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How Shamir's Secret Sharing Works

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Re: How Shamir's Secret Sharing Works

#21

Post by davkan »

3eb7988a1663 wrote: post #12

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-...

Re: How Shamir's Secret Sharing Works

#22

Post by proxysna »

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

Re: How Shamir's Secret Sharing Works

#23

Post by alfirous »

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.

Re: How Shamir's Secret Sharing Works

#24

Post by andreareina »

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.…

Do you remember why 1 bit more?

Re: How Shamir's Secret Sharing Works

#26

Post by plopilop »

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.…

You usually do secret sharing in a finite field because computers don't like real numbers. The size of your share is a point (x, y), x can be small (typically log n in case of n participants), y is a random point in the field.

Since Shamir Secret Sharing is information-theoretically secure (if you do not know k points from the k-out-of-n secret then all secrets are equally plausible even when bruteforcing), the bitsize of your field can be whatever you want (but obviously bigger than the bitsize of your secret, you can't hide 100 bits in a finite field of 5 elements).

Usually, you don't want an attacker to be able to bruteforce your secret (while the scheme is ITS, your secret typically isn't, e.g. the seed of your wallet), hence randomness can be added to your secret and the bitsize of the field is taken big enough to thwart these attacks.

Depending on your attack model, an 80-bits or 128-bits field is more than secure enough, hence a share bitsize slightly above 80 or 128 bits.

And regarding quantum computer, since the scheme is ITS no attacks can exist.

Re: How Shamir's Secret Sharing Works

#27

Post by ahazred8ta »

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.…

Plain vanilla Shamir is information-theoretic secure and is completely impervious to QC. I can take a 1-byte secret, make 'threshold of 10' Shamir shares from it, give you 9 of the 1-byte shares, and no computer in the universe can determine the secret. (In practice, Shamir systems need to add a MAC or checksum as an integrity check, so IRL they're a few bytes larger.)

Re: How Shamir's Secret Sharing Works

#30

Post by naths88 »

_jackdk_ wrote: post #8

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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