# Shamir's Secret Sharing - Proactive and dealer-free [duplicate]

I recently started studying about cryptography and I tried to search the internet but I can't find much about these subjects. I want to see the proof of Shamir's Secret Sharing being Proactive and dealer-free .

Later Edit: I found the proof of it being proactive, however I still struggle with the 2nd thing. Basically, if the users know (k,n,p) , how can they compute a secret with none of them knowing it ?

## marked as duplicate by e-sushiJul 8 '18 at 1:39

• Are you asking how any party of $k$ people amongst $n$ knowing each a different $p_i$, for $i \in \{1, \ldots, n\}$ can recover a secret value shared using Shamir's Secret Sharing scheme? – Lery May 22 '17 at 10:48
• As @MeirMaor notes, the usual definition of "dealer-free" seems to be that a trusted dealer is not required to proactively update the shares, even if such a dealer might be needed to generate the initial shares to begin with. Anyway, if you're asking for a scheme to let n semi-honest parties collaboratively generate a (random) $k$-out-of-$n$ shared secret, this answer describes one way to do it: basically, each party generates a random secret and shares it with the others using Shamir's scheme, and then everybody sums up the shares they received. – Ilmari Karonen May 22 '17 at 17:07