Score:1

Find the product of two sums via SMPC

sa flag

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!

cn flag
If you are going to compute the product of two secret numbers (in your case r*d), then, you can use Beaver's multiplication triple to do it.
Score:0
ng flag

Yes it is, see for example this page. Note that multiplication requires $O(n^2)$ additional communication, in contrast to addition (which is free).

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