I came across Shamir's Secret Sharing recently when thinking about how a partial password scheme might best be implemented. I even went as far as writing up an implementation of the cryptographic aspects.
Shamir's Secret Sharing
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Re: Shamir's Secret Sharing
#12Shamir’s Secret Sharing is one of my favorite algorithm names. It sounds straight out of a D&D wizard spell list. Especially when you interpret it as ”sharing in secret” instead of ”sharing a secret”.
Re: Shamir's Secret Sharing
#13I'm not a mathematician but here is my ELI5 understanding of it based on linked wikipedia article.
If you know the coordinates of any 2 points on a line you can recover the equation for that line. The same is true for 3 points on a quadratic curve and 4 points on cubic curve, etc.
So if our secret is the number c we can put it in the equation for, say, a quadratic: ax^2 + bx + c = 0 We can then give any number of people the coordinates for different single points on this curve.
None of these people know the equation but if any 3 of them share their coordinates they can work out the equation and thus the value of c.
Re: Shamir's Secret Sharing
#14Shamir’s Secret Sharing is one of my favorite algorithm names. It sounds straight out of a D&D wizard spell list. Especially when you interpret it as ”sharing in secret” instead of ”sharing a secret”.
It helps that Shamir as well as making the name alliterative also sounds like the stage name for some early 20th century magician
Re: Shamir's Secret Sharing
#15I'm not a mathematician but here is my ELI5 understanding of it based on linked wikipedia article. If you know the coordinates of any 2 points on a line you can recover the equation for that line. The same is true for 3 points on a quadratic curve and 4 points on cubic curve, etc. So if our secret is the number c we can put it in the equation for, say, a quadratic: ax^2 + bx + c = 0 We can then give any number of peo…
Just remember the caveat with the ELI5 explanation is that if I tell you the first two points on a parabola are (0,0) and (1,0) you will figure that the third point is more likely to be around (2,0) than, say, (2,2^30).
Re: Shamir's Secret Sharing
#16I'm not a mathematician but here is my ELI5 understanding of it based on linked wikipedia article. If you know the coordinates of any 2 points on a line you can recover the equation for that line. The same is true for 3 points on a quadratic curve and 4 points on cubic curve, etc. So if our secret is the number c we can put it in the equation for, say, a quadratic: ax^2 + bx + c = 0 We can then give any number of peo…
If you take it one step further and show how it still works modulo p, the algorithm serves as a great introduction to how and why finite fields are used in cryptography.
Re: Shamir's Secret Sharing
#17Reminds me a lot of my usenet newsgroup file sharing days and the PAR parity format. A file is split into say 200 pieces to fit within the limitations of a newsgroup post. Those 200 posts may or may not all make it to your usenet server, but an additional 10-20 parity files are also created such that you need to only find 200 total unique pieces to recreate the data.
It's different in that the data is totally readable other than the missing pieces (although practically unusable). The thing that blew my mind was just how a single parity file can fill a single gap regardless of where in the sequence of original files.
Re: Shamir's Secret Sharing
#18Vault( https://www.vaultproject.io/ ) and Phaistos KMS ( https://github.com/phaistos-networks/KMS ) both use SSD for sealing/unsealing, where a master key is created, 'divided' into multiple keys and a minimum number of such keys are required to unseal the service.
SSSS?
Re: Shamir's Secret Sharing
#19Shamir’s Secret Sharing is one of my favorite algorithm names. It sounds straight out of a D&D wizard spell list. Especially when you interpret it as ”sharing in secret” instead of ”sharing a secret”.
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Re: Shamir's Secret Sharing
#20Ever since learning about this I've wanted to use it for something, but I've never had the opportunity.
Consider you want to share the passwords to your bank accounts with your family after you die.
You take a list of those passwords, and encrypt it using SSSS with 4 of 7 keys needed to decrypt.
You then share these 7 keys with your 7 relatives.
After your death, they get together and unlock your passwords.