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Subject: [bitcoin-dev] BIP for Silent Payments
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Hi all,
After what has seemed like an eternity of refining and tweaking (pun inten=
ded) the original write-up proposed by Ruben Somsen back in March 2022, we=
'd like to submit a Silent Payments BIP for your consideration and review.


For convenience, the overview from the BIP is in plain text below. Please =
note: the overview is not the full specification; the full specification c=
an be found at https://github.com/bitcoin/bips/pull/1458/files , along wit=
h a WIP implementation for Bitcoin Core at https://github.com/bitcoin/bitc=
oin/pull/27827 .



Looking forward to hearing your thoughts!


-- Ruben, Josie


=3D=3D Silent Payments =3D=3D

Using a new address for each Bitcoin transaction is a crucial aspect of ma=
intaining privacy. This often requires a secure interaction between sender=
 and receiver so that the receiver can hand out a fresh address, a batch o=
f fresh addresses, or a method for the sender to generate addresses on-dem=
and, such as an xpub.

However, interaction is often infeasible and in many cases undesirable. To=
 solve for this, various protocols have been proposed which use a static p=
ayment address and notifications sent via the blockchain. These protocols =
eliminate the need for interaction, but at the expense of increased costs =
for one-time payments and a noticeable footprint in the blockchain, potent=
ially revealing metadata about the sender and receiver. Notification schem=
es also allow the receiver to link all payments from the same sender, comp=
romising sender privacy.

This proposal aims to address the limitations of these current approaches =
by presenting a solution that eliminates the need for interaction, elimina=
tes the need for notifications, and protects both sender and receiver priv=
acy. These benefits come at the cost of requiring wallets to scan the bloc=
kchain in order to detect payments. This added requirement is generally fe=
asible for full nodes but poses a challenge for light clients. While it is=
 possible today to implement a privacy-preserving light client at the cost=
 of increased bandwidth, light client support is considered an area of ope=
n research

=3D=3D Goals =3D=3D

We aim to present a protocol which satisfies the following properties:

-   No increase in the size or cost of transactions

-   Resulting transactions blend in with other bitcoin transactions and ca=
n=E2=80=99t be distinguished
-   Transactions can=E2=80=99t be linked to a silent payment address by an=
 outside observer
-   No sender-receiver interaction required
-   No linking of multiple payments to the same sender
-   Each silent payment goes to a unique address, avoiding accidental addr=
ess reuse
-   Supports payment labeling
-   Uses existing seed phrase or descriptor methods for backup and recover=
y
-   Separates scanning and spending responsibilities
-   Compatible with other spending protocols, such as CoinJoin
-   Light client/SPV wallet support
-   Protocol is upgrade-able


=3D=3D Overview =3D=3D

We first present an informal overview of the protocol. In what follows, up=
percase letters represent public keys, lowercase letters represent private=
 keys, || refers to byte concatenation, and G represents the generator poi=
nt for secp256k1. Each section of the overview is incomplete on its own an=
d is meant to build on the previous section in order to introduce and brie=
fly explain each aspect of the protocol.

=3D=3D=3D Simple case =3D=3D=3D

Bob publishes a public key B as a silent payment address. Alice discovers =
Bob's silent payment address, selects a UTXO with private key a, public ke=
y A and creates a destination output P for Bob in the following manner:

-   Let P =3D hash(a=C2=B7B)=C2=B7G + B
-   Encode P as a=C2=A0BIP341 taproot output


Since a=C2=B7B =3D=3D b=C2=B7A (Elliptic Curve Diffie-Hellman), Bob scans =
with his private key b by collecting the input public keys for each transa=
ction with at least one unspent taproot output and performing the ECDH cal=
culation until P is found (e.g. calculating P =3D hash(b=C2=B7A)=C2=B7G + =
B and seeing that P is present in the transaction outputs).

=3D=3D=3D Creating more than one output =3D=3D=3D

In order to allow Alice to create more than one output for Bob, we include=
d an integer in the following manner:

-   Let n =3D 0
-   Let P0 =3D hash(a=C2=B7B || n)=C2=B7G + B
-   For additional outputs:
    -   Increment n by one (n++)
    -   Let Pi =3D hash(a=C2=B7B || n)=C2=B7G + B

Bob detects this output the same as before by searching for P0 =3D hash(b=C2=
=B7A || 0)=C2=B7G + B. Once he detects the first output, he must:

-   Check for P1 =3D hash(b=C2=B7A || 1)=C2=B7G + B
-   If P1 is not found, stop
-   If P1 is found, continue to check for P2 and so on until an additional=
 output is not found


Since Bob will only perform these subsequent checks after a transaction wi=
th at least one output paying him is found, the increase to his overall sc=
anning requirement is negligible.

