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Bip Draft: Sending Silent Payments in PSBTs #1687

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Bip Draft: Sending Silent Payments in PSBTs #1687

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187 changes: 187 additions & 0 deletions bip-PSBT-SP.mediawiki
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<pre>
BIP: ?
Layer: Applications
Title: Sending Silent Payments with PSBTs
Author: Andrew Toth <andrewstoth@gmail.com>
Ava Chow <me@achow101.com>
josibake <josibake@protonmail.com>
Comments-Summary: No comments yet.
Comments-URI: TBD
Status: Draft
Type: Standards Track
Created: 2024-05-14
License: BSD-2-Clause
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Suggested change
License: BSD-2-Clause
License: BSD-2-Clause
Post-History: https://groups.google.com/g/bitcoindev/c/5G5wzqUXyk4
Requires: 352, 370

</pre>

==Introduction==

===Abstract===

This document proposes additional fields and updated role responsibilities for BIP 370 PSBTv2
which adds support for sending to silent payments as described in BIP352.
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Consistency nit: "BIP 370", but "BIP352"


===Copyright===

This BIP is licensed under the 2-clause BSD license.

===Motivation===

Partially Signed Bitcoin Transaction Version 2 as described in BIP 370 is not compatible with sending to silent payments as described in BIP352. In particular, the output script of a silent payment cannot be computed until after all transaction inputs have been added.
Also, any inputs that the Signer has the private keys for must be signed with SIGHASH_ALL and all inputs must not have any scriptPubKeys with Segwit version > 1.
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What creates the requirement to sign with SIGHASH_ALL? A quick check suggests that BIP 352 only recommends it, but doesn’t require it, and BIP 370 doesn’t seem to impose such a requirement. I might have missed something of course.

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I had the same question. The rationale in BIP 352 seems to imply that just forbidding ANYONECANPAY, i.e. that all signatures must fully commit to the input set, which seems sufficient even the PSBT setting?

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@andrewtoth andrewtoth Nov 17, 2024 •
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Signing with SIGHASH_NONE doesn't make sense because you will have to generate the ECDH shares for all payments, but they could then be removed or new ones added. So you will have to go back to the signer again. I suppose technically this could be allowed but I don't see a use for it, and it could be used by a griefer to force the party to keep going back to the signer. If you want to have a signer sign all non-eligible inputs with SIGHASH_NONE, give the signer the inputs before adding any silent payment outputs. It would then fall back to BIP 370.
Signing with SIGHASH_SINGLE would allow another participant to add a payment to the same scan key, but a lower lexicographic order, invalidating the k value in the output script.
Signing with SIGHASH_ANYONECANPAY is unsafe as per BIP 352.

I suppose I could add this as a footnote.
But also, I don't think this sentence should be in the motivation section.

Additionally, the silent payment outputs computed by a signer must be verifiable to other entities.
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If there is a single signer, why would others need to be able to verify? If there are multiple signers, wouldn’t all signers need to collaborate by putting forth shares rather than "computing silent payment outputs"?

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If there is a single signer, why would others need to be able to verify?

In the case of a hardware wallet connected to a software wallet, the hardware wallet is the single signer but the software wallet must verify that the output is computed properly before broadcasting.

If there are multiple signers, wouldn’t all signers need to collaborate by putting forth shares rather than "computing silent payment outputs"?

Yes, all signers need to collaborate and put forth shares, but they must also compute the output script before signing. This computed output script must be added to the PSBT before signing to be compatible with BIP 370 signing process. After it is added, the other signers can compute the output script to verify themselves before signing.

Therefore, new fields and role responsibilities must be added to carry, compute, and verify the silent payment data.

==Specification==

This document specifies new fields and new field inclusion/exclusion requirements.

<tt>PSBT_OUT_SCRIPT</tt> is modified to be optional for outputs in silent payments capable PSBTs. If this field is not included in the output, then the field PSBT_OUT_SP_V0_INFO must be included.
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Does it make sense to require the presence of either PSBT_OUT_SCRIPT or PSBT_OUT_SP_V0_INFO? What if there is another future extension of BIP 370 that provides a third option?

Would it perhaps be sufficient to declare an output that has both the fields PSBT_OUT_SCRIPT and PSBT_OUT_SP_V0_INFO to make the PSBT invalid (i.e. at most one of these two can be present)?

Perhaps the interplay of these two fields could be elaborated.

