How Shamir's Secret Sharing Works • Hacker News Board

Re: How Shamir's Secret Sharing Works

#41

Post by bigfatkitten » Tue, May 26, 2026, 11:04 AM UTC

proxysna wrote: post #22

ndr_ wrote: post #19

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.…

I think hashicorp still have an implementation for vaults seal/unseal process. Unless something changed ofc

They still do indeed.

Re: How Shamir's Secret Sharing Works

#42

Post by saidnooneever » Tue, May 26, 2026, 11:17 AM UTC

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.

Re: How Shamir's Secret Sharing Works

#43

Post by cynicalkane » Tue, May 26, 2026, 11:28 AM UTC

nitnelave wrote: post #40

Tepix wrote: post #32

Instead of going from two lines to curves, parabolas etc, couldn't you also add another dimension instead?

Two points make a line in any number of dimensions.

Think GP is suggesting an N-dimensional plane in K>N dimensions.

Re: How Shamir's Secret Sharing Works

#44

Post by Levitz » Tue, May 26, 2026, 11:30 AM UTC

nitnelave wrote: post #40

Tepix wrote: post #32

Instead of going from two lines to curves, parabolas etc, couldn't you also add another dimension instead?

Two points make a line in any number of dimensions.

Yes, but without a specific plane to intersect with, that still doesn't define a third point, if you want to check intersection with an axis, you'd need a third point in tridimensional space, for example.

Re: How Shamir's Secret Sharing Works

#45

Post by Hypomixolydian » Tue, May 26, 2026, 12:05 PM UTC

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".

Re: How Shamir's Secret Sharing Works

#46

Post by hamburglar » Tue, May 26, 2026, 12:23 PM UTC

ghostfoxgod wrote: post #18

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.

I’ve been noodling over this exact business idea for a couple years! Part of my value prop was to make ops scale down to as close to zero as possible by having the encrypted data and most of the front end for accessing it live in S3 objects (or some similar mega-cheap object store). Aside from that, all you need is the dead man’s switch mechanism. And the secret fragments would live on QR codes that bring you to the static SPA with one of the fragments already loaded up, prompting you to scan more to complete the decryption.

Good work doing it. I guess now I don’t have to. :D You may have gained a customer from this HN thread.

Re: How Shamir's Secret Sharing Works

#47

Post by cryptocod3 » Tue, May 26, 2026, 12:35 PM UTC

SSS is amazing, though managing shares over a long period (people come and go) and dealing with collusion risk can be rough.

Re: How Shamir's Secret Sharing Works

#48

Post by xtracto » Tue, May 26, 2026, 12:52 PM UTC

l1am0 wrote: post #28

Years ago I build a little tool to run shamir secret sharing in the browser (can be used full offline, just download the page) https://simon-frey.com/s4/

Ha! Years ago i downloaded your page and stored it in some usb disks along with my kdb keepass database and a share of my password.

I gave that to some members of my family and instruct them to give them to my wife in case I die.

Thanks a lot Sir.

Re: How Shamir's Secret Sharing Works

#49

Post by thisislife2 » Tue, May 26, 2026, 1:25 PM UTC

alfirous wrote: post #23

sreekanth850 wrote: post #16

ente means mine in Malayalam language. it's said to be one of the toughest Indian language to learn. FYI.

Interesting, in Indonesia Ente means you. Derived from Arabic word Anta. Fascinating how sometimes in different languages one word can have opposite meaning and the other times one word can have similar meaning.

Maybe it's the pronunciation - ente means "mine" and ante means "yours" (in Malayalam) which is what perhaps you may be referring to? (Former South Indian kingdoms and South East Asia have historical cultural ties due to trade and conquest, and thus they share some common words, which I assume is, largely borrowed from Tamil and Malayalam).

Re: How Shamir's Secret Sharing Works

#50

Post by phkahler » Tue, May 26, 2026, 2:00 PM UTC

This part:

"The useful part is not that the secret is hard to compute from too few shares. It is that too few shares contain no information about the secret. With one share missing, every possible secret is still possible."

Reminds me of factoring numbers with the Quadratic Sieve or its variants. You find a system of congruences mod n that eventually allow you to compute prime factors, but until you have enough of them that isn't possible. I've often wondered... Each congruence must contain some information right? What space are we reducing degrees of freedom in?

Same thing here, each piece restricts the space of polynomials, but does not restrict it enough to tell where the key crosses the axis.