📅 Original date posted:2023-02-22
🗒️ Summary of this message: A simpler approach to verify shares without a computer is suggested for Codex32. A mod N=0 checksum can be used for individual shares or all shares.
📝 Original message:After some poking around at the math, I do see that the 13 character
generator (for regular sized shares) is reasonably "smooth", having roots
at T{11}, S{16}, and C{24}.
This means we could build a "quick check" worksheet to evaluate the string
modulo (x - T) to verify a 5 bit checksum, whose operation would be similar
to the existing checksum worksheet in structure but significantly less work.
Perhaps 5 bits is too short, and it is more reasonable working modulo (x -
T)*(x - S) to get a 10 bit checksum. A worksheet for a 15 bit checksum is
also an option, and possibly others well depending on the size of the other
factors. I think this process is would be about as simple as any other
comparable hand operated checksum over the bech32 alphabet would be.
I haven't looked into the smoothness of the long generator for seeds that
are greater than 400 bits. If it isn't smooth and smoother options are
available, perhaps it should be changed.
On Wed, Feb 22, 2023 at 11:29 AM Peter Todd via bitcoin-dev <
bitcoin-dev at lists.linuxfoundation.org> wrote:
> On Sun, Feb 19, 2023 at 10:12:51PM +0000, Andrew Poelstra via bitcoin-dev
> wrote:
> > > What really did catch my attention, but which was kind of buried in the
> > > project documentation, is the ability to verify the integrity of each
> > > share independently without using a computer. For example, if I store
> a
> > > share with some relative who lives thousands of kilometers away, I'll
> be
> > > able to take that share out of its tamper-evident bag on my annual
> > > holiday visit, verify that I can still read it accurately by validating
> > > its checksum, and put it into a new bag for another year. For this
> > > procedure, I don't need to bring copies of any of my other shares,
> > > allowing them (and my seed) to stay safe.
> > >
> >
> > This is good feedback. I strongly agree that this is the big selling
> > point for this -- that you can vet shares/seeds which *aren't* being
> > actively used, without exposing them to the sorts of threats associated
> > with active use.
> >
> > We should make this more prominent in the BIP motivation.
>
> I don't think that use-case is a good selling point. The checksum that
> Codex32
> uses is much more complex than necessary if you are simply verifying a
> share by
> itself.
>
> A *much* simpler approach would be to use a simple mod N = 0 checksum,
> either
> by creating the seed such that each share passes, or by just storing an
> additional word/symbol with the seed in such a way that sum(words) mod N =
> 0
> passes. This approach is not only possible to compute by hand with a
> word/symbol->number lookup table, and pen and paper or a calculator. It's
> so
> simple they could probably *remember* how to do it themselves.
>
>
> Secondly, if all shares have mod N checksums, it may be sufficient for
> everyone
> to write down the checksums of the *other* shares, to verify they are the
> correct ones and a different (otherwise correct) share hasn't accidentally
> been
> substituted.
>
> Indeed, with some brute forcing and small checksums, I'd expect it to be
> mathematically possible to generate Shamir's secret sharing shards such
> that
> every shard can share the *same* checksum. In which case the share
> verification
> procedure would be to simply ask every share holder to verify the checksum
> manually using the mod N procedure, and then verify that each share holder
> has
> the same checksum. This would be less error prone in terms of leaking
> information accidentally if the checksum was obviously *not* part of the
> share:
> eg by encoding the share with words, and the checksum with a number.
>
> Obviously, small checksums aren't fool proof. But we're probably better off
> creating a relatively easy procedure with a 1-in-1000 chance of an error
> going
> undetected than a complex procedure that people don't actually do at all.
