BIP 0352

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  BIP: 352
  Layer: Applications
  Title: Silent Payments
  Author: josibake <josibake@protonmail.com>
          Ruben Somsen <rsomsen@gmail.com>
  Comments-URI: https://github.com/bitcoin/bips/wiki/Comments:BIP-0352
  Status: Proposed
  Type: Standards Track
  Created: 2023-03-09
  License: BSD-2-Clause
  Post-History: 2022-03-13: https://gist.github.com/RubenSomsen/c43b79517e7cb701ebf77eec6dbb46b8 [gist] Original proposal
                2022-03-28: https://gnusha.org/pi/bitcoindev/CAPv7TjbXm953U2h+-12MfJ24YqOM5Kcq77_xFTjVK+R2nf-nYg@mail.gmail.com/ [bitcoin-dev] Silent Payments – Non-interactive private payments with no on-chain overhead
                2022-10-11: https://gnusha.org/pi/bitcoindev/P_21MLHGJicZ-hkbC4DGu86c5BtNKiH8spY4TOw5FJsfimdi_6VyHzU_y-s1mZsOcC2FA3EW_6w6W5qfV9dRK_7AvTAxDlwVfU-yhWZPEuo=@protonmail.com/ [bitcoin-dev] Silent Payment v4 (coinjoin support added)
                2023-08-04: https://gnusha.org/pi/bitcoindev/ZM03twumu88V2NFH@petertodd.org/ [bitcoin-dev] BIP-352 Silent Payments addresses should have an expiration time

Introduction

Abstract

This document specifies a protocol for static payment addresses in Bitcoin without on-chain linkability of payments or a need for on-chain notifications.

Copyright

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

Motivation

Using a new address for each Bitcoin transaction is a crucial aspect of maintaining privacy. This often requires a secure interaction between sender and receiver, so that the receiver can hand out a fresh address, a batch of fresh addresses, or a method for the sender to generate addresses on-demand, 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 payment 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, potentially revealing metadata about the sender and receiver. Notification schemes also allow the receiver to link all payments from the same sender, compromising sender privacy.

This proposal aims to address the limitations of these current approaches by presenting a solution that eliminates the need for interaction, eliminates the need for notifications, and protects both sender and receiver privacy. These benefits come at the cost of requiring wallets to scan the blockchain in order to detect payments. This added requirement is generally feasible 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 open research (see Appendix A: Light Client Support).

The design keeps collaborative transactions such as CoinJoins and inputs with MuSig and FROST keys in mind, but it is recommended that the keys of all inputs of a transaction belong to the same entity as there is no formal proof that the protocol is secure in a collaborative setting.

Goals

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 can't be distinguished
• Transactions can't 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 address reuse
• Supports payment labeling
• Uses existing seed phrase or descriptor methods for backup and recovery
• Separates scanning and spending responsibilities
• Compatible with other spending protocols, such as CoinJoin
• Light client/SPV wallet support
• Protocol is upgradeable

Overview

We first present an informal overview of the protocol. In what follows, uppercase letters represent public keys, lowercase letters represent private keys, || refers to byte concatenation, · refers to elliptic curve scalar multiplication, G represents the generator point for secp256k1, and n represents the curve order for secp256k1. Each section of the overview is incomplete on its own and is meant to build on the previous section in order to introduce and briefly explain each aspect of the protocol. For the full protocol specification, see Specification.

Simple case

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 key A and creates a destination output P for Bob in the following manner:

• Let P = B + hash(a·B)·G
• Encode P as a BIP341 taproot output

Since a·B == b·A (Elliptic-curve Diffie–Hellman), Bob scans with his private key b by collecting the input public keys for each transaction with at least one unspent taproot output and performing the ECDH calculation until P is found (i.e. calculating P = B + hash(b·A)·G and seeing that P is present in the transaction outputs).

Creating more than one output

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

• Let k = 0
• Let P₀ = B + hash(a·B || k)·G
• For additional outputs:
  • Increment k by one (k++)
  • Let P_i = B + hash(a·B || k)·G

Bob detects this output the same as before by searching for P₀ = B + hash(b·A || 0)·G. Once he detects the first output, he must:

• Check for P₁ = B + hash(b·A || 1)·G
• 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 with at least one output paying him is found, the increase to his overall scanning requirement is negligible. It should also be noted that the order in which these outputs appear in the transaction does not affect the outcome.

