jamtis.md

JAMTIS

This document describes a new addressing scheme for Monero.

Chapters 1-2 are intended for general audience.

Chapters 3-7 contain technical specifications.

Table of Contents

• 1. Introduction
  • 1.1 Why a new address format?
  • 1.2 Current Monero addresses
  • 1.3 Jamtis
• 2. Features
  • 2.1 Address format
    • 2.1.1 Recipient IDs
  • 2.2 Light wallet scanning
    • 2.2.1 Wallet component
    • 2.2.2 Third party services
  • 2.3 Wallet tiers for merchants
    • 2.3.1 Address generator
    • 2.3.2 Payment validator
  • 2.4 Full view-only wallets
  • 2.5 Janus attack mitigation
  • 2.6 Robust output detection
• 3. Notation
  • 3.1 Serialization functions
  • 3.2 Hash function
  • 3.3 Elliptic curves
    • 3.3.1 Curve25519
    • 3.3.2 Ed25519
  • 3.4 Block cipher
  • 3.5 Base32 encoding
• 4. Wallets
  • 4.1 Wallet parameters
  • 4.2 New wallets
    • 4.2.1 Standard wallets
    • 4.2.2 Multisignature wallets
  • 4.3 Migration of legacy wallets
    • 4.3.1 Standard wallets
    • 4.3.2 Multisignature wallets
  • 4.4 Additional keys
  • 4.5 Key hierarchy
  • 4.6 Wallet access tiers
    • 4.6.1 Address generator (AddrGen)
    • 4.6.2 Output scanning wallet (FindReceived)
    • 4.6.3 Payment validator (ViewReceived)
    • 4.6.4 View-balance wallet (ViewAll)
    • 4.6.5 Master wallet (Master)
  • 4.7 Wallet public keys
• 5. Addresses
  • 5.1 Address generation
    • 5.1.1 Address keys
    • 5.1.2 Address tag
  • 5.2 Sending to an address
  • 5.3 Receiving an output
  • 5.4 Change and self-spends
  • 5.5 Transaction size
    • 5.5.1 Transactions with 2 outputs
    • 5.5.2 Transactions with 3 or more outputs
• 6. Address encoding
  • 6.1 Address structure
  • 6.2 Address header
    • 6.2.1 Version character
    • 6.2.2 Network type
  • 6.3 Checksum
  • 6.4 Binary-to-text encoding
    • 6.4.1 QR Codes
  • 6.5 Recipient authentication
• 7. Test vectors
• References
• Appendix A: Checksum

1. Introduction

1.1 Why a new address format?

Sometime in 2024, Monero plans to adopt a new transaction protocol called Seraphis [1], which enables much larger ring sizes than the current RingCT protocol. However, due to a different key image construction, Seraphis is not compatible with CryptoNote addresses. This means that each user will need to generate a new set of addresses from their existing private keys. This provides a unique opportunity to vastly improve the addressing scheme used by Monero.

1.2 Current Monero addresses

The CryptoNote-based addressing scheme [2] currently used by Monero has several issues:

1. Addresses are not suitable as human-readable identifiers because they are long and case-sensitive.
2. Too much information about the wallet is leaked when scanning is delegated to a third party.
3. Generating subaddresses requires view access to the wallet. This is why many merchants prefer integrated addresses [3].
4. View-only wallets need key images to be imported to detect spent outputs [4].
5. Subaddresses that belong to the same wallet can be linked via the Janus attack [5].
6. The detection of outputs received to subaddresses is based on a lookup table, which can sometimes cause the wallet to miss outputs [6].

1.3 Jamtis

Jamtis is a new addressing scheme that was developed specifically for Seraphis and tackles all of the shortcomings of CryptoNote addresses that were mentioned above. Additionally, Jamtis incorporates two other changes related to addresses to take advantage of this large upgrade opportunity:

• A new 16-word mnemonic scheme called Polyseed [7] that will replace the legacy 25-word seed for new wallets.
• The removal of integrated addresses and payment IDs [8].

