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Shamir's Secret Sharing

en.wikipedia.org

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Re: Shamir's Secret Sharing

#11

Post by lolidaisuki »

Xcelerate wrote: post #4

I've been wanting to use this in combination with Rabin's Information Dispersal algorithm to create an autonomous distributed file storage system. You would have redundancy, but redundancy in a way that you only require k of n "pieces" to recover your original file (or data object). This is pretty cool, because you don't need to have 10 copies of a 1 GB file (10 GB total) spread about the web in order to achieve a hi…

Sounds a lot like Tahoe-LAFS[1].

[1]: https://tahoe-lafs.org/trac/tahoe-lafs

Re: Shamir's Secret Sharing

#12

Post by Rygu »

Open source implementations available on GitHub:

Python - https://github.com/blockstack/secret-sharing

PHP - https://github.com/mathieuk/secretsharer

Node - https://github.com/amper5and/secrets.js

Go - https://github.com/codahale/sss

C - https://github.com/fletcher/c-sss

Ruby - https://github.com/lian/shamir-secret-sharing

Java - https://github.com/timtiemens/secretshare

Rust - https://github.com/sellibitze/secretshare

Re: Shamir's Secret Sharing

#13

Post by yoo1I »

I run a small operation providing websites/online storage/email for a couple of friends and small businesses, and I use this as recovery solution to a master key. I distributed the encrypted very big master key, full system documentation and a part of the decryption key to the master key to a couple of people including a public notary. This way, should it ever get necessary, it will be possible for them to access my encrypted files. Say I get hit by a bus or something similar.

Thank you, Shamir!

Re: Shamir's Secret Sharing

#14

Post by heinrich5991 »

dlgeek wrote: post #5
Xcelerate wrote: post #4

I've been wanting to use this in combination with Rabin's Information Dispersal algorithm to create an autonomous distributed file storage system. You would have redundancy, but redundancy in a way that you only require k of n "pieces" to recover your original file (or data object). This is pretty cool, because you don't need to have 10 copies of a 1 GB file (10 GB total) spread about the web in order to achieve a hi…

When you encode information with Shamir Secret Sharing, each share is actually bigger than the original secret. The computation requirements also don't scale very well. What you want is called Erasure Coding. ( https://en.wikipedia.org/wiki/Erasure_code )

>each share is actually bigger than the original secret

This is not true according to the Wikipedia article: Shamir's secret sharing is minimal, i.e. the size of each piece does not exceed the size of the original data.

https://en.wikipedia.org/w/index.php?title=Shamir%27s_Secret....

Re: Shamir's Secret Sharing

#15

Post by jacobkg »

What's especially cool about this technique is that unlike most crypto proofs it does not assume the existence of one-way functions (none have been found yet) nor does it require a computationally bounded adversary.

Instead this technique is information theoretically secure so even an adversary with the ability to perform exponentially slow algorithms instantly could not find the secret.

All this in a two page paper that only required high school math!

PS - The "Shamir" who found this technique is the S in RSA

Re: Shamir's Secret Sharing

#19

Post by tehrei »

Rygu wrote: post #12

Open source implementations available on GitHub: Python - https://github.com/blockstack/secret-sharing PHP - https://github.com/mathieuk/secretsharer Node - https://github.com/amper5and/secrets.js Go - https://github.com/codahale/sss C - https://github.com/fletcher/c-sss Ruby - https://github.com/lian/shamir-secret-sharing Java - https://github.com/timtiemens/secretshare Rust - https://github.com/sellibitze/secretsha…

You should be a bit careful with implementations and keep in mind that you can't split a number larger than the prime you've picked. I've seen people go "oh I'll just split an N-byte value into M * N-byte values, splitting each byte separately with the largest prime < 256, surely the loss of a few values per byte won't be of consequence...". It might not be in your case, but you need to be aware of that.
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