# Noisy secret sharing

I am looking for a secret sharing scheme that is robust against noise, the shares are going to be noisy. We do not want to reconstruct the secret perfectly and a noisy reconstruction with a bound on noise is good enough.

Assume we are using $$(n,k)$$ Shamir's scheme to distribute a secret among $$n$$ parties so that we need at least $$k$$ of them to recover. If we add noise to the shares, using $$k$$ points, the reconstructed polynomial would be very noisy. However, having access to an infinite amount of points would result in a perfect reconstruction. Are there any works that quantify this reconstruction noise?

If you know of any other idea or another sharing scheme, that would also be great!

• Did you have a look at Reed Solomon error correcting codes? Does that solve your problem in anyway? Oct 13 '20 at 18:06
• also see this: mortendahl.github.io/2017/08/13/secret-sharing-part3 Oct 13 '20 at 18:06
• – Mark
Oct 14 '20 at 4:26
• Possibly a duplicate of crypto.stackexchange.com/q/1760/819. Oct 14 '20 at 20:50
• The post you guys mention reconstructs the secret perfectly. However, here we can tolerate some level of noise. So the problem is a little bit different. Oct 15 '20 at 23:07