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From: Gregory Maxwell <greg@xiph.org>
Date: Mon, 8 Jan 2018 04:22:43 +0000
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To: Pavol Rusnak <stick@satoshilabs.com>, 
	Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: [bitcoin-dev] Satoshilabs secret shared private key scheme
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On Sun, Jan 7, 2018 at 3:16 PM, Pavol Rusnak via bitcoin-dev
<bitcoin-dev@lists.linuxfoundation.org> wrote:
> On 05/01/18 14:58, nullius via bitcoin-dev wrote:
> I am currently drafting a new standard[1] which will allow also Shamir
> Secret Scheme Splitting and there we disallow usage of a custom wordlist
> in order to eradicate this mess. Will try to push this as BIP too once
> we get it to the point we are OK with the contents.
>
> https://github.com/satoshilabs/slips/blob/master/slip-0039.md

This specification forces the key being used through a one way
function, -- so you cannot take a pre-existing key and encode it with
this scheme.  The KDF it specifies is unconfigurable and fairly weak
(20000xhmac-sha2-- which can be cracked at about 0.7M passwords a
second on a single motherboard GPU cracker).  The construction also
will silently result in the user getting a different private key if
they enter the wrong passphrase-- which could lead to funds loss. It
is again, unversioned-- so it kinda of seems like it is intentionally
constructed in a way that will prevent interoperable use, since the
lack of versioning was a primary complaint from other perspective
users.  Of course, it fine if you want to make a trezor only thing,
but why bother BIPing something that was not intended for
interoperability?  Even for a single vendor spec the lack of
versioning seems to make things harder to support new key-related
features such as segwit.

The 16-bit "checksum" based on sha2 seems pretty poor since basing
small checksums on a cryptographic hash results in a fairly poor
checksum that is surprisingly likely to accept an errored string. Your
wordlist is 10 bits and you have much less than 1023*10 bits of input,
so you could easily have a 20 bit code (two words) which guaranteed
that up to two errored words would always be detected, and probably
could choose one which catches three words much more often 1:2^20
(sipa's crc tools can help find codes like this).

The metadata seems to make fairly little affordance to help users
avoid accidentally mixing shares from distinct sharings of the same
key. Is it the idea that this is the only likely cause of a checksum
error? (1:2^16 chance of silently returning the wrong key seems kinda
bad). -- I'm not sure much could be done here, though, since
additional payload is precious.

As an aside, your specification might want to give some better advice
about the SSS since my experience virtually everyone gets it wrong in
ways that degrade or destroy its properties e.g. many fail to generate
the additional coefficients of the polynominal randomly which results
in insecurity (see armory for an example).   Oh, also, I believe it is
normally refereed to as "SSS" (three S)-- four S is the name of a
linux program for secret sharing.

I'm happy to see that there is no obvious way to abuse this one as a
brainwallet scheme!