2. Features

2.1 Address format

Jamtis addresses, when encoded as a string, start with the prefix xmra and consist of 196 characters. Example of an address: xmra1mj0b1977bw3ympyh2yxd7hjymrw8crc9kin0dkm8d3wdu8jdhf3fkdpmgxfkbywbb9mdwkhkya4jtfn0d5h7s49bfyji1936w19tyf3906ypj09n64runqjrxwp6k2s3phxwm6wrb5c0b6c1ntrg2muge0cwdgnnr7u7bgknya9arksrj0re7whkckh51ik

There is no "main address" anymore - all Jamtis addresses are equivalent to a subaddress.

2.1.1 Recipient IDs

Jamtis introduces a short recipient identifier (RID) that can be calculated for every address. RID consists of 25 alphanumeric characters that are separated by underscores for better readability. The RID for the above address is regne_hwbna_u21gh_b54n0_8x36q. Instead of comparing long addresses, users can compare the much shorter RID. RIDs are also suitable to be communicated via phone calls, text messages or handwriting to confirm a recipient's address. This allows the address itself to be transferred via an insecure channel.

2.2 Light wallet scanning

Jamtis introduces new wallet tiers below view-only wallet. One of the new wallet tiers called "FindReceived" is intended for wallet-scanning and only has the ability to calculate view tags [9]. It cannot generate wallet addresses or decode output amounts.

View tags can be used to eliminate 99.6% of outputs that don't belong to the wallet. If provided with a list of wallet addresses, this tier can also link outputs to those addresses. Possible use cases are:

2.2.1 Wallet component

A wallet can have a "FindReceived" component that stays connected to the network at all times and filters out outputs in the blockchain. The full wallet can thus be synchronized at least 256x faster when it comes online (it only needs to check outputs with a matching view tag).

2.2.2 Third party services

If the "FindReceived" private key is provided to a 3rd party, it can preprocess the blockchain and provide a list of potential outputs. This reduces the amount of data that a light wallet has to download by a factor of at least 256. The third party will not learn which outputs actually belong to the wallet and will not see output amounts.

2.3 Wallet tiers for merchants

Jamtis introduces new wallet tiers that are useful for merchants.

2.3.1 Address generator

This tier is intended for merchant point-of-sale terminals. It can generate addresses on demand, but otherwise has no access to the wallet (i.e. it cannot recognize any payments in the blockchain).

2.3.2 Payment validator

This wallet tier combines the Address generator tier with the ability to also view received payments (including amounts). It is intended for validating paid orders. It cannot see outgoing payments and received change.

2.4 Full view-only wallets

Jamtis supports full view-only wallets that can identify spent outputs (unlike legacy view-only wallets), so they can display the correct wallet balance and list all incoming and outgoing transactions.

2.5 Janus attack mitigation

Janus attack is a targeted attack that aims to determine if two addresses A, B belong to the same wallet. Janus outputs are crafted in such a way that they appear to the recipient as being received to the wallet address B, while secretly using a key from address A. If the recipient confirms the receipt of the payment, the sender learns that they own both addresses A and B.

Jamtis prevents this attack by allowing the recipient to recognize a Janus output.

2.6 Robust output detection

Jamtis addresses and outputs contain an encrypted address tag which enables a more robust output detection mechanism that does not need a lookup table and can reliably detect outputs sent to arbitrary wallet addresses.

3. Notation

3.1 Serialization functions

1. The function BytesToInt256(x) deserializes a 256-bit little-endian integer from a 32-byte input.
2. The function Int256ToBytes(x) serialized a 256-bit integer to a 32-byte little-endian output.

3.2 Hash function

The function Hb(k, x) with parameters b, k, refers to the Blake2b hash function [10] initialized as follows:

• The output length is set to b bytes.
• Hashing is done in sequential mode.
• The Personalization string is set to the ASCII value "Monero", padded with zero bytes.
• If the key k is not null, the hash function is initialized using the key k (maximum 64 bytes).
• The input x is hashed.

The function SecretDerive is defined as:

SecretDerive(k, x) = H32(k, x)

3.3 Elliptic curves

Two elliptic curves are used in this specification:

1. Curve25519 - a Montgomery curve. Points on this curve include a cyclic subgroup 𝔾1.
2. Ed25519 - a twisted Edwards curve. Points on this curve include a cyclic subgroup 𝔾2.

