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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!

FBK

#FBK #TheSupremeTeam Artist Name: FBK Who are you? Lyricist, genre is mainly Trap/UK rap with a foreign vibe. Love using Spanish guitar beats. Where are you from? I’m a rapper that lives in London, originally from Egypt. How can we follow you? Spotify – https://open.spotify.com/artist/3BZdn1FAhpCjHJ2A4z2M0A?si=EiY9H1olTiuGf21IQGwkXQ Linktree – https://linktr.ee/fbkyoungmo Song Title: Tony Montana Listen to FBK:::Listen

#FBK #TheSupremeTeam
Artist Name: FBK

Who are you?

Lyricist, genre is mainly Trap/UK rap with a foreign vibe. Love using Spanish guitar beats.

Where are you from?

I’m a rapper that lives in London, originally from Egypt.

How can we follow you?

Spotify – https://open.spotify.com/artist/3BZdn1FAhpCjHJ2A4z2M0A?si=EiY9H1olTiuGf21IQGwkXQ

Linktree – https://linktr.ee/fbkyoungmo

Song Title: Tony Montana

Listen to FBK:

Source: https://supremepr.us/

Find the product of two sums via SMPC

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