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Subject: [bitcoin-dev] BIP352: Silent Payments
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Hi all,

Since first posting the BIP for Silent Payments back in June, we've gone t=
hrough several rounds of review and revision (a big thanks to everyone who=
 has reviewed so far!). We've also updated the BIP with a python reference=
 implementation and wallet test vectors. To summarize a few of the major c=
hanges:


-   Use 33-byte compressed keys instead of 32-byte x-only keys, except whe=
n creating the outputs
-   Negate the private key if necessary when spending taproot outputs
    =


-   If the receiving wallet uses labels, add a step to also check the nega=
ted output
-   Add a versioning scheme for silent payment addresses


For those interested, the implementation for Bitcoin Core has been updated=
 to reflect these changes here: https://github.com/bitcoin/bitcoin/pull/27=
827 . For convenience, and in the hopes of soliciting another round of rev=
iew, the full specification is posted below and the full text of the BIP i=
ncluding the overview, test vectors and appendix on light client support c=
an be found here: https://github.com/bitcoin/bips/pull/1458).

Cheers!
-- Ruben, Josie


=3D=3D Specification =3D=3D

--------------------

We use the following functions and conventions:

-   outpoint (36 bytes): the COutPoint of an input (32-byte txid, least si=
gnificant byte first || 4-byte vout, least significant byte first)[6]
-   sortoutpoints(v): sorts a vector v of outpoints in ascending order by =
doing a byte by byte comparison lexicographically.
-   ser32(i): serializes a 32-bit unsigned integer i as a 4-byte sequence,=
 most significant byte first.
-   ser256(p): serializes the integer p as a 32-byte sequence, most signif=
icant byte first.
-   serP(P): serializes the coordinate pair P =3D (x,y) as a byte sequence=
 using SEC1's compressed form: (0x02 or 0x03) || ser256(x), where the head=
er byte depends on the parity of the omitted y coordinate.


For everything not defined above, we use the notation from BIP340.

### =3D=3D=3D Versions =3D=3D=3D

This document defines Silent Payments v0. Version is communicated through =
the address in the same way as Segwit addresses. Future upgrades to silent=
 payments will require a new version. As much as possible, future upgrades=
 should support receiving from older wallets (e.g. a silent payments v0 wa=
llet can send to both v0 and v1 addresses). Any changes that break compati=
bility with older silent payment versions should be a new BIP.

Future Silent Payments versions will use the following versioning scheme:



0

1

2

3

4

5

6

7

Compatibility

+0

q

p

z

r

y

9

x

8

=C2=A0=C2=A0 backwards compatible

+8

g

f

2

t

v

d

w

0

+16

s

3

j

n

5

4

k

h

+24

c

e

6

m

u

a

7

-

v31 (l) is reserved for a backwards incompatible change, if needed. For Si=
lent Payments v0:

-   If the receiver's silent payment address version is:
    -   v0: check that the data part is exactly 66-bytes. Otherwise, fail
    -   v1 through v30: read the first 66-bytes of the data part and disca=
rd the remaining bytes (if any)
    -   v31: fail
-   Receiver addresses are always BIP341 taproot outputs[7]
-   The sender should sign with one of the sighash flags DEFAULT, ALL, SIN=
GLE, NONE (ANYONECANPAY is unsafe). It is strongly recommended implementat=
ions use SIGHASH_DEFAULT when applicable, or SIGHASH_ALL[8]
-   Inputs used to derive the shared secret are from the Inputs For Shared=
 Secret Derivation list

### =3D=3D=3D Scanning transactions =3D=3D=3D

A transaction is a Silent Payments v0 transaction and MUST be scanned if a=
nd only if all of the following are true:

-   The transaction contains at least one BIP341 taproot output
-   The transaction has at least one input from the Inputs For Shared Secr=
et Derivation list
-   The transaction does not spend a new, undefined output type (e.g. SegW=
it versions > 1)[9]


Otherwise, skip the transaction. This is to ensure forward compatibility w=
ith future versions of silent payments without requiring future versions t=
o scan a transaction multiple times with different rule sets.