Both curves are birationally equivalent, so the subgroups 𝔾1 and 𝔾2 have the same prime order ℓ = 2252 + 27742317777372353535851937790883648493. The total number of points on each curve is 8ℓ.

3.3.1 Curve25519

Curve25519 is used exclusively for the Diffie-Hellman key exchange [11].

Only a single generator point B is used:

Point	Derivation	Serialized (hex)
B	generator of 𝔾1	0900000000000000000000000000000000000000000000000000000000000000

Private keys for Curve25519 are 32-byte integers denoted by a lowercase letter d. They are generated using the following KeyDerive1(k, x) function:

1. d = H32(k, x)
2. d[31] &= 0x7f (clear the most significant bit)
3. d[0] &= 0xf8 (clear the least significant 3 bits)
4. return d

All Curve25519 private keys are therefore multiples of the cofactor 8, which ensures that all public keys are in the prime-order subgroup. The multiplicative inverse modulo ℓ is calculated as d-1 = 8*(8*d)-1 to preserve the aforementioned property.

Public keys (elements of 𝔾1) are denoted by the capital letter D and are serialized as the x-coordinate of the corresponding Curve25519 point. Scalar multiplication is denoted by a space, e.g. D = d B.

3.3.2 Ed25519

The Edwards curve is used for signatures and more complex cryptographic protocols [12]. The following three generators are used:

Point	Derivation	Serialized (hex)
G	generator of 𝔾2	5866666666666666666666666666666666666666666666666666666666666666
U	Hp("seraphis U")	126582dfc357b10ecb0ce0f12c26359f53c64d4900b7696c2c4b3f7dcab7f730
X	Hp("seraphis X")	4017a126181c34b0774d590523a08346be4f42348eddd50eb7a441b571b2b613

Here Hp refers to an unspecified hash-to-point function.

Private keys for Ed25519 are 32-byte integers denoted by a lowercase letter k. They are generated using the following function:

KeyDerive2(k, x) = H64(k, x) mod ℓ

Public keys (elements of 𝔾2) are denoted by the capital letter K and are serialized as 256-bit integers, with the lower 255 bits being the y-coordinate of the corresponding Ed25519 point and the most significant bit being the parity of the x-coordinate. Scalar multiplication is denoted by a space, e.g. K = k G.

3.4 Block cipher

The function BlockEnc(s, x) refers to the application of the Twofish [13] permutation using the secret key s on the 16-byte input x. The function BlockDec(s, x) refers to the application of the inverse permutation using the key s.

3.5 Base32 encoding

"Base32" in this specification referes to a binary-to-text encoding using the alphabet xmrbase32cdfghijknpqtuwy01456789. This alphabet was selected for the following reasons:

1. The order of the characters has a unique prefix that distinguishes the encoding from other variants of "base32".
2. The alphabet contains all digits 0-9, which allows numeric values to be encoded in a human readable form.
3. Excludes the letters o, l, v and z for the same reasons as the z-base-32 encoding [14].

4. Wallets

4.1 Wallet parameters

Each wallet consists of two main private keys and a timestamp:

Field	Type	Description
km	private key	wallet master key
kvb	private key	view-balance key
birthday	timestamp	date when the wallet was created

The master key km is required to spend money in the wallet and the view-balance key kvb provides full view-only access.

The birthday timestamp is important when restoring a wallet and determines the blockchain height where scanning for owned outputs should begin.

4.2 New wallets

4.2.1 Standard wallets

Standard Jamtis wallets are generated as a 16-word Polyseed mnemonic [7], which contains a secret seed value used to derive the wallet master key and also encodes the date when the wallet was created. The key kvb is derived from the master key.

Field	Derivation
km	BytesToInt256(polyseed_key) mod ℓ
kvb	kvb = KeyDerive1(km, "jamtis_view_balance_key")
birthday	from Polyseed

4.2.2 Multisignature wallets

Multisignature wallets are generated in a setup ceremony, where all the signers collectively generate the wallet master key km and the view-balance key kvb.