Preventing address reuse

If Alice were to use a different UTXO from the same public key A for a subsequent payment to Bob, she would end up deriving the same destinations P_i. To prevent this, Alice should include an input hash in the following manner:

• Let input_hash = hash(outpoint || A)
• Let P₀ = B + hash(input_hash·a·B || 0)·G

Bob must calculate the same input_hash when scanning.

Using all inputs

In our simplified example we have been referring to Alice's transactions as having only one input A, but in reality a Bitcoin transaction can have many inputs. Instead of requiring Alice to pick a particular input and requiring Bob to check each input separately, we can instead require Alice to perform the tweak with the sum of the input public keys. This significantly reduces Bob's scanning requirement, makes light client support more feasible, and protects Alice's privacy in collaborative transaction protocols such as CoinJoin.

Alice performs the tweak with the sum of her input private keys in the following manner:

• Let A = A₁ + A₂ + ... + A_n
• Let input_hash = hash(outpoint_L || A), where outpoint_L is the smallest outpoint lexicographically
• Let a = a₁ + a₂ + ... + a_n
• Let P₀ = B + hash(input_hash·a·B || 0)·G

Spend and Scan Key

Since Bob needs his private key b to check for incoming payments, this requires b to be exposed to an online device. To minimize the risks involved, Bob can instead publish an address of the form (B_scan, B_spend). This allows Bob to keep b_spend in offline cold storage and perform the scanning with the public key B_spend and private key b_scan. Alice performs the tweak using both of Bob's public keys in the following manner:

• Let P₀ = B_spend + hash(input_hash·a·B_scan || 0)·G

Bob detects this payment by calculating P₀ = B_spend + hash(input_hash·b_scan·A || 0)·G with his online device and can spend from his cold storage signing device using (b_spend + hash(input_hash·b_scan·A || 0)) mod n as the private key.

Labels

For a single silent payment address of the form (B_scan, B_spend), Bob may wish to differentiate incoming payments. Naively, Bob could publish multiple silent payment addresses, but this would require him to scan for each one, which becomes prohibitively expensive. Instead, Bob can label his spend public key B_spend with an integer m in the following way:

• Let B_m = B_spend + hash(b_scan || m)·G where m is an incrementable integer starting from 1
• Publish (B_scan, B₁), (B_scan, B₂) etc.

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

• Let P₀ = B_spend + hash(input_hash·b_scan·A || 0)·G
• Subtract P₀ from each of the transaction outputs and check if the remainder matches any of the labels (hash(b_scan || 1)·G, hash(b_scan || 2)·G etc.) that the wallet has previously used

It is important to note that an outside observer can easily deduce that each published (B_scan, B_m) pair is owned by the same entity as each published address will have B_scan in common. As such, labels are not meant as a way for Bob to manage separate identities, but rather a way for Bob to determine the source of an incoming payment.

Labels for change

Bob can also use labels for managing his own change outputs. We reserve m = 0 for this use case. This gives Bob an alternative to using BIP32 for managing change, while still allowing him to know which of his unspent outputs were change when recovering his wallet from the master key. It is important that the wallet never hands out the label with m = 0 in order to ensure nobody else can create payments that are wrongly labeled as change.

While the use of labels is optional, every receiving silent payments wallet should at least scan for the change label when recovering from backup in order to ensure maximum cross-compatibility.

Specification

We use the following functions and conventions:

• outpoint (36 bytes): the COutPoint of an input (32-byte txid, least significant byte first || 4-byte vout, least significant byte first)
• 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 significant byte first.
• ser_P(P): serializes the coordinate pair P = (x,y) as a byte sequence using SEC1's compressed form: (0x02 or 0x03) || ser₂₅₆(x), where the header byte depends on the parity of the omitted Y coordinate.

For everything not defined above, we use the notation from BIP340. This includes the hash_tag(x) notation to refer to SHA256(SHA256(tag) || SHA256(tag) || x).

Versions

This document defines version 0 (sp1q). Version is communicated through the address in the same way as bech32 addresses (see BIP173. 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 wallet can send to both v0 and v1 addresses). Any changes that break compatibility with older silent payment versions should be a new BIP.

