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I would like to perform a dot product operation among $m$ parties using Shamir's $(m,m)$ secret sharing that is used for Secure Multiparty Computation.
I am aware that Shamir's $(m,m)$ scheme is additively homomorphic, but can someone please provide an example of how I can use it for multiplicative homomorphism for SMC?
As far as I know, you can not do multiplication with (m,m) shamir secret sharing. The typical method to do multiplication on shamir secret shares increases the degree of the sharing polynomial, which is why the parties run an additional protocol to reduce the degree. That is why the degree of the sharing polynomial must be less than $m/2$ if there are $m$ parties.
If you indeed need (m,m) (or $m$ out of $m$ parties must be present to do reconstruction and multiplication), and the only operation you need to compute is multiplication (which I'm not sure about since your comments state you want to do multiplication, but your question mentions dot product), then I'd suggest using multiplicative secret sharing.
If instead you need $m$ out of $m$ computation/reconstruction, but need to do both addition and multiplication operations, you'll have to go with some of the newer MPC constructions which achieve full-threshold security (SPDZ and some of it's references or subsequent works which cite it).