Field	Derivation
km	setup ceremony
kvb	setup ceremony
birthday	setup ceremony

4.3 Migration of legacy wallets

Legacy pre-Seraphis wallets define two private keys:

• private spend key ks
• private view-key kv

4.3.1 Standard wallets

Legacy standard wallets can be migrated to the new scheme based on the following table:

Field	Derivation
km	km = ks
kvb	kvb = KeyDerive1(km, "jamtis_view_balance_key")
birthday	entered manually

Legacy wallets cannot be migrated to Polyseed and will keep using the legacy 25-word seed.

4.3.2 Multisignature wallets

Legacy multisignature wallets can be migrated to the new scheme based on the following table:

Field	Derivation
km	km = ks
kvb	kvb = kv
birthday	entered manually

4.4 Additional keys

There are additional keys derived from kvb:

Key	Name	Derivation	Used to
dfr	find-received key	kfr = KeyDerive1(kvb, "jamtis_find_received_key")	scan for received outputs
dua	unlock-amounts key	kid = KeyDerive1(kvb, "jamtis_unlock_amounts_key")	decrypt output amounts
sga	generate-address secret	sga = SecretDerive(kvb, "jamtis_generate_address_secret")	generate addresses
sct	cipher-tag secret	ket = SecretDerive(sga, "jamtis_cipher_tag_secret")	encrypt address tags

The key dfr provides the ability to calculate the sender-receiver shared secret when scanning for received outputs. The key dua can be used to create a secondary shared secret and is used to decrypt output amounts.

The key sga is used to generate public addresses. It has an additional child key sct, which is used to encrypt the address tag.

4.5 Key hierarchy

The following figure shows the overall hierarchy of wallet keys. Note that the relationship between km and kvb only applies to standard (non-multisignature) wallets.

4.6 Wallet access tiers

Tier	Knowledge	Off-chain capabilities	On-chain capabilities
AddrGen	sga	generate public addresses	none
FindReceived	dfr	recognize all public wallet addresses	eliminate 99.6% of non-owned outputs (up to § 5.3.5), link output to an address (except of change and self-spends)
ViewReceived	dfr, dua, sga	all	view all received except of change and self-spends (up to § 5.3.14)
ViewAll	kvb	all	view all
Master	km	all	all

4.6.1 Address generator (AddrGen)

This wallet tier can generate public addresses for the wallet. It doesn't provide any blockchain access.

4.6.2 Output scanning wallet (FindReceived)

Thanks to view tags, this tier can eliminate 99.6% of outputs that don't belong to the wallet. If provided with a list of wallet addresses, it can also link outputs to those addresses (but it cannot generate addresses on its own). This tier should provide a noticeable UX improvement with a limited impact on privacy. Possible use cases are:

1. An always-online wallet component that filters out outputs in the blockchain. A higher-tier wallet can thus be synchronized 256x faster when it comes online.
2. Third party scanning services. The service can preprocess the blockchain and provide a list of potential outputs with pre-calculated spend keys (up to § 5.2.4). This reduces the amount of data that a light wallet has to download by a factor of at least 256.

4.6.3 Payment validator (ViewReceived)

This level combines the tiers AddrGen and FindReceived and provides the wallet with the ability to see all incoming payments to the wallet, but cannot see any outgoing payments and change outputs. It can be used for payment processing or auditing purposes.

4.6.4 View-balance wallet (ViewAll)

This is a full view-only wallet than can see all incoming and outgoing payments (and thus can calculate the correct wallet balance).

4.6.5 Master wallet (Master)

This tier has full control of the wallet.

4.7 Wallet public keys

There are 3 global wallet public keys. These keys are not usually published, but are needed by lower wallet tiers.

Key	Name	Value
Ks	wallet spend key	Ks = kvb X + km U
Dua	unlock-amounts key	Dua = dua B
Dfr	find-received key	Dfr = dfr Dua

5. Addresses

5.1 Address generation

Jamtis wallets can generate up to 2¹²⁸ different addresses. Each address is constructed from a 128-bit index j. The size of the index space allows stateless generation of new addresses without collisions, for example by constructing j as a UUID [15].

Each Jamtis address encodes the tuple (K1j, D2j, D3j, tj). The first three values are public keys, while tj is the "address tag" that contains the encrypted value of j.

