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Two-Round Adaptively Secure Protocols from Standard Assumptions

Two-Round Adaptively Secure Protocols from Standard Assumptions. Fabrice Benhamouda (IBM) Huijia (Rachel) Lin (UCSB) Antigoni Polychroniadou (Cornell Tech) Muthuramakrishnan Venkitasubramaniam ( University of Rochester). UC. Secure Multi-Party Computation.

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Two-Round Adaptively Secure Protocols from Standard Assumptions

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  1. Two-Round Adaptively Secure Protocols from Standard Assumptions Fabrice Benhamouda (IBM) Huijia(Rachel) Lin (UCSB) Antigoni Polychroniadou (Cornell Tech) MuthuramakrishnanVenkitasubramaniam (University of Rochester)

  2. UC Secure Multi-Party Computation f(x1, x2, x3, x4) = (y1, y2 ,y3 ,y4 ) x1 x1 x1 y4 y1 x4 • Goal: • Correctness: Everyone computes f(x1,…,x4) • Security: Nothing else but the output is revealed Adversary PPT Malicious Adaptive x2 y3 y2 x3

  3. Static vs. Adaptive Adversaries Static Corruption … Corrupt only on the onset of π … … Adaptive Corruption … Corrupt adaptively during the executionof π

  4. Static vs. Adaptive Adversaries • Dealersecret shares s among O(√n)random parties and publishes the set of such parties s=(s1,s2) s1 s2 Static vs. Adaptive Learns s

  5. Adaptive Corruption of all parties Crucial in the composition of protocols. • If adversary corrupts all m parties in πinner,wherem<n,security ofπoutershould still hold. n-party protocol πouter m-party protocol πinner

  6. Adaptive vs. Semi-Adaptive Adversaries Semi-Adaptive Corruption … Static corruption of one party and adaptive corruption of the other party …

  7. State-of-the-art for Malicious MPC In the CRS model Partial Solutions for constant-round adaptive protocols: • UsingIndist. Obf.[GP15,DKR15,CGP15]

  8. State-of-the-art for Malicious MPC In the CRS model Partial Solutions for constant-round adaptive protocols: • UsingIndist. Obf.[GP15,DKR15,CGP15]

  9. Our Goal 2-round adaptive MPC From standard assumptions 2-round adaptive OT

  10. Our Results Theorem (informal) O(1)-round malicious adaptive MPC + 2-round malicious adaptive OT 2-roundmalicious adaptive UC MPC  Corollary (informal) LWE/QR/DDH  2-round malicious adaptive UC OT LWE/QR/DDH  2-round malicious adaptive UC MPC

  11. Tools for Static 2-round MPC [BL18] Arbitrary round static MPC Garbled circuits Arbitrary round malicious static MPC 2-round malicious static OT NIZK

  12. Tools for Adaptive 2-round MPC EquivocalGarbled circuits Constant round malicious adaptive MPC 2-round malicious adaptiveOT ? 3-round adaptive malicious MPC from DDH [ABP17] 2-round adaptive malicious OT from iO [GP15]

  13. Adaptive 2-round Oblivious Transfer 2-round malicious adaptive OT 3 2 2-round semi-adaptive malicious OT 2-round sender-semi-adaptive malicious OT 1 sender & receiver oblivious sampleability 2-round static malicious OT with: LWE/QR/DDH

  14. Adaptive 2-round Oblivious Transfer 2-round malicious adaptive OT 3 2 2-round semi-adaptive malicious OT 2-round sender-semi-adaptive malicious OT 1 This talk sender & receiver oblivious sampleability 2-round static malicious OT with: LWE/QR/DDH

  15. 2-round Sender-semi-adaptive Malicious OT Theorem (informal) UC static malicious OT with sender oblivious sampleability sender-semi-adaptive malicious UC OT 

  16. Definition: 2-round OT m0,m1 b R S OT1(b) OT2(m0,m1) mb • Goal: • The Sender should not learn b • The Receiver should not learn m1-b

  17. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT m0,m1 b R S OT1(b) OT2(m0,m1)

  18. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT m0,m1 b R S OT1(b) Sim OT2(mb) Problem Not possible to explain OT2 for m1-b

  19. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT with Sender Sampleability m0,m1 b=0 R S OT1(b) Sim OT2(m0,0) OT2(m0,1) Problem Not possible to obliviously sample one-out-of-two OT2wrt. m0 in the real world

  20. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT with Sender Sampleability m0,m1 b=0 R S OT1(b) OT2($,m1) OT2(m0,$) OT2(.) OT2(.)

  21. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT with Sender Sampleability m0,m1 b=0 R S OT1(b) Sim OT2(m0,$) OT2($,0) OT2($,1) OT2(.)

  22. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT with Sender Sampleability m0,m1 b=0 R S OT1(b) OT2(m0,$) OT2($,m1) OT2(.) OT2(.)

  23. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT with Sender Sampleability m0,m1 b=0 R S OT1(b) OT2(m0,$) OT2($,m1) OT2(.) OT2(.) Problemwith correctness Which OT output is the right one?

  24. 2-round Sender-semi-adaptive Malicious OT Building block: Let OT=(OT1,OT2) be a UC staticmalicious OT with Sender Sampleability m0,m1 b=0 R S OT1(b) OT2($,rm1) OT2(rm0,$) OT2(.) rm0, rm1 OT2(.)

  25. Adaptive 2-round Oblivious Transfer 2-round malicious adaptive OT 3 2 2-round semi-adaptive malicious OT This talk 2-round sender-semi-adaptive malicious OT 1 sender & receiver oblivious sampleability 2-round static malicious OT with: LWE/QR/DDH

  26. Adaptive 2-round Oblivious Transfer Hash proof systems with projection key oblivious sampleability 2-round malicious adaptive OT 3 Encryption scheme with ciphertext oblivious sampleability 2 2-round semi-adaptive malicious OT This talk 2-round sender-semi-adaptive malicious OT 1 sender & receiver oblivious sampleability 2-round static malicious OT with: LWE/QR/DDH

  27. Adaptive 2-round Oblivious Transfer Equivocal garbled circuits 2-round malicious adaptive OT 3 2 2-round semi-adaptive malicious OT 2-round sender-semi-adaptive malicious OT with oblivious sampleability This talk 2-round sender-semi-adaptive malicious OT 1 sender & receiver oblivious sampleability Non-interactive equivocal commitment 2-round static malicious OT with: LWE/QR/DDH

  28. Adaptive 2-round Oblivious Transfer 2-round malicious adaptive OT 3 2 2-round semi-adaptive malicious OT 2-round semi-adaptive malicious OT This talk 2-round sender-semi-adaptive malicious OT 1 Augmented non-committing encryption sender & receiver oblivious sampleability 2-round static malicious OT with: LWE/QR/DDH

  29. Our Results 2-round adaptive MPC From standard assumptions 2-round adaptive OT LWE/QR/DDH  2-round malicious adaptive UC OT LWE/QR/DDH  2-round malicious adaptive UC MPC

  30. Open Problems • Efficient adaptive 2-round MPC • Adaptive Laconic Function evaluation • 4-round adaptive MPC in the plain model

  31. Thank you!

  32. Transformation 3 Tools 2-round malicious adaptive OT 3 2-round semi-adaptive malicious OT Augmented non-committing encryption

  33. 2-round Malicious Adaptive OT m0,m1 b R S OT2(b) pk0,pk1 OT2(m0+r0) OT2(m1+r1) NCE(pk0,r0) OT2(pk1,r1)

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