Efficient Multiparty Protocols via Log-Depth Threshold Formulae Ron Rothblum Weizmann Institute Joint work with Gil Cohen, Ivan Damgard, Yuval Ishai, Jonas.

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Presentation transcript:

Efficient Multiparty Protocols via Log-Depth Threshold Formulae Ron Rothblum Weizmann Institute Joint work with Gil Cohen, Ivan Damgard, Yuval Ishai, Jonas Kolker, Peter Bro Miltersen and Ran Raz

Secure Multiparty Computation (MPC) [Yao86,GMW87] An adversary that controls a (limited) subset of the parties learns nothing more than the inputs and outputs of the parties it controls.

Feasibility Results: Perfect Security [BGW88,CCD88]

Our Contribution Huge body of work on secure MPC but protocols are fairly complicated. We suggest a conceptually simple and flexible approach to designing efficient MPC protocols. Building blocks: 1.Player emulation - builds on Hirt-Maurer [HM00] but with a different motivation. 2.Simple constant-party MPC protocols. 3.Threshold formulae composed of threshold gates.

Applications 1.Conceptually simple protocols for perfectly secure MPC – obtaining passive/active security. 2.New results on feasibility of MPC in a variety of settings, e.g., secure MPC over algebraic structures such as non-Abelian groups. 3.Distributed computing – broadcast/Byzantine agreement.

MPC via Player Emulation [HM00]

MPC via Player Emulation Minimal number of parties needed for security against one passive party

MPC with a Trusted Party

MPC via Player Emulation

The output is sent back to the parties.

MPC via Player Emulation

Associate wires with parties and place 1 on input wires that the adversary controls. If output is 0 then the protocol is secure against this adversary.

MPC via Player Emulation

Comparison with [HM00]

MPC via Player Emulation

3-Party Protocols Can use BGW restricted to 3 parties or better yet use the MPC made simple protocol of [Maurer02]. Maurers protocol is simple and elegant but exponential in the number of parties. For 3 parties– not an issue!

MPC via Player Emulation

Majority from Majorities

Active Security Minimal number of parties for security against one active party

Applications Simplifications*: 1.MPC over fields ([BGW88], [CCD88], [AL13]). 2.MPC over rings ([CFIK03]). 3.MPC over groups ([DPSW07,DPS+12a,DPS12+b]). 4.Distributed computing: broadcast, broadcast from 2-cast ([FM00]). * Caveats: non-optimal threshold and higher polynomial complexity.

Applications

Conclusions and Open Questions MPC methodology: 1.Design simple constant-party protocols. 2.Prove player emulation theorem. Intriguing connections to open questions in complexity-theory: 1.Explicit exact majority-from-majorities formula. 2.Exact threshold-from-thresholds formula (even non-explicit).

Thank you!