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Find the product of two sums via SMPC

I’m currently working on a distributed threshold DSA scheme that requires to find the product of two sums via secure multi-party computation.
Specifically speaking, every one of $n$ parties $P_i$ possesses a DSA key pair $(sk_i, pk_i)$, where $sk_i=d_i in mathbb{Z}_q$ and $pk_i = g^{d_i}$. I want to collectively generate a signature $S_{Sigma} = k_{Sigma}^{-1}(m+r_{Sigma}d_{Sigma})$, where$k_{Sigma}=k_1+dots k_n$, $r_{Sigma}d_{Sigma}=(r_1+dots+r_n)cdot(d_1+dots+d_n)$. My prior question is that is there a proper paradigm to compute $r_{Sigma}d_{Sigma}$ without leaking information about secret keys $(d_1,dots,d_n)$? For computing $k_{Sigma}$, I’m using the BGW Protocol and Shamir threshold secret sharing scheme. Is it possible to compute $r_{Sigma}d_{Sigma}$ using BGW protocol as well?

PS: I’m new to SMPC, and English is not my first language. Sorry for the troubles. Thanks!

Find the product of two sums via SMPC

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