Add button to test shares produce original mnemonic

[jsanjuas]

Added a button to the UI that tests that the mnemonic is always recovered given enough shares to buy the user peace of mind.

Caveat: since it exhaustively checks all combinations of shares, it is only practical for a rather small number of shares, though -- my laptop already needs ~40s for n=15.

[iancoleman]

Very interesting idea. Thanks for the pull request. Leave it with me to consider for a while.

My initial feeling is it's not in the interest of the user to be casting doubt like this. If the shares are created they will work, end of story, and users should have trust in it as a mathematical certainty.

It's sort of like how you wouldn't put a button in a calculator app to test all the combos of 2+3+4+5+6+7=27

But considering the newness and 'complexity' of shamir39, I can understand the motivation for this feature.

[jsanjuas]

Sure!

Let me clarify that, as a user, I wouldn't be doubting the math as much as a particular implementation of it in a dynamic language that features surprising behaviours in edge cases. Consider how critical the correctness of this tool is to a user - in this case, I would say there is never "too much reassurance" that it indeed works.

I understand your point, though. I'd argue that a measure of doubt is already cast by the warnings you have (very responsibly) included at the top.

[yorickdowne]

My initial feeling is it's not in the interest of the user to be casting doubt like this. If the shares are created they will work, end of story, and users should have trust in it as a mathematical certainty.

Something that is in the interest of the user is to type the shares back in, and verify them. Transcription errors happen, so it's a good step to take the shares from their eventual storage place - steel, or paper - and verify that they recreate the original seed, before destroying all copies of the seed phrase itself.