>
> --
> https://petertodd.org 'peter'[:-1]@petertodd.org
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev at lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20230222/8b9500fc/attachment.html>;
Russell O'Connor [ARCHIVE] /
npub1dw…8plrw
2023-06-07 23:19:44
in reply to nevent1q…u4qn
Author Public Key
npub1dw88wd5gqsqn6ufxhf9h03uk8087l7gfzdtez5csjlt6pupu4pwsj8plrwPublished at
2023-06-07 23:19:44Event JSON
{
"id": "23da8c9d37edc6ab7dc13d66f2ed9ad88b00d09ff08660abb0eb6dbea5cb9cad",
"pubkey": "6b8e77368804013d7126ba4b77c7963bcfeff909135791531097d7a0f03ca85d",
"created_at": 1686179984,
"kind": 1,
"tags": [
[
"e",
"a3a3f4bb7a4f76a4dd4ffb9bad737c4cf2aefb0496fa4b312d6d5bf1fd8cde22",
"",
"root"
],
[
"e",
"87a12f1d42a02de7ef5d995f4dc13a0c6167424a01d2fa3eb1b4663f9e9d88c0",
"",
"reply"
],
[
"p",
"daa2fc676a25e3b5b45644540bcbd1e1168b111427cd0e3cf19c56194fb231aa"
]
],
"content": "📅 Original date posted:2023-02-22\n🗒️ Summary of this message: A simpler approach to verify shares without a computer is suggested for Codex32. A mod N=0 checksum can be used for individual shares or all shares.\n📝 Original message:After some poking around at the math, I do see that the 13 character\ngenerator (for regular sized shares) is reasonably \"smooth\", having roots\nat T{11}, S{16}, and C{24}.\n\nThis means we could build a \"quick check\" worksheet to evaluate the string\nmodulo (x - T) to verify a 5 bit checksum, whose operation would be similar\nto the existing checksum worksheet in structure but significantly less work.\n\nPerhaps 5 bits is too short, and it is more reasonable working modulo (x -\nT)*(x - S) to get a 10 bit checksum. A worksheet for a 15 bit checksum is\nalso an option, and possibly others well depending on the size of the other\nfactors. I think this process is would be about as simple as any other\ncomparable hand operated checksum over the bech32 alphabet would be.\n\nI haven't looked into the smoothness of the long generator for seeds that\nare greater than 400 bits. If it isn't smooth and smoother options are\navailable, perhaps it should be changed.\n\nOn Wed, Feb 22, 2023 at 11:29 AM Peter Todd via bitcoin-dev \u003c\nbitcoin-dev at lists.linuxfoundation.org\u003e wrote:\n\n\u003e On Sun, Feb 19, 2023 at 10:12:51PM +0000, Andrew Poelstra via bitcoin-dev\n\u003e wrote:\n\u003e \u003e \u003e What really did catch my attention, but which was kind of buried in the\n\u003e \u003e \u003e project documentation, is the ability to verify the integrity of each\n\u003e \u003e \u003e share independently without using a computer. For example, if I store\n\u003e a\n\u003e \u003e \u003e share with some relative who lives thousands of kilometers away, I'll\n\u003e be\n\u003e \u003e \u003e able to take that share out of its tamper-evident bag on my annual\n\u003e \u003e \u003e holiday visit, verify that I can still read it accurately by validating\n\u003e \u003e \u003e its checksum, and put it into a new bag for another year. For this\n\u003e \u003e \u003e procedure, I don't need to bring copies of any of my other shares,\n\u003e \u003e \u003e allowing them (and my seed) to stay safe.\n\u003e \u003e \u003e\n\u003e \u003e\n\u003e \u003e This is good feedback. I strongly agree that this is the big selling\n\u003e \u003e point for this -- that you can vet shares/seeds which *aren't* being\n\u003e \u003e actively used, without exposing them to the sorts of threats associated\n\u003e \u003e with active use.\n\u003e \u003e\n\u003e \u003e We should make this more prominent in the BIP motivation.\n\u003e\n\u003e I don't think that use-case is a good selling point. The checksum that\n\u003e Codex32\n\u003e uses is much more complex than necessary if you are simply verifying a\n\u003e share by\n\u003e itself.\n\u003e\n\u003e A *much* simpler approach would be to use a simple mod N = 0 checksum,\n\u003e either\n\u003e by creating the seed such that each share passes, or by just storing an\n\u003e additional word/symbol with the seed in such a way that sum(words) mod N =\n\u003e 0\n\u003e passes. This approach is not only possible to compute by hand with a\n\u003e word/symbol-\u003enumber lookup table, and pen and paper or a calculator. It's\n\u003e so\n\u003e simple they could probably *remember* how to do it themselves.\n\u003e\n\u003e\n\u003e Secondly, if all shares have mod N checksums, it may be sufficient for\n\u003e everyone\n\u003e to write down the checksums of the *other* shares, to verify they are the\n\u003e correct ones and a different (otherwise correct) share hasn't accidentally\n\u003e been\n\u003e substituted.\n\u003e\n\u003e Indeed, with some brute forcing and small checksums, I'd expect it to be\n\u003e mathematically possible to generate Shamir's secret sharing shards such\n\u003e that\n\u003e every shard can share the *same* checksum. In which case the share\n\u003e verification\n\u003e procedure would be to simply ask every share holder to verify the checksum\n\u003e manually using the mod N procedure, and then verify that each share holder\n\u003e has\n\u003e the same checksum. This would be less error prone in terms of leaking\n\u003e information accidentally if the checksum was obviously *not* part of the\n\u003e share:\n\u003e eg by encoding the share with words, and the checksum with a number.\n\u003e\n\u003e Obviously, small checksums aren't fool proof. But we're probably better off\n\u003e creating a relatively easy procedure with a 1-in-1000 chance of an error\n\u003e going\n\u003e undetected than a complex procedure that people don't actually do at all.\n\u003e\n\u003e --\n\u003e https://petertodd.org 'peter'[:-1]@petertodd.org\n\u003e _______________________________________________\n\u003e bitcoin-dev mailing list\n\u003e bitcoin-dev at lists.linuxfoundation.org\n\u003e https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev\n\u003e\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20230222/8b9500fc/attachment.html\u003e",
"sig": "216a03f3629487ecce6c5b6f0a74d8d411bc622e1b3191b2d4b2bf3a79fc57184da047af4d604716f905b6064aa13f9c4316b04c9b66ccd68f42dff8ae7eb925"
}