Future silent payments versions will use the following scheme:

	0	1	2	3	4	5	6	7	Compatibility
+0	q	p	z	r	y	9	x	8	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 silent 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 discard the remaining bytes
  • v31: fail
• Receiver addresses are always BIP341 taproot outputs
• The sender should sign with one of the sighash flags DEFAULT, ALL, SINGLE, NONE (ANYONECANPAY is unsafe). It is strongly recommended implementations use SIGHASH_ALL (SIGHASH_DEFAULT for taproot inputs) when possible
• Inputs used to derive the shared secret are from the Inputs For Shared Secret Derivation list

Scanning silent payment eligible transactions

For silent payments v0 a transaction MUST be scanned if and only if all of the following are true:

• The transaction contains at least one BIP341 taproot output (note: spent transactions optionally can be skipped by only considering transactions with at least one unspent taproot output)
• The transaction has at least one input from the Inputs For Shared Secret Derivation list
• The transaction does not spend an output with SegWit version > 1

Address encoding

A silent payment address is constructed in the following manner:

• Let B_scan, b_scan = Receiver's scan public key and corresponding private key
• Let B_spend, b_spend = Receiver's spend public key and corresponding private key
• Let B_m = B_spend + hash_{BIP0352/Label}(ser₂₅₆(b_scan) || ser₃₂(m))·G, where hash_{BIP0352/Label}(ser₂₅₆(b_scan) || ser₃₂(m))·G is an optional integer tweak for labeling
  • If no label is applied then B_m = B_spend
• 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 version 0
    • The 66-byte concatenation of the receiver's public keys, ser_P(B_scan) || ser_P(B_m)

Note: BIP173 imposes a 90 character limit for Bech32 segwit addresses and limits versions to 0 through 16, whereas a silent payment address requires at least 117 characters and allows versions up to 31. Additionally, since higher versions may add to the data field, it is recommended implementations use a limit of 1023 characters (see BIP173: Checksum design for more details).

Inputs For Shared Secret Derivation

While any UTXO with known output scripts can be used to fund the transaction, the sender and receiver MUST use inputs from the following list when deriving the shared secret:

• P2TR
• P2WPKH
• P2SH-P2WPKH
• P2PKH

Inputs with conditional branches or multiple public keys (e.g. CHECKMULTISIG) are excluded from shared secret derivation as this introduces malleability and would allow a sender to re-sign with a different set of public keys after the silent payment 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 protocols, where a malicious participant can participate in deriving the silent payment address with one set of keys and then re-broadcast the transaction with signatures for a different set of public keys. P2TR can have hidden conditional branches (script path), but we work around this by using only the output public key.

For all of the output types listed, only X-only and compressed public keys are permitted.

P2TR

Keypath spend

   witness:      <signature>
   scriptSig:    (empty)
   scriptPubKey: 1 <32-byte-x-only-key>
                 (0x5120{32-byte-x-only-key})

The sender uses the private key corresponding to the taproot output key (i.e. the tweaked private key). This can be a single private key or an aggregate key (e.g. taproot outputs using MuSig or FROST). The receiver obtains the public key from the scriptPubKey (i.e. the taproot output key).

Script path spend

   witness:      <optional witness items> <leaf script> <control block>
   scriptSig:    (empty)
   scriptPubKey: 1 <32-byte-x-only-key>
                 (0x5120{32-byte-x-only-key})

Same as a keypath spend, the sender MUST use the private key corresponding to the taproot output key. If this key is not available, the output cannot be included as an input to the transaction. Same as a keypath spend, the receiver obtains the public key from the scriptPubKey (i.e. the taproot output key).

The one exception is script path spends that use NUMS point H as their internal key (where H is constructed by taking the hash of the standard 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 input will be skipped for the purposes of shared secret derivation. The receiver determines whether or not to skip the input by checking in the control block if the taproot internal key is equal to H.

P2WPKH

   witness:      <signature> <33-byte-compressed-key>
   scriptSig:    (empty)
   scriptPubKey: 0 <20-byte-key-hash>
                 (0x0014{20-byte-key-hash})

The sender performs the tweak using the private key for the output and the receiver obtains the public key as the last witness item.

P2SH-P2WPKH

   witness:      <signature> <33-byte-compressed-key>
   scriptSig:    <0 <20-byte-key-hash>>
                 (0x160014{20-byte-key-hash})
   scriptPubKey: HASH160 <20-byte-script-hash> EQUAL
                 (0xA914{20-byte-script-hash}87)

The sender performs the tweak using the private key for the nested P2WPKH output and the receiver obtains the public key as the last witness item.