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I don't think making these fields exclusive will work. The PSBT_OUT_SCRIPT must be added to sign the PSBT. The PSBT_OUT_SP_V0_INFO must be present to verify that the PSBT_OUT_SCRIPT is actually correct after it is added.

What if there is another future extension of BIP 370 that provides a third option?

That would indeed soften this requirement. This BIP would have to be modified to support that extension, making it

If either PSBT_OUT_SCRIPT or PSBT_OUT_NEW_EXTENSION are not included in the output, then the field PSBT_OUT_SP_V0_INFO must be included.

I don't really have an idea on how this could be made more graceful for that scenario.

Perhaps the interplay of these two fields could be elaborated.

I will add some more context in a footnote, thanks.


The new global types are defined as follows:

{|
! Name
! <tt><keytype></tt>
! <tt><keydata></tt>
! <tt><keydata></tt> Description
! <tt><valuedata></tt>
! <tt><valuedata></tt> Description
! Versions Requiring Inclusion
! Versions Requiring Exclusion
! Versions Allowing Inclusion
|-
| Silent Payment Global ECDH Share
| <tt>PSBT_GLOBAL_SP_ECDH_SHARE = 0x07</tt>
| <tt><33 byte scan key> <36 byte outpoint>*</tt>
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This seems to imply any subset of the inputs can be specified, presumably for grouping by owner.

The main advantage over allowing only one outpoint per ECDH share seems to be a reduction in proving complexity for signers who choose to provide DLEQ proofs, since the 36 byte outpoint outweighs a a * B_scan if it were provided in a per input field with an output index or even B_scan as the keydata.

Some disadvantages:

  1. Mostly theoretical privacy concern: the DLEQ proof is publicly verifiable, and so much stronger heuristic for common ownership than the traditional common input ownership heuristic. Other parties or observers of the PSBT might store or leak such values, which hurts Signers' deniability.
  2. If the outpoint lists are not disjoint, then the correct sum might not be computable even if all inputs are accounted for by some share. If every ECDH_SHARE corresponded to only a single outpoint, as long as each signer contributes a value for each input, in any order, the sum can always be computed. If users modify a PSBT over multiple devices with partly overlapping access to private keys, single input shares ensure all intermediate states can lead to a fully signed state, regardless of the order in which the user proceeded.

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The main advantage over allowing only one outpoint per ECDH share seems to be a reduction in proving complexity for signers who choose to provide DLEQ proofs

The main advantage is reduction in both ECDH share generation and proving complexity.
All outpoint private keys can be summed, and then only a single ECC mult for the shares, and 2 ECC mults for the proof.

Consider the common case of a single sig wallet using a hardware signing device receiving many small inputs over time. The wallet now contains 100 utxos and wants to spend to a single silent payment address.
By using single share and proof for each outpoint, that is 100 * ECDH share + 100 * DLEQ proof (2 ECC mults) + 100 * signatures = 400 ECC mults.
By summing all inputs, the result is now 1 * ECDH share + 1 * DLEQ proof (2 ECC mults) + 100 signatures = 103 ECC mults.
On a simple hardware signing device, this makes the signing time 4x, making it potentially a few minutes to over 10.

re: disadvantages

  1. It is only an option to combine the inputs. You can still provide a share and proof per input or whatever combination of inputs you'd like. I will make this more clear in the text. I believe the single sig with hardware wallet is the most common case though, so we should optimize for that case.
  2. This is indeed a potential pitfall. It could also be addressed by providing a share and proof per input as a fallback. I will add some text to address this situation.

| The scan key and a list of outpoints corresponding to the prevouts of the inputs that this ECDH share is for. The outpoints are composed of a 32 byte txid followed by a 32-bit little endian uint.
| <tt><32 byte share></tt>
| An ECDH share for a scan key, followed by a list of outpoints. The ECDH shared is computed with ''a * B_scan'', where ''a'' is the sum of all private keys of the inputs matching the list of outpoints, and ''B_scan'' is the scan key of a recipient.
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as already noted in the DLEQ gist, this should have a size of 33 bytes instead, as it represents a point on the curve (https://gist.github.com/andrewtoth/df97c3260cc8d12f09d3855ee61322ea?permalink_comment_id=5250407#gistcomment-5250407), and representing it as x-only very likely only increases complexity for the DLEQ proof.

