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I want to implement computing ECC operations(i.e multiplication) in BMR scheme (secure Multi-party computation)

What is the best way to do it?

I found Fairplay MPC - to allow BMR computation through sdfl language, but it does not provide a good library for ECC operations.

Instead, CHARM, implements several cryptographic functionality, but without MPC.

is there anything that combines the two approaches? (Both MPC and ECC operations).

Edit: This question is about ECC operations as one component in general MPC scheme.

CHARM- https://eprint.iacr.org/2011/617.pdf

FairPlay - https://www.cs.huji.ac.il/project/Fairplay/FairplayMP.html

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If you are looking to implement private ECC operations using BMR, then you need to convert these operations first into a Boolean circuit. This will be extremely expensive and not the way to go. Rather, you need a direct protocol for this. Note that there are secure protocols for ECDSA, if this is what you are looking for.

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    $\begingroup$ The problem is that the ECC operation is just one component in the function that I try to compute. The full computation involves ECC multiplication, modular multiplication, modular addition, hash and Lagrange extrapolation. I know it seems a lot, but it uses only one ECC multiplication. That is the reason I try to use general MPC scheme. When you say extremely expensive is a matter of months or minutes/ seconds? (I don't mind that it will take minutes..) $\endgroup$ – user1387682 Jun 19 '18 at 19:26
  • $\begingroup$ Do you think to implement it with spdz2k protocol will be better? (It is working over the ring $Z_{2^k}$) $\endgroup$ – user1387682 Jul 1 '18 at 15:43
  • $\begingroup$ I suggest that you estimate the size of the circuit and then use that to estimate the running time. $\endgroup$ – Yehuda Lindell Jul 1 '18 at 18:34

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