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Subject: Re: [Bitcoin-development] Presenting a BIP for Shamir's Secret
Sharing of Bitcoin private keys
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On Thursday, 3 April 2014, at 4:41 pm, Nikita Schmidt wrote:
> I agree with the recently mentioned suggestion to make non-essential
> metadata, namely key fingerprint and degree (M), optional. Their
> 4-byte and 1-byte fields can be added individually at an
> implementation's discretion. During decoding, the total length will
> determine which fields are included.
The fingerprint field, Hash16(K), is presently specified as a 16-bit fi=
eld. Rationale: There is no need to consume 4 bytes just to allow share=
s to be grouped together. And if someone has more than 100 different se=
crets, they probably have a good system for managing their shares and w=
on't need the hash anyway.
> Encoding for the testnet is not specified.
Hmm, is that actually needed?
> Speaking of encoding, is it not wasteful to allocate three different
> application/version bytes just for the sake of always starting with
> 'SS'? It would be OK if it were accepted as a BIP, but merely as a
> de-facto standard it should aim at minimising future chances of
> collision.
I agree on principle, however I think the more user-acceptable behavior=
is for all base58-encoded Shamir shares to begin with a common prefix,=
such as "SS". Users are accustomed to relying on the prefix of the bas=
e58 encoding to understand what the object is: "1" for mainnet pubkey h=
ash, "3" for mainnet script hash, "5" for uncompressed private key, "P"=
for passphrase-protected private key, etc.
> I'd add a clause allowing the use of random coefficients instead of
> deterministic, as long as the implementation guarantees to never make=
> another set of shares for the same private key or master seed.
I'm not sure that's necessary, as this is an Informational BIP. Impleme=
ntations are free to ignore it. Shares with randomly selected coefficie=
nts would work just fine in a share joiner that conforms to the BIP, so=
I would expect implementors to feel free to ignore the deterministic f=
ormula and use randomly selected coefficients.
> What about using the same P256 prime as for the elliptic curve? Just=
> for consistency's sake.
The initial draft of this BIP used the cyclic order (n) of the generato=
r point on the secp256k1 elliptic curve as the modulus. The change to t=
he present scheme was actually done for consistency's sake, so all size=
s of secret can use a consistently defined modulus.
> Also, I'm somewhat inclined towards using the actual x instead of j i=
n
> the encoding. I find it more direct and straightforward to encode th=
e
> pair (x, y). And x=3D0 can denote a special case for future extensio=
ns.
> There is no technical reason behind this, it's just for (subjective)=
> clarity and consistency.
There is a technical reason for encoding j rather than x[j]: it allows =
for the first 256 shares to be encoded, rather than only the first 255 =
shares.
If you want a sentinel value reserved for future extensions, then you m=
ight take notice that 0xFFFF is an invalid key fingerprint, along with =
several other values, and also that 0xFF is an unusable value of M=E2=88=
=922, as that would imply M=3D257, but the scheme can only encode up to=
256 shares, so one would never have enough shares to meet the threshol=
d. I considered having the two optional fields be mandatory and allowin=
g 0xFFFF and 0xFF as "redacted" field values, but I like allowing the s=
hares to be shorter if the optional fields are omitted. (Imagine engrav=
ing Shamir secret shares onto metal bars by hand with an engraving tool=
. Fewer characters is better!)
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