How Shamir's Secret Sharing Works
https://ente.com/blog/how-shamirs-secret-sharing-works/My masters thesis was on this! I created an app where you can store your data across all the common data storage providers (dropbox, google drive, onedrive, etc.) and used the secret sharing to aid with the encryption. The benefit was that:
- They could no longer read your data
- Additional redundancy (as you only need 2 to be available)
- Compared to other secure storage apps which rely on a master password, which if you forget, you are screwed, you could still use all the usual account recovery methods.
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We use this technique in our team to distribute passphrases for our secondary secret stores (that contain instructions on how to access our primary secret stores) in a "democratically secure and safe" manner.
https://packages.debian.org/trixie/ssss is a nice and rather straightforward implementation.
Shamir saved my bottom once, by helping me reconstruct random password used for almost forgotten backup, suddenly needed to be restored at once. Thank God I distributed shares in my family, "just in case".
Bruce Schneier described this in his seminal book Applied Cryptography, and HashiCorp Vault used to have an implementation in Go. On the practical side, I always wondered how large - in bits - the shares should be. One answer I got on a news group was "1 bit more than the actual key length". Nowadays, I wonder how the quantum computing threat would inform 1) share size choice and 2) pro/con Secret Sharing in general. Does anyone know?
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This is such a cool technique, and you could even teach it in secondary schools as a neat thing computer scientists can do with polynomials.
I am a secondary math teacher and I do exactly this with my students.
When working on retrieving the expression of an affine function, I tell them about Shamir'..., they choose a secret pin as the slope, generate two points, give them to two other students who have to pair together to find the pin again. The students are always very engaged.
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Here is Ente's implementation: (https://2of3.ente.com/)
There's an implementation packaged up for most Linux distros: http://point-at-infinity.org/ssss
There are several browser-based versions which can be used online or downloaded to use offline.
https://bs.parity.io/ -- http://passguardian.com/ -- https://iancoleman.io/shamir/
Years ago I build a little tool to run shamir secret sharing in the browser (can be used full offline, just download the page)
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this is very nice explanation which needs no maths. really cool. I read about this a few times in articles without images etc and its hard to digest if you dont have a good background but this was wonderfully easy to understand. Thanks a lot.
It's an incredible technique, when I came across it, it just changed the way I thought of solving giving out keys without "truly" giving them out.
This gave me confidence for eternalvault.app, a project of mine.
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Do the people who hold the root DNS keys do anything like this? Or is that too much complexity when a safe in a secure room works as an effective backup?
They do something similar. Basically 5 people are needed in order to access the dns root keys plus some extra administrative/witness people. 3 Crypto Officers with smartcards to unlock the hsm, 2 other officials to unlock the vault that contains the hsm and the vault that contains safety deposit boxes with the smartcards. There are 7 crypto officers, of which any three will do.
https://www.cloudflare.com/learning/dns/dnssec/root-signing-...
SSS is amazing, though managing shares over a long period (people come and go) and dealing with collusion risk can be rough.
Instead of going from two lines to curves, parabolas etc, couldn't you also add another dimension instead?
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if the secret is large usually it's encrypted and the payload is distributed along with the shares of the key.
but you can also just use Reed-Solomon and split the payload, the difference with Shamir is that you lose information-theoretic security (you lose it the moment you use encryption anyway) and the payload also needs to undergo an all-or-nothing-transform (AONT).
AONT transforms the entire payload into an encrypted blob which also serves as its own key, a withheld piece is a de facto encryption key. this is required because Reed-Solomon can have pathological cases where pieces leak information.
Reed-Solomon is an Erasure code, and I definitely wouldn't look to that for Secret Splitting. Those leakage models are gnarly. But if you want something else that is more general - there are Monotone Span Programs. Seriously underused.
> Reed-Solomon is an Erasure code
> Those leakage models are gnarly.
I also had written an article on the subject a while ago if you want to dig a bit deeper: https://petal.cafe/posts/shamir/
before I learned of shamir secret sharing, I wondered why one couldn't do the same exact thing with a par2 like system (albiet with smaller pieces than a par2 system would traditionally have). i.e. you have X bits of data, you create Y*X/N sized recovery blocks (where Y > N). You hand each recovery block to individual users. and any N users can get together to recover the key and decrypt the contents.
Well in theory the base math is indeed the same; unfortunately though the "randomly chosen" part of shamir's secret sharing is fairly important to the security because information theoretic security of the scheme requires each fragment to be as large as the original secret by way of essentially including a desired count of random data blocks to the original before applying the reed-solomon-like erasure coding to it where now enough fragments to reconstruct the secret plus all random blocks have to be combined.
Also the way of usage of the erasure code has to be selected to not be leaking information but that's more of an issue of not picking a bad way of how to implement the basic concept here. Basically just a case of "do follow the instructions to shamir's secret sharing, don't do something different just because it's a popular way of implementing reed-Solomon".
Yes, you can just GF(256), but if you're worried I'd also just use a prime field instead.
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This is such a cool neat trick.
Vibe-coded a little playground where you can generate secrets, see the polynomial, combine the secrets, and in general, play around:
SSS works pretty well. IIRC somebody in bitcoin community started using this for storing private keys using 3/5 schema. they basically divide the secret keys into 5 parts out of which you only need 3 to recover original private key. IDK if there are any hardware wallets that actually support it yet though.
ente means mine in Malayalam language. it's said to be one of the toughest Indian language to learn. FYI.
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something tangentially i am interested in is computing following the 'two person rule' for things like sudo. Yes I am logged into server X at terinal Y, and so is my co-worker and we both sign off on running command X
Had something like this at Google. There's a service running as root (or equivalent) which receives your desired command to run, and it has to get authorization from another user for the specific command to run, then runs it. That makes sense at Google, because those are production machines and have access to LDAP and who is allowed to run a command on a machine is defined by an LDAP group and you would need two of them (or more?) and there's already existing management website this can be shoe-horned into.
Your environment is unlikely to have all of that already, so you'll need to figure out equivalents for all those. But I think you're going to need a local service running as root and it's going to need to be able to tell the difference between distinct human users, if you want secure. Just typos is way easier.
There's a related 2-man sudo login system here, not sure how finegrained it is.
https://github.com/Argonne-National-Laboratory/Pam-2man-Auth
That sounds like you might want to look into digital signatures.
See also a story about an implementation from Max Levchin: https://max.levch.in/post/724289457144070144/shamir-secret-s...
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