|
| 0
| 2
|-
| Silent Payment Global DLEQ Proof
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Suggest defining "Discrete Log Equality Proofs (DLEQ)" above this / on first use, and discuss overlap with #1689 (if any) or linkage to be made between the two.

| <tt>PSBT_GLOBAL_SP_DLEQ = 0x08</tt>
| <tt><33 byte scan key> <36 byte outpoint>*</tt>
| The scan key and a list of outpoints corresponding to the prevouts of the inputs that this proof covers. The outpoints are composed of a 32 byte txid followed by a 32-bit little endian uint.
| <tt><64-byte proof></tt>
| A DLEQ proof computed for the matching ECDH share.
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For a given set of outpoints, there are multiple relevant B_scan generators all of which share share the same a witness in their respective proofs. This could be one batch proof per SP output set, instead of per individual B_scan. Although only a single 64 byte proof per input set is required, the prover and verifier complexity is the same as n proofs, where n is the number of SP outputs.

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Yes, this is a great insight, thank you!

Would it not also reduce the complexity, since it would only be one proof to verify after summing the B_scan generators instead of verifying each proof individually?

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If you mean given $P = aG$, and scan keys $(B_i)_{i=1}^n$, it's possible to prove knowlege of $a$ in $Q = a (n^{-1} \sum B_i)$ where $n^{-1} \sum B_i$ is a public input, but I'm not sure this is sound / proving the same thing.

This reference (section 3.2.3.3) seems to suggest it isn't, see footnote 16 on page 73, there's additional delinearization terms which are similar to key cancellation mitigation (and afaict are amenable to Fiat-Shamir just the same). This is an improvement over my implied suggestion as batched multiplication be used, but it does not reduce it to a single multiplication. Admittedly I don't yet see how to actually attack soundness as a malicious prover, especially when the prover does not control the choice of the the B_scan keys.

The batch proof I'm familiar with involves having an R point per generator, so same structure as proposed in the DLEQ BIP, just generalized from 2 to n+1 verification equations. When the proof is encoded as the challenge and the response, the encoding the n+1 R points is implicit, so the size would still be 64 bytes and both prover and verifier work is concretely reduced (~half the verification equations, and a shared challenge hash), but not asymptotically as the total work is still linear for both prover and verifier.

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Using the mentioned protocol, "RME-based common exponent Schnorr protocol" (Henry14 3.2.3.3), the verifier performs 2+k ECC mults per proof, where k is the number of silent payment outputs, but the k mults can be shared for a batch of proofs, which large transactions can be a significant improvement in verifier complexity.

Compared to this protocol the strawman protocol I described in the previous comment is broken in two ways, not just one:

  • two verification equations are needed, instead of only one (section 4.2 describes a lattice basis attack on soundness since the prover's responses are undetermined)
  • de-linearization (or in the multiplicative terms of Henry14, RME) is needed for soundness as well (see section 3.1.4.3)

In a non-interactive setting, the t_i terms of the random linear combination is generated by hashing.

If $t_i = H(B_1, B_2, \dots, B_k)$ ($B_i$ is supposed to be {B_{scan}}_i but that apparently isn't in github's latex regex =P) the $k$ proofs would share the same delinearized sum $\sum_{i=1}^k t_i B_i$, which appears as a term in the 2nd verification equation. This reduces $k^2$ ECC mults to $k$ (but asymptotically is the same because of other side of the equation still has a $\sum_{i=1}^{k} t_i S_i$ term where $S_i = aB_i$ is a public input).

Unfortunately the full set of SP_V0_INFO fields to be finalized before DLEQ proofs can be computed in that case, but if I understand Lemma 3.5 I think the $t_i$ values used for this can be derived as $t_i = H(B_i)$ without destroying the proof of soundness. If this is correct then this reduction in verifier computation could be applied to batch-verify whatever $k$ batch-DLEQs, but number of roundtrips is not reduced because new proofs would be needed for the new outputs, and verifiers would need to be given explicit subsets of the outputs for each batch proof indicating what it covers, instead of being able to construct the proof statements implicitly from the set of all SP_V0_INFO fields, so it's not clear that this is a meaningful improvement over hashing all of the $B_i$s to delinearize.

|
| 0
| 2
|}

One new per-output type is defined as follows:

{|
! Name
! <tt><keytype></tt>
! <tt><keydata></tt>
! <tt><keydata></tt> Description
! <tt><valuedata></tt>
! <tt><valuedata></tt> Description
! Versions Requiring Inclusion
! Versions Requiring Exclusion
! Versions Allowing Inclusion
|-
| Silent Payment Data
| <tt>PSBT_OUT_SP_V0_INFO = 0x08</tt>
| None
| No key data
| <tt><33 byte scan key> <33 byte spend key></tt>
| The scan and spend public keys from the silent payments address.
|
| 0
| 2
|}

===Unique Identification===

Silent payment capable PSBTs can be uniquely identified the same way as PSBTv2s, except when including silent payment outputs. For silent payment capable PSBTs, all silent payment outputs must use the PSBT_OUT_SP_V0_INFO instead of PSBT_OUT_SCRIPT as the output script when creating the unsigned transaction used for unique identification.
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I found this sentence confusing. Does this also hold if both PSBT_OUT_SP_V0_INFO and PSBT_OUT_SCRIPT are specified on an output?

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No, it does not hold once PSBT_OUT_SCRIPT is added to an output. Only outputs without that field would need to fall back to PSBT_OUT_SP_V0_INFO. I will clarify this in the text.


==Roles==

This document modifies some existing roles.

===Constructor===

All rules must be followed from PSBTv2 for this role, with the following exception:
When an output is added, it must have either PSBT_OUT_SCRIPT or PSBT_OUT_SP_V0_INFO, or both, set.
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I only understood here that both of these fields can be set at the same time. Perhaps that could be explained above where PSBT_OUT_SP_V0_INFO is first introduced.


Additionally to PSBTv2, the Constructor must also follow additional rules:

Inputs spending an output with script using Segwit version > 1 may only be added if there are no outputs with PSBT_OUT_SP_V0_INFO set.
Outputs with PSBT_OUT_SP_V0_INFO set may only be added if there are no inputs spending an output script using Segwit version > 1.
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This might be a bit out of scope for your PR, but I was just wondering:
Silent Payment transactions disallow inputs spending native segwit outputs with version > 1, but should it perhaps also exclude native segwit outputs with version 1 that are not P2TR inputs? Most of version 1 is yet unencumbered, are Silent Payments robust in regard to Pay to Anchor?

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I believe BIP 352 specifies that only the script template OP_1 <32 bytes> is used, and not that it is segwit v1. So, P2A does not follow that template, and will be ignored. But, segwit versions higher than v1 specifically are prohibited for forward compatibility reasons.

This is what I understood from @josibake's explanation.


===Signer===

All rules must be followed from PSBTv2 for this role. If there are any outputs with PSBT_OUT_SP_V0_INFO set, then the following additional rules must also be adhered to:

If any input is spending an output with script using Segwit version > 1, the Signer must fail.

For all outputs with PSBT_OUT_SP_V0_INFO set, the Signer should:
- Compute and set an ECDH share and DLEQ proof using all inputs it has the private key for.
- Verify the DLEQ proofs for all inputs it does not have the private keys for.
- If all eligible inputs have an ECDH share, compute and set the PSBT_OUT_SCRIPT.
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Suggested change
- Compute and set an ECDH share and DLEQ proof using all inputs it has the private key for.
- Verify the DLEQ proofs for all inputs it does not have the private keys for.
- If all eligible inputs have an ECDH share, compute and set the PSBT_OUT_SCRIPT.
* Compute and set an ECDH share and DLEQ proof using all inputs it has the private key for.
* Verify the DLEQ proofs for all inputs it does not have the private keys for.
* If all eligible inputs have an ECDH share, compute and set the PSBT_OUT_SCRIPT.


If the Signer sets any missing PSBT_OUT_SCRIPTs, it must set the Inputs Modifiable flag to False.

If any output does not have PSBT_OUT_SCRIPT set, the Signer must not yet add a signature.
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IIUC, if it were not for this, blinding the SP_V0_INFO field would be technically be possible.

Since that would necessarily add another round of communication between the various entities, as only only updaters with access to the blinding keys could set the output.

A global flag to indicate whether the additional round is required might make sense?

This flag might have 3 values, indicating if blinding is not used (allowing signers to update outputs), optional (precluding that), or required in which case all outputs must have SP_V0_INFO, with dummy values used for non-SP outputs. "required" or "mandatory" blinding is a bit misleading, it's providing deniability as to which outputs use SP, not requiring SP and blinding actually be used.


