Round-efficient black-box constructions of composable multi-party computation

Result by Susumu Kiyoshima
Blog written by Samuel Ranellucci

The protocols are black-box and composable and allow realization of all
tasks in MPC.

UC secure protocol impossible in the standard model but in Angel based UC
protocol are realizable in the plain model.

In this work, they construct a Angel-UC commitment with log(n^2) rounds
based on semi-hones OT

The old recipe is CCA-Com plus Semi-Honest OT provides MPC angel-UC.

CCA-Com are commitment which are hiding even with a
commitment extraction oracle which can query any other element
then the one that was committed to.

CCA-com in this paper are constructed from OWF by creating
a) good Concurrent extractable commitments
b) non-malleable commitment

A good concurrent commitment is one where an oracle
can only extract a value from a valid commitment.

This is done by making a weakly extractable commitments where extraction fails
with probability 1/2 .
but accepted commitment are invalid with probability less then 1/2.
This weakly extractable commitments when combined with previous approaches
based on cut-and-choose allow construction of good CECOM.

The techniques in this paper could provide useful techniques for further
reducing the complexity of composable MPC.

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