Shamir's scheme is related to Reed-Solomon error correction.
Ssss: Shamir's Secret Sharing Scheme (2006)
11–20 of 51 posts
Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#12Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#13Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#14Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#15Shamir's scheme is related to Reed-Solomon error correction.
Some more context here is that Reed Solomon and Shamir's Secret Sharing both take some data and produce N pieces (commonly called shards or horocruxes), any K of which can reconstruct the original data (K The difference is that Shamir's makes it so that having up to K-1 pieces reveals _no_ information about the original data. You may be able to infer certain data from less than K shards in Reed Solomon.
Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#16Here is a great talk on new SSS library from Daan Sprenkels at 34C3: https://www.youtube.com/watch?v=ojMFCpUt7OU
Implementation: https://github.com/dsprenkels/sss
Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#17Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#18This is a wonderfully simple scheme to split up keys between parties, but this still involves a party (the one that made the key) at some point knowing the key. This scheme implies you trust this distributor not to make copies of the key for himself (queue sauron references...). I've wondered if there's a scheme that does NOT trust the distributor of the key. What if the only time they key was known was when the parties reached quorum after the fact?
Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#19This is a wonderfully simple scheme to split up keys between parties, but this still involves a party (the one that made the key) at some point knowing the key. This scheme implies you trust this distributor not to make copies of the key for himself (queue sauron references...). I've wondered if there's a scheme that does NOT trust the distributor of the key. What if the only time they key was known was when the part…
Plenty. Look into publicly verifiable secret sharing.
https://en.wikipedia.org/wiki/Publicly_Verifiable_Secret_Sha...
Re: Ssss: Shamir's Secret Sharing Scheme (2006)
#20This is a wonderfully simple scheme to split up keys between parties, but this still involves a party (the one that made the key) at some point knowing the key. This scheme implies you trust this distributor not to make copies of the key for himself (queue sauron references...). I've wondered if there's a scheme that does NOT trust the distributor of the key. What if the only time they key was known was when the part…
Interesting question. Are there any restrictions on the relationship between t and n, i.e. can I have 1 <= t <= n? I had a thought for solving your problem but it might not work for arbitrary t.