P2PKH

   scriptSig:    <signature> <33-byte-compressed-key>
   scriptPubKey: OP_DUP HASH160 <20-byte-key-hash> OP_EQUALVERIFY OP_CHECKSIG
                 (0x76A914{20-byte-key-hash}88AC)

The receiver obtains the public key from the scriptSig. The receiver MUST parse the scriptSig for the public key, even if the scriptSig does not match the template specified (e.g. <dummy> OP_DROP <Signature> <Public Key>). This is to address the third-party malleability of P2PKH scriptSigs.

Input hash

The sender and receiver MUST calculate an input hash for the transaction in the following manner:

• Let A = A₁ + A₂ + ... + A_n, where each A_i is the public key of an input from the Inputs For Shared Secret Derivation list
• Let input_hash = hash_{BIP0352/Inputs}(outpoint_L || A), where outpoint_L is the smallest outpoint lexicographically by txid and vout used in the transaction

Sender

Selecting inputs

The sending wallet performs coin selection as usual with the following restrictions:

• At least one input MUST be from the Inputs For Shared Secret Derivation list
• Exclude inputs with SegWit version > 1 (see Scanning silent payment eligible transactions)
• For each taproot output spent the sending wallet MUST have access to the private key corresponding to the taproot output key, unless H is used as the internal public key

Creating outputs

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

• Generate the input_hash with the smallest outpoint lexicographically, using the method described above
• Collect the private keys for each input from the Inputs For Shared Secret Derivation list
• For each private key a_i corresponding to a BIP341 taproot output, check that the private key produces a point with an even Y coordinate and negate the private key if not
• Let a = a₁ + a₂ + ... + a_n, where each a_i has been negated if necessary
• Group receiver silent payment addresses by B_scan (e.g. each group consists of one B_scan and one or more B_m)
• For each group:
  • Let ecdh_shared_secret = input_hash·a·B_scan
  • Let k = 0
  • For each B_m in the group:
    • Let t_k = hash_{BIP0352/SharedSecret}(ser_P(ecdh_shared_secret) || ser₃₂(k))
      • If t_k is not valid tweak, i.e., if t_k = 0 or t_k is larger or equal to the secp256k1 group order, fail
    • Let P_mn = B_m + t_k·G
    • Encode P_mn as a BIP341 taproot output
    • Optionally, repeat with k++ to create additional outputs for the current B_m
    • If no additional outputs are required, continue to the next B_m with k++
  • Optionally, if the sending wallet implements receiving silent payments, it can create change outputs by sending to its own silent payment address using label m = 0, following the steps above

Receiver

Key Derivation

Two keys are needed to create a silent payments address: the spend key and the scan key. To ensure compatibility, wallets MAY use BIP32 derivation with the following derivation paths for the spend and scan key. When using BIP32 derivation, wallet software MUST use hardened derivation for both the spend and scan key.

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

    scan_private_key: m / purpose' / coin_type' / account' / 1' / 0
   spend_private_key: m / purpose' / coin_type' / account' / 0' / 0

purpose is a constant set to 352 following the BIP43 recommendation. Refer to BIP43 and BIP44 for more details.

Scanning

If each of the checks in Scanning silent payment eligible transactions passes, the receiving wallet must:

• Generate the input_hash with the smallest outpoint lexicographically, using the method described above
• Let A = A₁ + A₂ + ... + A_n, where each A_i is the public key of an input from the Inputs For Shared Secret Derivation list
• Let ecdh_shared_secret = input_hash·b_scan·A
• Check for outputs:
  • Let outputs_to_check be the taproot output keys from all taproot outputs in the transaction (spent and unspent).
  • Starting with k = 0:
    • Let t_k = hash_{BIP0352/SharedSecret}(ser_P(ecdh_shared_secret) || ser₃₂(k))
      • If t_k is not valid tweak, i.e., if t_k = 0 or t_k is larger or equal to the secp256k1 group order, fail
    • Compute P_k = B_spend + t_k·G
    • For each output in outputs_to_check:
      • If P_k equals output:
        • Add P_k to the wallet
        • Remove output from outputs_to_check and rescan outputs_to_check with k++
      • Else, check for labels (always check for the change label, i.e. hash_{BIP0352/Label}(ser₂₅₆(b_scan) || ser₃₂(m)) where m = 0):
        • Compute label = output - P_k
        • Check if label exists in the list of labels used by the wallet
        • If a match is found:
          • Add P_k + label to the wallet
          • Remove output from outputs_to_check and rescan outputs_to_check with k++
        • If a label is not found, negate output and check a second time
    • If no matches are found, stop

