I recently discovered shamirs secret sharing scheme. Pretty interesting stuff. I noticed that a common case is to split a secret which is used to encrypt/decrypt something else. For example Vault is sealed with a master key that is split using shamirs scheme.

I thought it might be interesting to split a whole file into shards instead of the key that encrypts it. But I noticed shamirs scheme isn't pretty performant. Are there faster alternatives?

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    $\begingroup$ What's wrong with the usual procedure: draw and share a random secret key, and use that for authenticated encryption of the whole file? That way the bulk of the data is the same for all participants, which reduces the amount of data generated in proportion of the number of participants, and greatly simplifies its diffusion. Performance relies on that of the authenticated encryption, which is a solved problem. $\endgroup$ – fgrieu Mar 21 '20 at 7:44
  • $\begingroup$ You can turn the scheme into an additive one, where you add each share instead of doing the full Lagrange interpolation. Depending on your requirements, this may be faster. $\endgroup$ – Aman Grewal Mar 23 '20 at 13:15

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