The Signer should additionally compute the silent payment addresses, optionally showing this data to the user instead of the computed segwit v1 addresses.

If a sighash type is provided and there are silent payment outputs present, the signer must fail if the sighash type is not SIGHASH_ALL.
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As mentioned above, this seems to be stricter than BIP 352 itself. Is this intentional?

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This is intentional. SIGHASH_SINGLE is unsafe for k values. SIGHASH_NONE does not make sense since you will have to compute ECDH shares for the outputs, but you presumably don't care about the outputs if you are signing with that flag.

If a sighash type is not provided and there are silent payment outputs present, the signer must sign using SIGHASH_ALL.

====Computing the DLEQ Proof====

For each output with PSBT_OUT_SP_V0_INFO set, the Signer may generate a proof for other entities to generate the output scripts and verify that the output scripts were generated correctly.

Generate a global ECDH share for each scan key ''B<sub>scan</sub>'' and all eligible inputs the Signer has private keys for as follows:

Using the notation from [https://github.com/bitcoin/bips/blob/master/bip-0352.mediawiki#specification BIP352]

* Let ''A<sub>n</sub>'' be the sum of the public keys ''A'' of all eligible inputs
* Let ''a<sub>n</sub>'' be the sum of the private keys ''a'' of all eligible inputs
* Let ''C = a<sub>n</sub>·B<sub>scan</sub>''

Use a key ''B<sub>scan</sub>'' followed by a list of the outpoints of all eligible inputs.
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I was surprised that we provide a single share and a single DLEQ proof per participant rather than one per input. In case there are multiple participants, this leaks to all other participants which inputs were provided in bulk by one party. I was wondering if there might be better privacy properties if participants provide a separate share for each input, that way all subsequent participants do not know how previous inputs group if the PSBT is passed in a circle rather than shared with all participants after each step. Maybe I’m overthinking this, though.

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This is provided as a performance optimization so that there is only one proof for multiple inputs.
It is not required to combine all your inputs. You could selectively add different shares and proofs for each inputs you don't want to link. I suppose I could make that option more explicit in the text.


Set the value for the key of PSBT_GLOBAL_SP_ECDH_SHARE to ''C''.

Compute the DLEQ proof for ''C'' using ''a<sub>n</sub>'' and ''B<sub>scan</sub>''.
Set the value for the key of PSBT_GLOBAL_SP_DLEQ to the proof.

====Verifying the DLEQ Proof====

For each output with PSBT_OUT_SP_V0_INFO set, the Signer should verify the ECDH shares for all eligible inputs it does not have the private key for using the proofs provided by other Signers.

====Computing the Output Scripts====

Compute the PSBT_OUT_SCRIPT using the procedure in [https://github.com/bitcoin/bips/blob/master/bip-0352.mediawiki#user-content-Creating_outputs BIP352] but substituting ''a·B<sub>scan</sub>'' with the sum of all PSBT_GLOBAL_SP_ECDH_SHAREs for that scan key.
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Assuming my suggestion to make shares be one per input is rejected, this needs to verify that the sets of outpoints in all ECDH_SHARE fields for a given scan key form a valid partition of the BIP 352 input set (no duplicates, no missing outpoints) before computing the sum of the values, or this sum might differ from b_scan·A where A is also is computed as in BIP 352 scanning.

If there are multiple silent payment codes with the same scan key, sort the codes lexicographically in ascending order to determine the ordering of the ''k'' value.
If there are multiple silent payment codes with both the same scan and spend keys, sort the subgroup by output index in ascending order.

====Change Detection====

Updaters may add two PSBT_OUT_BIP32_DERIVATION key-value-pairs with the corresponding derivation path of both the scan and spend keys. The Signer can then use these fields to verify that the silent payment code is change.
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Should the "Updater" role perhaps appear before the "Signer"? Adding change would probably happen at the same time participants add inputs, so surely before signing?


===Transaction Extractor===

For silent payment capable PSBTs, the transaction extractor should compute all output scripts for silent payment codes and verify they are correct using the ECDH shares and DLEQ proofs, otherwise fail.

==Backwards Compatibility==

Silent payment capable PSBTs are backwards compatible with PSBTv2 once all outputs have PSBT_OUT_SCRIPT set. Otherwise they are not backwards compatible.

==Test Vectors==

Todo

==Rationale==

<references/>

==Reference implementation==

Todo