Spending

Recall that a silent payment output is of the form B_spend + t_k·G + hash_{BIP0352/Label}(ser₂₅₆(b_scan) || ser₃₂(m))·G, where hash_{BIP0352/Label}(ser₂₅₆(b_scan) || ser₃₂(m))·G is an optional label. To spend a silent payment output:

• Let d = (b_spend + t_k + hash_{BIP0352/Label}(ser₂₅₆(b_scan) || ser₃₂(m))) mod n, where hash_{BIP0352/Label}(ser₂₅₆(b_scan) || ser₃₂(m)) is the optional label
• Spend the BIP341 output with the private key d

Backup and Recovery

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

If using a seed/seed phrase only style backup, the user can recover the wallet'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, this information SHOULD be included in the backup. If the user does not know whether labels were used, it is strongly recommended they always precompute and check a large number of labels (e.g. 100k labels) to use when re-scanning. This ensures that the wallet can recover all funds from only a seed/seed phrase backup. The change label should simply always be scanned for, even when no other labels were used. This ensures the use of a change label is not critical for backups and maximizes cross-compatibility.

Backward Compatibility

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

Test Vectors

A collection of test vectors in JSON format are provided, along with a python reference implementation. Each test vector consists of a sending test case and corresponding receiving test case. This is to allow sending and receiving to be implemented separately. To ensure determinism while testing, sort the array of B_m by amount (see the reference implementation). Test cases use the following schema:

test_case

   {
       "comment": "Comment describing the behavior being tested",
       "sending": [<array of sender test objects>],
       "receiving": [<array of recipient test objects>],
   }

sender

   {
       "given": {
           "vin": [<array of vin objects with an added field for the private key. These objects are structured to match the `vin` output field from `getrawtransaction verbosity=2`>],
           "recipients": [<array of strings, where each string is a bech32m encoding representing a silent payment address>]
       },
       "expected": {
           "outputs": [<array of strings, where each string is a hex encoding of 32-byte X-only public key; contains all possible output sets, test must match a subset of size `n_outputs`>],
           "n_outputs": <integer for the exact number of expected outputs>,
       },
   }

recipient

   {
       "given": {
           "vin": [<array of vin objects. These objects are structured to match the `vin` output field from `getrawtransaction verbosity=2`>],
           "key_material": {
               "scan_priv_key": <hex encoded scan private key>,
               "spend_priv_key": <hex encoded spend private key>,
           }
           "labels": [<array of ints, representing labels the receiver has used>],
        },
        "expected": {
            "addresses": [<array of bech32m strings, one for the silent payment address and each labeled address (if used)>],
            "outputs": [<array of outputs with tweak and signature; contains all possible output sets, tester must match a subset of size `n_outputs`>
                {
                    "priv_key_tweak": <hex encoded private key tweak data>,
                    "pub_key": <hex encoded X-only public key>,
                    "signature": <hex encoded signature for the output (produced with spend_priv_key + priv_key_tweak)>
                },
                ...
            ],
            "n_outputs": <integer for the exact number of expected outputs>
        }
    }

Wallets should include inputs not in the Inputs For Shared Secret Derivation list when testing to ensure that only inputs from the list are being used for shared secret derivation. Additionally, receiving wallets should include non-silent payment outputs for themselves in testing to ensure silent payments scanning does not interfere with regular outputs detection.

Functional tests

Below is a list of functional tests which should be included in sending and receiving implementations.

Sending

• Ensure taproot outputs are excluded during coin selection if the sender does not have access to the key path private key (unless using H as the taproot internal key)
• Ensure the silent payment address is re-derived if inputs are added or removed during RBF

Receiving

• Ensure the public key can be extracted from non-standard P2PKH scriptSigs
• Ensure taproot script path spends are included, using the taproot output key (unless H is used as the taproot internal key)
• Ensure the scanner can extract the public key from each of the input types supported (e.g. P2WPKH, P2SH-P2WPKH, etc.)