### =3D=3D=3D Address encoding =3D=3D=3D

A silent payment address is constructed in the following manner:

-   Let Bscan, bscan =3D Receiver's scan public key and corresponding priv=
ate key
-   Let Bspend, bspend =3D Receiver's spend public key and corresponding p=
rivate key
-   Let Bm =3D Bspend + m=C2=B7G, where m an optional integer tweak for la=
beling
    -   In the case of m =3D 0, no label is applied and Bm =3D Bspend
-   The final address is a Bech32m encoding of:
    -   The human-readable part "sp" for mainnet, "tsp" for testnets (e.g.=
 signet, testnet)
    -   The data-part values:
        -   The character "q", to represent a silent payment address of ve=
rsion 0
        -   The 66 byte concatenation of the receiver's public keys, serP(=
Bscan) || serP(Bm)

Note: BIP173 imposes a 90 character limit for Bech32 strings, whereas a si=
lent payment address requires at least 117 characters[10]. Additionally, s=
ince higher versions may add to the data field, it is recommended implemen=
tations use a limit of 1023 characters (see BIP173: Checksum design for mo=
re details).

### =3D=3D=3D Outpoints hash =3D=3D=3D

The sender and receiver MUST calculate an outpoints hash for the transacti=
on in the following manner:

-   Collect each outpoint used as an input to the transaction
-   Sort the outpoints with sortoutpoints(outpoints)[11]
-   Let outpoints =3D outpoint0 || =E2=80=A6 || outpointn
-   Let outpoints_hash =3D sha256(outpoints)

### =3D=3D=3D Inputs For Shared Secret Derivation =3D=3D=3D

While any UTXO with known output scripts can be used to fund the transacti=
on, the sender and receiver MUST use inputs from the following list when d=
eriving the shared secret:

-   P2TR
-   P2WPKH
-   P2SH-P2WPKH
-   P2PKH


Inputs with conditional branches or multiple public keys (e.g. CHECKMULTIS=
IG) are not included as this introduces malleability and would allow a sen=
der to re-sign with a different set of public keys after the silent paymen=
t output has been derived. This is not a concern when the sender controls =
all of the inputs, but is an issue for CoinJoins and other collaborative p=
rotocols, where a malicious participant can participate in deriving the si=
lent payment address with one set of keys and then re-broadcast the transa=
ction with signatures for a different set of public keys. P2TR can have hi=
dden conditional branches (script path), but we work around this as descri=
bed below.

=3D=3D=3D=3D P2TR =3D=3D=3D=3D

The sender MUST use the private key corresponding to the taproot output ke=
y (i.e. the tweaked private key for a key path spend). This can be a singl=
e private key or an aggregate key (e.g. taproot outputs using MuSig2 or FR=
OST)[12]. If this key is not available, the output cannot be included as a=
n input to the transaction. The receiver always uses the taproot output ke=
y when scanning, regardless of whether the taproot output is using a key p=
ath spend or a script path spend[13].

The one exception is script path spends that use NUMS point H as their int=
ernal key (where H =3D lift_x(0x50929b74c1a04954b78b4b6035e97a5e078a5a0f28=
ec96d547bfee9ace803ac0) which is constructed by taking the hash of the sta=
ndard uncompressed encoding of the secp256k1 base point G as X coordinate,=
 see BIP341: Constructing and spending Taproot outputs for more details), =
in which case the output will be skipped for the purposes of shared secret=
 derivation[14].

=3D=3D=3D=3D P2WPKH =3D=3D=3D=3D

The sender performs the tweak using the private key for the output and the=
 receiver obtains the public key from the witness.

=3D=3D=3D=3D P2SH-P2WPKH =3D=3D=3D=3D

The sender performs the tweak using the private key for the nested P2WPKH =
output and the receiver obtains the public key from the witness.

=3D=3D=3D=3D P2PKH =3D=3D=3D=3D

The sender performs the tweak using the private key for the output and SHO=
ULD sign using the standard script template:

=C2=A0 =C2=A0 scriptSig: <Signature> <Public Key>

The receiver obtains the public key from the scriptSig. The receiver MUST =
parse the scriptSig for the public key, even if the scriptSig is non-stand=
ard (e.g. <dummy> OP_DROP <Signature> <Public Key>). This is to address th=
e third-party malleability of P2PKH scriptSigs.

### =3D=3D=3D Sender =3D=3D=3D

#### =3D=3D=3D=3D Selecting inputs =3D=3D=3D=3D

The sending wallet performs coin selection as usual with the following res=
trictions:

-   At least one input MUST be from the Inputs For Shared Secret Derivatio=
n list
-   Exclude inputs with witness version > 1 (see Scanning transactions)
-   For each taproot output spent the sending wallet MUST have access to t=
he private key corresponding to the taproot output key, unless H is used a=
s the internal public key

#### =3D=3D=3D=3D Creating outputs =3D=3D=3D=3D

After the inputs have been selected, the sender can create one or more out=
puts for one or more silent payment addresses in the following manner:

-   Collect the private keys for each input from the Inputs For Shared Sec=
ret Derivation list
-   For each private key ai corresponding to a BIP341 taproot output, chec=
k that the private key produces a point with an even y-value and negate th=
e private key if not[15]
-   Let a =3D a0 + a1 + =E2=80=A6 an, where each ai has been negated if ne=
cessary
-   Generate the outpoints_hash, using the method described above
-   Group receiver silent payment addresses by Bscan (e.g. each group cons=
ists of one Bscan and one or more Bm)
-   For each group:
    -   Let ecdh_shared_secret =3D outpoints_hash=C2=B7a=C2=B7Bscan
    -   Let n =3D 0
    -   For each Bm in the group:
        -   Let tn =3D sha256(serP(ecdh_shared_secret) || ser32(n))
        -   Let Pmn =3D Bm + tn=C2=B7G
        -   Encode Pmn as a BIP341 taproot output
        -   Optionally, repeat with n++ to create additional outputs for t=
he current Bm
        -   If no additional outputs are required, continue to the next Bm=
 with n++[16]
    -   Optionally, if the sending wallet implements receiving silent paym=
ents, it can create change outputs in the following manner:
        -   Let Achange =3D Aspend + sha256(ser256(ascan))=C2=B7G
        -   Let change_shared_secret =3D outpoints_hash=C2=B7a=C2=B7Ascan
        -   Let n =3D 0
        -   For each change output desired:
            -   Let cn =3D sha256(serP(change_shared_secret) || ser32(n))
            -   Let Cn =3D Achange + cn=C2=B7G
            -   Encode Cn as a BIP341 taproot output
            -   Repeat with n++ for additional change outputs

### =3D=3D=3D Receiver =3D=3D=3D

#### =3D=3D=3D=3D Key Derivation =3D=3D=3D=3D

Two keys are needed to create a silent payments address: the spend key and=
 the scan key. While these keys can be generated independently, wallet sof=
tware SHOULD use BIP32 derivation[17] to ensure compatibility across walle=
ts.

A scan and spend key pair using BIP32 derivation are defined (taking inspi=
ration from BIP44) in the following manner:

=C2=A0 =C2=A0 =C2=A0Scan private key: m / purpose' / coin_type' / account'=
 / 1' / 0
=C2=A0 =C2=A0 Spend private key: m / purpose' / coin_type' / account' / 0'=
 / 0

Wallet software MUST use hardened derivation to ensure the master key is n=
ot exposed in the event the scan private key is compromised. Purpose is a =
constant set to 352 following the BIP43 recommendation. Refer to BIP43 and=
 BIP44 for more details.

#### =3D=3D=3D=3D Scanning =3D=3D=3D=3D

If each of the checks in Scanning transactions passes, the receiving walle=
t must:

-   Generate the outpoints_hash, using the method described above
-   Let A =3D A0 + A1 + =E2=80=A6 An, where each Ai is the public key of a=
n input from the Inputs For Shared Secret Derivation list
-   Let ecdh_shared_secret =3D outpoints_hash=C2=B7bscan=C2=B7A
-   Check for outputs:
    -   Let outputs_to_check =3D the taproot output key from each unspent =
taproot output in the transaction
    -   Starting with n =3D 0:
        -   Let tn =3D sha256(serP(ecdh_shared_secret) || ser32(n))
        -   Compute Pn =3D Bspend + tn=C2=B7G
        -   For each output in outputs_to_check:
            -   If Pn equals output:
                -   Add Pn to the wallet
                -   Remove output from outputs_to_check and rescan outputs=
_to_check with n++
            -   Else, if the wallet has precomputed labels (including the =
change label, if used)[18]:
                -   Compute m=C2=B7G =3D output - Pn
                -   Check if m=C2=B7G exists in the list of labels used by=
 the wallet
                -   If a match is found:
                    -   Add the Pn + m=C2=B7G to the wallet
                    -   Remove output from outputs_to_check and rescan out=
puts_to_check with n++
                -   If the label is not found, negate output and check aga=
in
        -   If no matches are found, stop

#### =3D=3D=3D=3D Backup and Recovery =3D=3D=3D=3D

Since each silent payment output address is derived independently, regular=
 backups are recommended. When recovering from a backup, the wallet will n=
eed to scan since the last backup to detect new payments.

If using a seed/seed phrase only style backup, the user can recover the wa=
llet's unspent outputs from the UTXO set (i.e. only scanning transactions =
with at least one unspent taproot output) and can recover the full wallet =
history by scanning the blockchain starting from the wallet birthday. If a=
 wallet uses labels or generates its change addresses using the change lab=
el, this information SHOULD be included in the backup. If the user does no=
t know whether labels or the change label were used, it is strongly recomm=
ended they always check for the change label when recovering from backup a=
nd precompute a large number of labels (e.g. 100k labels) to use when re-s=
canning. This ensures that the wallet can recover all funds from only a se=
ed/seed phrase backup.

