📅 Original date posted:2018-05-23
📝 Original message:On Wed, May 23, 2018 at 01:50:13PM +0000, Andrew Poelstra via bitcoin-dev wrote:
>
> Graftroot also break blind signature schemes. Consider a protocol such as [1]
> where some party has a bunch of UTXOs all controlled (in part) by the same
> key X. This party produces blind signatures on receipt of new funds, and can
> only verify the number of signatures he produces, not anything about what he
> is signing.
>
> BTW, the same concern holds for SIGHASH_NOINPUT, which I'd also like to be
> disable-able. Maybe we should extend one of ZmnSCPxj's suggestions to include
> a free "flags" byte or two in the witness?
>
> (I also had the same concern about signature aggregation. It seems like it's
> pretty hard to preserve the "one signature = at most one input" invariant of
> Bitcoin, but I think it's important that it is preserved, at least for
> outputs that need it.)
>
> Or maybe, since it appears it will require a space hit to support optional
> graftroot anyway, we should simply not include it in a proposal for Taproot,
> since there would be no opportunity cost (in blockchain efficiency) to doing
> it later.
>
> [1] https://github.com/apoelstra/scriptless-scripts/pull/1
>
On further thought, I rescind this concern (ditto for SIGHASH_NOINPUT) (but
not for aggregate sigs, they still interact badly with blind signatures).
As long as graftroot (and NOINPUT) sigs commit to the public key, it is
possible for a server to have unique keys for every output, even while
retaining the same private key, and thereby ensure that "one sig can spend
only one output" holds. To do this, suppose the server has a BIP32 xpubkey
(xG, cc). A blind signer using the private key x can be made to sign not
only for xG, but also for any publicly-derived child keys of (xG, cc).
Here is a simple scheme that does this:
1. Signer provides a nonce R = kG
2. Challenger computes bip32 tweak h, chooses blinders alpha and beta,
and computes:
R' = R + alpha*G + beta*P
e = H(P + hG || R' || tx)
e' = e + beta
and sends e' to the signer.
3. Signer replies with s = k + xe' (= k + beta*x + (x + h)e - he)
4. Challenger unblinds this as s' = s + alpha + he
(This blind signature scheme is vulnerable to Wagner's attack, though see
Schnorr 2004 [1] for mitigations that are perfectly compatible with this
modified BIP32ish scheme.)
I'm unsure whether key-prefixing is _actually_ necessary for this, but it
makes the security argument much clearer since the messagehash contains
some data which can be made unique per-utxo and is committed in the chain.
Andrew
[1] http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=8ECEF929559865FD68D1D873555D18FE?doi=10.1.1.68.9836&rep=rep1&type=pdf
--
Andrew Poelstra
Mathematics Department, Blockstream
Email: apoelstra at wpsoftware.net
Web: https://www.wpsoftware.net/andrew
"A goose alone, I suppose, can know the loneliness of geese
who can never find their peace,
whether north or south or west or east"
--Joanna Newsom
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Andrew Poelstra [ARCHIVE] /
npub1ae…z5t04
2023-06-07 18:12:24
in reply to nevent1q…qu20
Author Public Key
npub1ae27kq6z802dkqw4ey4dgdx493szm8dpmcm76d7vt0ma9gf6fj4svz5t04Published at
2023-06-07 18:12:24Event JSON
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"content": "📅 Original date posted:2018-05-23\n📝 Original message:On Wed, May 23, 2018 at 01:50:13PM +0000, Andrew Poelstra via bitcoin-dev wrote:\n\u003e \n\u003e Graftroot also break blind signature schemes. Consider a protocol such as [1]\n\u003e where some party has a bunch of UTXOs all controlled (in part) by the same\n\u003e key X. This party produces blind signatures on receipt of new funds, and can\n\u003e only verify the number of signatures he produces, not anything about what he\n\u003e is signing.\n\u003e \n\u003e BTW, the same concern holds for SIGHASH_NOINPUT, which I'd also like to be\n\u003e disable-able. Maybe we should extend one of ZmnSCPxj's suggestions to include\n\u003e a free \"flags\" byte or two in the witness?\n\u003e \n\u003e (I also had the same concern about signature aggregation. It seems like it's\n\u003e pretty hard to preserve the \"one signature = at most one input\" invariant of\n\u003e Bitcoin, but I think it's important that it is preserved, at least for\n\u003e outputs that need it.)\n\u003e \n\u003e Or maybe, since it appears it will require a space hit to support optional\n\u003e graftroot anyway, we should simply not include it in a proposal for Taproot,\n\u003e since there would be no opportunity cost (in blockchain efficiency) to doing\n\u003e it later.\n\u003e \n\u003e [1] https://github.com/apoelstra/scriptless-scripts/pull/1 \n\u003e\n\nOn further thought, I rescind this concern (ditto for SIGHASH_NOINPUT) (but\nnot for aggregate sigs, they still interact badly with blind signatures).\n\nAs long as graftroot (and NOINPUT) sigs commit to the public key, it is\npossible for a server to have unique keys for every output, even while\nretaining the same private key, and thereby ensure that \"one sig can spend\nonly one output\" holds. To do this, suppose the server has a BIP32 xpubkey\n(xG, cc). A blind signer using the private key x can be made to sign not\nonly for xG, but also for any publicly-derived child keys of (xG, cc).\n\nHere is a simple scheme that does this:\n\n 1. Signer provides a nonce R = kG\n\n 2. Challenger computes bip32 tweak h, chooses blinders alpha and beta,\n and computes:\n R' = R + alpha*G + beta*P\n e = H(P + hG || R' || tx)\n e' = e + beta\n and sends e' to the signer.\n\n 3. Signer replies with s = k + xe' (= k + beta*x + (x + h)e - he)\n\n 4. Challenger unblinds this as s' = s + alpha + he\n\n(This blind signature scheme is vulnerable to Wagner's attack, though see\nSchnorr 2004 [1] for mitigations that are perfectly compatible with this\nmodified BIP32ish scheme.)\n\nI'm unsure whether key-prefixing is _actually_ necessary for this, but it\nmakes the security argument much clearer since the messagehash contains\nsome data which can be made unique per-utxo and is committed in the chain.\n\n\nAndrew\n\n\n[1] http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=8ECEF929559865FD68D1D873555D18FE?doi=10.1.1.68.9836\u0026rep=rep1\u0026type=pdf\n\n\n-- \nAndrew Poelstra\nMathematics Department, Blockstream\nEmail: apoelstra at wpsoftware.net\nWeb: https://www.wpsoftware.net/andrew\n\n\"A goose alone, I suppose, can know the loneliness of geese\n who can never find their peace,\n whether north or south or west or east\"\n --Joanna Newsom\n\n-------------- next part --------------\nA non-text attachment was scrubbed...\nName: signature.asc\nType: application/pgp-signature\nSize: 455 bytes\nDesc: not available\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20180523/5debf87f/attachment-0001.sig\u003e",
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