garbled RAM [LOβ13, GHLORWβ14, GLOSβ15, GLOβ15]
π· βGData π· π βGProg π π₯ βGInput π₯ π¦β π π· ( π₯ ) MPC for circuits [GMWβ87, BGWβ88, CCDβ88, BMRβ90, β¦]
![MPC + RAM Garbled RAM [LOβ13, GHLORWβ14, GLOSβ15, GLOβ15]](http://slideplayer.com./slide/14699779/90/images/4/MPC+%2B+RAM+Garbled+RAM+%5BLO%E2%80%9913%2C+GHLORW%E2%80%9914%2C+GLOS%E2%80%9915%2C+GLO%E2%80%9915%5D.jpg "π· βGData π·. π βGProg π. π₯ βGInput π₯. π¦β π π· ( π₯ ) MPC for circuits. [GMWβ87, BGWβ88, CCDβ88, BMRβ90, β¦]")
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π· π· π· π± GData π· 1 π· 3 π· 2 π· βGData π· π βGProg π π₯ βGInput π₯
π¦β π π· ( π₯ )
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π π π π π π± GProg π π· βGData π· π βGProg π π₯ βGInput π₯ π¦β π π· ( π₯ )
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π₯ π₯ π₯ π± GInput π₯ 1 π₯ 3 π₯ 2 π· βGData π· π βGProg π π₯ βGInput π₯
π¦β π π· ( π₯ )
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π¦β π π· π₯ π· βGData π· π βGProg π π₯ βGInput π₯ π¦β π π· ( π₯ )
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Round Complexity & Efficiency of Multi-Party Computation
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Round complexity?
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Our goal: MPC for RAM in πͺ 1 rounds
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πͺ 1 -round MPC + πͺ 1 -round RAM
Garbled RAM [LOβ13, GHLORWβ14, GLOSβ15, GLOβ15] π· βGData π· π βGProg π π₯ βGInput π₯ π¦β π π· ( π₯ ) MPC for circuits [GMWβ87, BGWβ88, CCDβ88, BMRβ90, β¦] Constant Rounds! Constant Rounds!
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Our goal: MPC for RAM in πͺ 1 rounds
πͺ 1 -round MPC + πͺ 1 -round RAM !
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Round Complexity & Efficiency of Multi-Party Computation
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Efficiency?
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Our goal: MPC for RAM in πͺ 1 rounds
+ black-box use of cryptographic primitives
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Black-box π± What? Why? Theoretical Practical π π π(π) πβπ π π
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Our goal: MPC for RAM in πͺ 1 rounds
+ black-box use of OWFs
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Black-box MPC + Black-box RAM
Garbled RAM [LOβ13, GHLORWβ14, GLOSβ15, GLOβ15] π· βGData π· π βGProg π π₯ βGInput π₯ π¦β π π· ( π₯ ) MPC for circuits [GMWβ87, BGWβ88, CCDβ88, BMRβ90, β¦] Black box? Black box?
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Black-box MPC + Black-box RAM
Black-box garbled RAM [Garg, Lu, Ostrovskyβ15] πͺ 1 -round black-box MPC [Beaver, Micali, Rogawayβ90]
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Black-box garbled RAM π· π· GData π· βGData π· π βGProg π π₯ βGInput π₯
π¦β π π· ( π₯ )
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Black-box MPC πΆ π± πΆ π± πΆ π± πΆ
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Black-box RAM + Black-box MPC
GData π± πΆ π± πΆ π± πΆ
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Black-box RAM + Black-box MPC
GData π± πΆ π± πΆ π± πΆ
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Black-box garbled RAM [GLOβ15]
GData π· π·
![Black-box garbled RAM [GLOβ15]](http://slideplayer.com./slide/14699779/90/images/25/Black-box+garbled+RAM+%5BGLO%E2%80%9915%5D.jpg "GData. π·. π·.")
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Black-box RAM + Black-box MPC
GData π± πΆ π± πΆ π± πΆ
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Against malicious adversaries
GData π± πΆ π± πΆ π± πΆ
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Our result: MPC for RAM in πͺ 1 rounds
+ black-box use of OWFs Semi-honest / Malicious adversaries
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Thank you!
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