How does Shamir's Secret Sharing deal with the Murder on the Orient Express Problem?

Shamir's Secret Sharing (henceforth "SSS") is clever. Far too clever for most people to understand - but let's give it a go.

Suppose you have a super-secure password for a Really Important Thing.


You can remember this - because you're awesome. But it might be a good idea to share the password with someone else, just in case. Of course, if you share it with one person, they'll be able to use it. No good! So you split the password into several overlapping pieces and give each one to a different trusted friend.





And so on and so forth. As you can see, no one person has the entire password. All the participants need to get together in order to reconstruct the whole things.

(This is a massive simplification. The real SSS is so mind-boggling complex that your brain will melt before you understand even half of it. At a minimum, you need to be able to understand maths like this:

{\displaystyle a_{0}=f(0)=\sum _{j=0}^{k-1}y_{j}\prod _{\begin{smallmatrix}m\,=\,0\\m\,\neq \,j\end{smallmatrix}}^{k-1}{\frac {x_{m}}{x_{m}-x_{j}}}}

before you can even make a start.)

You can make it so that a simple majority of secret-holders are mathematically guaranteed to be able to reconstruct the password. So you could split it between 10 friends, safe in the knowledge that your security is impenetrable until at least 6 of them betray you.

"Murder on the Orient Express" is one of Agatha Christie's most beloved murder mysteries. It's 88 years old which, so I'm told, is beyond the statute of limitation for spoilers.

In the book, American businessman Samuel Ratchett is murdered while travelling on the Orient Express train. But which passenger murderised him?

All of them. They all did it. Individually they all had motive, so they ganged up and each stabbed him.

I'm sure none of your friends would do the same.

If you used SSS to split your Cryptocurrency password between a dozen trusted friends, I'm sure the promise of untold riches wouldn't be enough to tempt half of them. Would it?

Of course, you don't tell the secret-keepers who their fellows are. But social graphs are fairly easy to navigate. And not all of your friends have perfect security. A few hacks here, a gentle inquiry there, a bribe or two, and a threatening word in the right ear - suddenly you find yourself drugged, in the dark, and being stabbed. Metaphorically.

There are no simple technological solutions to complex social problems.

There is no fancy mathematics which can fix this. If you split a secret in such a way that it can be reconstructed for a sanctioned purpose, then it can be reconstructed for an unsanctioned purpose.

SSS is a technologically excellent scheme - but it requires strong social bonds to operate effectively.

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