Secure Multiparty RAM Computation in Constant Rounds

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Presentation transcript:

Secure Multiparty RAM Computation in Constant Rounds Sanjam Garg Divya Gupta Peihan Miao Omkant Pandey

𝐷 1 𝐷 2 𝐷 3 𝐷 𝑃 𝑃 𝐷 (𝑥) 𝑃 𝐷 (𝑥) 𝑃 𝐷 (𝑥) 𝑥 1 𝑥 3 𝑥 2

Our goal: MPC for RAM How about MPC + RAM ?

MPC + RAM Garbled RAM [LO’13, GHLORW’14, GLOS’15, GLO’15] 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 ) MPC for circuits [GMW’87, BGW’88, CCD’88, BMR’90, …]

𝐷 𝐷 𝐷 𝛱 GData 𝐷 1 𝐷 3 𝐷 2 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 )

𝑃 𝑃 𝑃 𝑃 𝑃 𝛱 GProg 𝑃 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 )

𝑥 𝑥 𝑥 𝛱 GInput 𝑥 1 𝑥 3 𝑥 2 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 )

𝑦← 𝑃 𝐷 𝑥 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 )

Round Complexity & Efficiency of Multi-Party Computation

Round complexity?

Our goal: MPC for RAM in 𝒪 1 rounds

𝒪 1 -round MPC + 𝒪 1 -round RAM Garbled RAM [LO’13, GHLORW’14, GLOS’15, GLO’15] 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 ) MPC for circuits [GMW’87, BGW’88, CCD’88, BMR’90, …] Constant Rounds! Constant Rounds!

Our goal: MPC for RAM in 𝒪 1 rounds 𝒪 1 -round MPC + 𝒪 1 -round RAM !

Round Complexity & Efficiency of Multi-Party Computation

Efficiency?

Our goal: MPC for RAM in 𝒪 1 rounds + black-box use of cryptographic primitives

Black-box 𝛱 What? Why? Theoretical Practical 𝑓 𝑎 𝑓(𝑎) 𝑏←𝑓 𝑎 𝑓

Our goal: MPC for RAM in 𝒪 1 rounds + black-box use of OWFs

Black-box MPC + Black-box RAM Garbled RAM [LO’13, GHLORW’14, GLOS’15, GLO’15] 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 ) MPC for circuits [GMW’87, BGW’88, CCD’88, BMR’90, …] Black box? Black box?

Black-box MPC + Black-box RAM Black-box garbled RAM [Garg, Lu, Ostrovsky’15] 𝒪 1 -round black-box MPC [Beaver, Micali, Rogaway’90]

Black-box garbled RAM 𝐷 𝐷 GData 𝐷 ←GData 𝐷 𝑃 ←GProg 𝑃 𝑥 ←GInput 𝑥 𝑦← 𝑃 𝐷 ( 𝑥 )

Black-box MPC 𝐶 𝛱 𝐶 𝛱 𝐶 𝛱 𝐶

Black-box RAM + Black-box MPC GData 𝛱 𝐶 𝛱 𝐶 𝛱 𝐶

Black-box RAM + Black-box MPC GData 𝛱 𝐶 𝛱 𝐶 𝛱 𝐶

Black-box garbled RAM [GLO’15] GData 𝐷 𝐷

Black-box RAM + Black-box MPC GData 𝛱 𝐶 𝛱 𝐶 𝛱 𝐶

Against malicious adversaries GData 𝛱 𝐶 𝛱 𝐶 𝛱 𝐶

Our result: MPC for RAM in 𝒪 1 rounds + black-box use of OWFs Semi-honest / Malicious adversaries

Thank you!