[Cryptography] About Secret Sharing Schemes and a Question

[Natanael]

Den mån 3 juni 2019 17:38Osman Kuzucu <bizbucaliyiz at hotmail.com> skrev:

> Hello,
>
> I am a cryptography fan and a beginner in the field and I wanted to hear
> opinions from the Cryptography mailing list members. I have been searching
> about the "Secret Sharing Schemes" and came across to the Shamir's Secret
> Sharing Scheme.
>
[...]
> Also, as for the application of the scheme, I wanted to ask one more
> situation. Assuming we have a secret *S* (a private key maybe?)
> distributed to *n* different secret share holders by using a secret
> sharing scheme, and we are periodically (say every month) producing data,
> namely *D1, D2, D3 ... Dn*. Our rule is, if *k* amount of people come
> together, they should be able to produce a data * Di*, which would be
> verifiable by the public that it was generated by at least *k* amount of
> share holders' collaboration. However, we do not want any share holder, or
> anyone from public to learn the actual secret *S*, so that no share
> holder, who contributed to the data production, will not be able to produce
> any other data *D*i+1 in the future without other share holders' help.
>

What you're looking for is the general class of threshold cryptography, of
which Shamir's secret sharing scheme is just one variant.

For example, consider threshold signatures and threshold encryption.

In both of those cases you have a number of asymmetric keypairs that are
combined in an operation without revealing your private key to any other
party. Depending on the specific implementation, such a scheme might work
by deriving a combined group public key (from the public keys of the
participants) to be used for verification of signatures or encryption of
data, while a special protocol is used by the private key holders to work
together to sign or decrypt data.

Does that sound like what you're looking for?
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