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chris-wood / draft-wood-cfrg-threshold-secret-sharing

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conversion of Shamir Secret shares to additive secret sharing #5

Open armfazh opened 1 year ago

armfazh commented 1 year ago

We might consider to cover the conversion of Shamir Secret shares to shares of an additive secret sharing.

(s1,...sN) -> (a1,..aN), such that the secret is a1+...+aN.

This technique can be hinted to the reader without any actual enforcement to be implemented in document.

chris-wood commented 1 year ago

Can you elaborate on this? I'm not sure how one converts shares to those that can be additively combined in this way.

armfazh commented 1 year ago

See Section 3.2.7 of https://eprint.iacr.org/2020/1390 or Section 2,2 of FROST paper (https://eprint.iacr.org/2020/852)

chris-wood commented 1 year ago

Unless I'm misunderstanding something, those techniques are for converting additive shares into threshold shares, not the other way around.

Edit: I haven't worked out the math, but I suppose one could invert the process based on a quick look. So, is there a use case worth mentioning this property? If not, I don't think we should add it.