=3D=3D=3D Preventing address reuse =3D=3D=3D

If Alice were to use a different UTXO from the same public key A for a sub=
sequent payment to Bob, she would end up deriving the same destination P. =
To prevent this, Alice should include a hash of the outpoint in the follow=
ing manner:

-   Let outpoint_hash =3D hash(txid || vout)
-   Let P0 =3D hash(outpoint_hash=C2=B7a=C2=B7B || 0)=C2=B7G + B


Bob must include the same outpoint_hash when scanning.

=3D=3D=3D Using all inputs =3D=3D=3D

In our simplified example we have been referring to Alice=E2=80=99s transa=
ctions as having only one input A, but in reality a Bitcoin transaction ca=
n have many inputs. Instead of requiring Alice to pick a particular input =
and requiring Bob to check each input separately, we can instead require A=
lice to perform the tweak with the sum of the input public keys[3]. This s=
ignificantly reduces Bob's scanning requirement, makes light client suppor=
t more feasible[4], and protects Alice's privacy in collaborative transact=
ion protocols such as CoinJoin[5].

Alice performs the tweak with the sum of her input private keys in the fol=
lowing manner:

-   Let outpoints_hash =3D hash(txid0 || vout0 || =E2=80=A6 txidn || voutn=
)
-   Let a =3D a0 + a1 =E2=80=A6 + an
-   Let P0 =3D hash(outpoints_hash=C2=B7a=C2=B7B || 0)=C2=B7G + B


=3D=3D=3D Spend and Scan Key =3D=3D=3D

Since Bob needs his private key b to check for incoming payments, this req=
uires b to be exposed to an online device. To minimize the risks involved,=
 Bob can instead publish an address of the form (Bscan, Bspend). This allo=
ws Bob to keep bspend in offline cold storage and perform the scanning wit=
h the public key Bspend and private key bscan. Alice performs the tweak us=
ing both of Bob=E2=80=99s public keys in the following manner:

-   Let P0 =3D hash(outpoints_hash=C2=B7a=C2=B7Bscan || 0)=C2=B7G + Bspend



Bob detects this payment by calculating P0 =3D hash(outpoints_hash=C2=B7bs=
can=C2=B7A)=C2=B7G + Bspend with his online device and can spend from his =
cold storage signing device using (hash(outpoints_hash=C2=B7bscan=C2=B7A) =
+ bspend) mod p as the private key.

=3D=3D=3D Labels =3D=3D=3D

For a single silent payment address of the form (Bscan, Bspend), Bob may w=
ish to differentiate incoming payments. Naively, Bob could publish multipl=
e silent payment addresses, but this would require him to scan for each on=
e, which becomes prohibitively expensive. Instead, Bob can label his spend=
 public key Bspend with an integer m in the following way:

-   Let Bm =3D Bspend + m=C2=B7G
-   Publish (Bscan, B0), (Bscan, B1) =E2=80=A6



Alice performs the tweak as before using one of the published (Bscan, Bm) =
pairs. Bob detects the labeled payment in the following manner:


-   Let P0 =3D hash(outpoints_hash=C2=B7bscan=C2=B7A || 0)=C2=B7G + Bspend
-   Subtract P0 from each of the transaction outputs and check if the rema=
inder matches any of the labels (1=C2=B7G, 2=C2=B7G ..) that the wallet ha=
s previously used



It is important to note that an outside observer can easily deduce that ea=
ch published (Bscan, Bm) pair is owned by the same entity as each publishe=
d address will have Bscan in common. As such, labels are not meant as a wa=
y for Bob to manage separate identities, but rather a way for Bob to deter=
mine the source of an incoming payment.

=3D=3D=3D Labels for change =3D=3D=3D

Bob can also use labels for managing his own change outputs. To do so, he =
can reserve a secret change label in the following manner:

-   Let Bchange =3D Bspend + hash(bscan)=C2=B7G



Now, whenever Bob is spending (to a silent payment address or otherwise), =
he can create a change output for himself using the silent payments protoc=
ol and his change label in the following manner:



-   Let a =3D a0 + a1 =E2=80=A6 + an represent the private keys of the inp=
uts Bob is using to fund the transaction
-   Let Pchange =3D hash(outpoints_hash=C2=B7a=C2=B7Bchange || 0)=C2=B7G +=
 Bspend



This gives Bob an alternative to using BIP32 for managing change, while st=
ill allowing him to know which of his unspent outputs were change when rec=
overing his wallet from the master key. The change label needs to remain a=
 secret in order to ensure nobody else can label payments as change.


Sent with Proton Mail secure email.
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Content-Description: OpenPGP digital signature
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-----BEGIN PGP SIGNATURE-----
Version: ProtonMail

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