Appendix A: Light Client Support

This section proposes a few ideas for how light clients could support scanning for incoming silent payments (sending is fairly straightforward) in ways that preserve bandwidth and privacy. While this is out of scope for the current BIP, it is included to motivate further research into this topic. In this context, a light client refers to any bitcoin wallet client which does not process blocks and does not have a direct connection to a node which does process blocks (e.g. a full node). Based on this definition, clients that directly connect to a personal electrum server or a bitcoin node are not light clients.

This distinction makes the problem for light clients more clear: light clients need a way to source the necessary data for performing the tweaks and a way of determining if any of the generated outputs exist in a block.

Tweak Data

Recall that a silent payment eligible transaction follows certain conditions and should have at least one unspent taproot output. Full nodes (or any index server backed by a full node, such as electrum server) can build an index which collects all of the eligible public keys for a silent payments eligible transaction, sums them up, multiplies the sum by the input_hash, and serves them to clients. This would be 33 bytes per silent payment eligible transaction.

For a typical bitcoin block of ~3500 txs, lets assume every transaction is a silent payments eligible transaction. This means a client would need to request 33 bytes * 3500 of data per block (roughly 100 kB per block). If a client were to request data for every block, this would amount to ~450 MB per month, assuming 100% taproot usage and all outputs remain unspent for > 1 month. As of today, these numbers are closer to 2–10 kB per block (10–50 MB per month).

Transaction cut-through

It is unlikely a light client would need to scan every block and as such can take advantage of transaction cut-through, depending on how often they choose to scan for new blocks. Empirically, ~75% of transactions with at least one unspent taproot output will have spent all taproot UTXOs in 326 blocks or less. This means a client which only scans once every 3 days could significantly cut down on the number of blocks and the number of transactions per block that they need to request by only asking for data on transactions that were created since their last scan and that still have at least one unspent taproot output as of the current block height. Assuming 100% taproot usage, a client that scans once a month would likely only need around 50 MB worth of data. Based on current taproot adoption, a light client scanning once every 3 days would use roughly 15 MB per month and a client scanning once per month would use less than 5 MB per month.

BIP158

Once a light client has the tweak data for a block, they can determine whether or not an output to them exists in the block using BIP158 block filters. Per BIP158, they would then request the entire block and add the transaction to their wallet, though it maybe be possible to only request the prevout txids and vouts for all transactions with at least one taproot output, along with the scriptPubKeys and amounts. This would allow the client to download the necessary data for constructing a spending transaction, without downloading the entire block. How this affects the security assumptions of BIP158 is an open question.

Out-of-band notifications

Assuming a secure messaging protocol exists, the sender can send an encrypted (using the scan public key of the silent payment address) notification to the receiver with the following information:

• The spend public key (communicates the label)
• The shared secret portion of the private key (i.e hash(ecdh_shared_secret || k))
• The outpoint and amount (so it's immediately spendable)

It is important to note that these notifications are not required. At any point, the receiver can fall back to scanning for silent payment transactions if they don't trust the notifications they are receiving, are being spammed with fake notifications, or if they are concerned that they are not receiving notifications.

A malicious notification could potentially cause the following issues:

• You did not actually receive money to the stated key
  • This can be probabilistically resolved by matching the key against the BIP158 block filters and assuming it's not a false positive, or fully resolved by downloading the block
• You received money but the outpoint or amount is incorrect, so attempts to spend it will fail or cause you to overpay fees
  • There doesn't seem to be much motivation for malicious senders to ever do this, but light clients need to take into account that this can occur and should ideally check for it by downloading the block
• The private key is correct but it wasn't actually derived using the silent payment protocol, causing recovery from back-up to fail (unsafe - no implementation should ever allow this)
  • This can be detected by downloading the tweak data of the corresponding block and should be resolved by immediately spending the output

Wallet designers can choose which tradeoffs they find appropriate. For example, a wallet could check the block filter to at least probabilistically confirm the likely existence of the UTXO, thus efficiently cutting down on spam. The payment could then be marked as unconfirmed until a scan is performed and the existence of the UTXO in accordance to the silent payment specification is verified.

Acknowledgements

This document is the result of many discussions and contains contributions by a number of people. The authors wish to thank all those who provided valuable feedback and reviews, including the participants of the BIP47 Prague discussion, the Advancing Bitcoin silent payments Workshop, and coredev. The authors would like to also thank w0xlt for writing the initial implementation of silent payments.