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I see that a lot of multiparty computation and garbling protocols are implemented for circuits like AES or SHA256. For my project, I would like to garble a circuit that performs some group operations on elliptic curves and RSA groups.

Are there any circuit compiler libraries or garbling libraries that support this? Are there any estimates on the size of a circuit that performs one group operation?

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  • $\begingroup$ Do you just need group operations (i.e. a MPC scheme only supporting group operations would be fine)? $\endgroup$ – SEJPM Mar 30 at 17:54
  • $\begingroup$ @SEJPM My actual plan is to implement IBE from DDH protocol proposed by Dottling and Garg. Their circuit performs a bunch of group exponentiations. If I can estimate the circuit size for one group operation, then I can estimate the overall circuit size. $\endgroup$ – satya Mar 30 at 18:01
  • $\begingroup$ I'm pretty sure there was a twitter thread within the last year or so (that I can't find anymore) where Nigel Smart asked a similar question. Also on a relevant note, I just want to place the reminder that MPC circuits can be arithmetic or binary and the former should easily support just describing ECC operations as you'd in software (especially when choosing the MPC field prime to be the ECC prime). $\endgroup$ – SEJPM Mar 30 at 21:16

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