1

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 ?

e-sushi
  • 17,891
  • 12
  • 83
  • 229
Gimv13
  • 19
  • 2
  • 1
    Does this paper help? – Ilmari Karonen May 21 '17 at 19:37
  • I suspect what you are trying to prove is that the parties can make adjustments to defend the secret without the dealer not that there was never a dealer to begin with. – Meir Maor May 21 '17 at 19:54
  • 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
  • 2
    Anyway, could you please edit your question further to clarify exactly what you're asking? I feel like I could probably answer your question, if I just knew exactly what it was. Hence all these comments. – Ilmari Karonen May 22 '17 at 17:09
  • I'm not sure how much this helps because this is applied research, but this article mentions a system where polynomial secret sharing can be done verifiably without a trusted dealer. You can find it in §5.3.3. https://pdfs.semanticscholar.org/0782/11a74dcb15d2f3844a4971e48e361d68af4f.pdf – Expectator Jul 03 '18 at 13:46
  • Standard secret sharing is not dealer free. However there are some protocols for dealer free initiation. https://eprint.iacr.org/2011/241.pdf – Erik Aronesty Jul 01 '18 at 18:33

0 Answers0