=3D=3D Backward Compatibility =3D=3D

-----------------------------

Silent payments introduces a new address format and protocol for sending a=
nd as such is not compatible with older wallet software or wallets which h=
ave not implemented the silent payments protocol.

=3D=3D Rationale and References =3D=3D

-------------------------------

1.  =C2=A0Why not use out-of-band notifications Out of band notifications =
(e.g. using something other than the Bitcoin blockchain) have been propose=
d as a way of addressing the privacy and cost concerns of using the Bitcoi=
n blockchain as a messaging layer. This, however, simply moves the privacy=
 and cost concerns somewhere else and increases the risk of losing money d=
ue to a notification not being reliably delivered, or even censored, and m=
akes this notification data critical for backup to recover funds.
2.  Why allow for more than one output? Allowing Alice to break her paymen=
t to Bob into multiple amounts opens up a number of privacy improving tech=
niques for Alice, making the transaction look like a CoinJoin or better hi=
ding the change amount by splitting both the payment and change outputs in=
to multiple amounts. It also allows for Alice and Carol to both have their=
 own unique output paying Bob in the event they are in a collaborative tra=
nsaction and both paying Bob's silent payment address.
3.  What about inputs without public keys? Inputs without public keys can =
still be spent in the transaction but are simply ignored in the Silent Pay=
ments protocol.
4.  How does using all inputs help light clients?  If Alice uses a random =
input for the tweak, Bob necessarily has to have access to and check all t=
ransaction inputs, which requires performing an ECC multiplication per inp=
ut. If instead Alice performs the tweak with the sum of the input public k=
eys, Bob only needs the summed 33 byte public key per transaction and only=
 does one ECC multiplication per transaction. Bob can then use BIP158 bloc=
k filters to determine if any of the outputs exist in a block and thus avo=
ids downloading transactions which don't belong to him. It is still an ope=
n question as to how Bob can source the 32 bytes per transaction in a trus=
tless manner, see Appendix A: Light Client Support for more details.
5.  Why does using all inputs matter for CoinJoin? If Alice uses a random =
input to create the output for Bob, this necessarily reveals to Bob which =
input Alice has control of. If Alice is paying Bob as part of a CoinJoin, =
this would reveal which input belongs to her, degrading the anonymity set =
of the CoinJoin and giving Bob more information about Alice. If instead al=
l inputs are used, Bob has no way of knowing which input(s) belong to Alic=
e. This comes at the cost of increased complexity as the CoinJoin particip=
ants now need to coordinate to create the silent payment output and would =
need to use Blind-Diffie-Hellman to prevent the other participants from le=
arning who Alice is paying.
6.  Why are outpoints little-endian? Despite using big endian throughout t=
he rest of the BIP, outpoints are sorted and hashed matching their transac=
tion serialization, which is little-endian. This allows a wallet to parse =
a serialized transaction for use in silent payments without needing to re-=
order the bytes when compute the outpoint hash. Note: despite outpoints be=
ing stored and serialized as little-endian, the transaction hash (txid) is=
 always displayed as big-endian.
7.  Why only taproot outputs? Providing too much optionality for the proto=
col makes it difficult to implement and can be at odds with the goal of pr=
oviding the best privacy. Limiting to taproot outputs helps simplify the i=
mplementation significantly while also putting users in the best eventual =
anonymity set.
8.  Why recommend SIGHASH_[DEFAULT|ALL]? Since the output address for the =
receiver is derived from from the sum of the Inputs For Shared Secret Deri=
vation public keys, the inputs must not change once the sender has signed =
the transaction. If the inputs are allowed to change after the fact, the r=
eceiver will not be able to calculate the shared secret needed to find and=
 spend the output. It is currently an open question on how a future versio=
n of silent payments could be made to work with new sighash flags such as =
SIGHASH_GROUP and SIGHASH_ANYPREVOUT.
9.  Why skip transactions that spend unknown output scripts? Skipping tran=
sactions that spend unknown output scripts allows us to have a clean upgra=
de path for Silent Payments by avoiding the need to scan the same transact=
ion multiple times with different rule sets. If a fancy new output type is=
 added in the future and Silent Payments v1 is released with support, we w=
ould want to avoid having to first scan the transaction with the silent pa=
yment v0 rules and then again with the silent payment v1 rules. Note: this=
 restriction only applies to the inputs of a transaction.
10.  Why do silent payment addresses need at least 117 characters? A silen=
t payment address is a bech32m encoding comprised of the following parts:
    =


    -   HRP [2-3]
    -   separator [1]
    -   version [1-2]
    -   payload, 66 bytes concatenated pubkeys [ceil(66*8/5)]
    -   checksum [6]
    =


    For a silent payments v0 address, this results in a 117 character addr=
ess when using a 3 character HRP. Future versions of silent payment addres=
ses may add to the payload, which is why a 1023 character limit is suggest=
ed.
11.  Why are outpoints sorted before hashing? This way the silent payment =
otuput does not need to be recalculated if the wallet changes the order of=
 inputs, e.g. at signing time or during an RBF bump.
12.  Are key aggregation techniques like FROST and MuSig2 supported? Any t=
aproot output able to do a key path spend is supported. While a full speci=
fication of how to do this securely is outside the scope of this BIP, in t=
heory any offline key aggregation technique can be used, such as FROST or =
MuSig2. This would require participants to perform the ECDH step collabora=
tively e.g. ECDH =3D a0=C2=B7Bscan + a1=C2=B7Bscan + ... + at=C2=B7Bscan a=
nd P =3D Bspend + hash(outpoints_hash=C2=B7ECDH || 0)=C2=B7G. Additionally=
, it may be necessary for the participants to provide a DLEQ proof to ensu=
re they are not acting maliciously.
13.  Why not skip all taproot script path spends? This causes malleability=
 issues for CoinJoins. If the silent payments protocol skipped taproot scr=
ipt path spends, this would allow an attacker to join a CoinJoin round, pa=
rticipate in deriving the silent payment address using the tweaked private=
 key for a key path spend, and then broadcast their own version of the tra=
nsaction using the script path spend. If the receiver were to only conside=
r key path spends, they would skip the attacker's script path spend input =
when deriving the shared secret and not be able to find the funds. Additio=
nally, there may be scenarios where a sender has access to the key path pr=
ivate key but spends the output using the script path.
14.  Why skip outputs with H as the internal taproot key? If use cases get=
 popularized where the taproot key path cannot be used, these outputs can =
still be included without getting in the way of making a silent payment, p=
rovided they specifically use H as their internal taproot key.
15.  Why do taproot private keys need to be checked? Recall from BIP340 th=
at each x-only public key has two corresponding private keys, d and n - d.=
 To maintain parity between sender and receiver, it is necessary to use th=
e private key corresponding to the even y-value when performing the ECDH s=
tep since the receiver will assume the even y-value when summing the tapro=
ot x-only public keys.
16.  Why not re-use tn? when paying different labels to the same receiver?=
 If paying the same entity but to two separate labeled addresses in the sa=
me transaction without incrementing n, the two outputs would be Bspend + t=
n=C2=B7G + i=C2=B7G and Bspend + tn=C2=B7G + j=C2=B7G. The attacker could =
subtract the two values and observe that the distance between i and j is s=
mall. This would allow them to deduce that this transaction is a silent pa=
yment transaction and that a single entity received two outputs, but won't=
 tell them who the entity is.
17.  Why use BIP32 hardened derivation? Using BIP32 derivation allows user=
s to add silent payments to an existing master seed. It also ensures that =
a user's silent payment funds are recoverable in any wallet which supports=
 BIP32 derivation. Using hardened derivation ensures that it is safe to ex=
port the scan private key without exposing the master key or spend private=
 key.
18.  ^Why precompute labels? Precomputing the labels is not strictly neces=
sary: a wallet could track the max number of labels it has used (call it M=
) and scan for labels by adding m=C2=B7G to P0 for each label m up to M an=
d comparing to the transaction outputs. This is more performant than preco=
mputing the labels and checking via subtraction in cases where the number =
of eligible outputs exceeds the number of labels in use. In practice this =
will mainly apply to users that choose never to use labels, or users that =
use a single label for generating silent payment change outputs. If using =
a large number of labels, the wallet would need to add all possible labels=
 to each output. This ends up being n=C2=B7M additions, where n is the num=
ber of outputs in the transaction and M is the number of labels in the wal=
let. By precomputing the labels, the wallet only needs to compute m=C2=B7G=
 once when creating the labeled address and can determine if a label was u=
sed via a lookup, rather than adding each label to each output.
19.  Data for Appendix A These numbers are based on data from January 2023=
 until June 2023 (the last 6 months of data at time time of writing). See =
Silent payments light client data for the full analysis.

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