5.1.1 Address keys

The three public keys are constructed as:

• K1j = Ks + kuj U + kxj X + kgj G
• D2j = daj Dfr
• D3j = daj Dua

The private keys kuj, kxj, kgj and daj are derived as follows:

Keys	Name	Derivation
kuj	spend key extensions	kuj = KeyDerive2(sga, "jamtis_spendkey_extension_u" || j)
kxj	spend key extensions	kxj = KeyDerive2(sga, "jamtis_spendkey_extension_x" || j)
kgj	spend key extensions	kgj = KeyDerive2(sga, "jamtis_spendkey_extension_g" || j)
daj	address keys	daj = KeyDerive1(sga, "jamtis_address_privkey" || j)

5.1.2 Address tag

Each address additionally includes an 18-byte tag tj = (j', hj'), which consists of the encrypted value of j:

• j' = BlockEnc(sct, j)

and a 2-byte "tag hint", which can be used to quickly recognize owned addresses:

• hj' = H2(sct, "jamtis_address_tag_hint" || j')

5.2 Sending to an address

TODO

5.3 Receiving an output

TODO

5.4 Change and self-spends

TODO

5.5 Transaction size

Jamtis has a small impact on transaction size.

5.5.1 Transactions with 2 outputs

The size of 2-output transactions is increased by 28 bytes. The encrypted payment ID is removed, but the transaction needs two encrypted address tags t~ (one for the recipient and one for the change). Both outputs can use the same value of De.

5.5.2 Transactions with 3 or more outputs

Since there are no "main" addresses anymore, the TX_EXTRA_TAG_PUBKEY field can be removed from transactions with 3 or more outputs.

Instead, all transactions with 3 or more outputs will require one 50-byte tuple (De, t~) per output.

6. Address encoding

6.1 Address structure

An address has the following overall structure:

Field	Size (bits)	Description
Header	30*	human-readable address header (§ 6.2)
K1	256	address key 1
D2	255	address key 2
D3	255	address key 3
t	144	address tag
Checksum	40*	(§ 6.3)

* The header and the checksum are already in base32 format

6.2 Address header

The address starts with a human-readable header, which has the following format consisting of 6 alphanumeric characters:

"xmra" <version char> <network type char>

Unlike the rest of the address, the header is never encoded and is the same for both the binary and textual representations. The string is not null terminated.

The software decoding an address shall abort if the first 4 bytes are not 0x78 0x6d 0x72 0x61 ("xmra").

The "xmra" prefix serves as a disambiguation from legacy addresses that start with "4" or "8". Additionally, base58 strings that start with the character x are invalid due to overflow [16], so legacy Monero software can never accidentally decode a Jamtis address.

6.2.1 Version character

The version character is "1". The software decoding an address shall abort if a different character is encountered.

6.2.2 Network type

network char	network type
"t"	testnet
"s"	stagenet
"m"	mainnet

The software decoding an address shall abort if an invalid network character is encountered.

6.3 Checksum

The purpose of the checksum is to detect accidental corruption of the address. The checksum consists of 8 characters and is calculated with a cyclic code over GF(32) using the polynomial:

x8 + 3x7 + 11x6 + 18x5 + 5x4 + 25x3 + 21x2 + 12x + 1

The checksum can detect all errors affecting 5 or fewer characters. Arbitrary corruption of the address has a chance of less than 1 in 10¹² of not being detected. The reference code how to calculate the checksum is in Appendix A.

6.4 Binary-to-text encoding

An address can be encoded into a string as follows:

address_string = header + base32(data) + checksum

where header is the 6-character human-readable header string (already in base32), data refers to the address tuple (K1, D2, D3, t), encoded in 910 bits, and the checksum is the 8-character checksum (already in base32). The total length of the encoded address 196 characters (=6+182+8).

6.4.1 QR Codes

While the canonical form of an address is lower case, when encoding an address into a QR code, the address should be converted to upper case to take advantage of the more efficient alphanumeric encoding mode.

6.5 Recipient authentication

TODO

7. Test vectors

TODO

References

1. https://github.com/UkoeHB/Seraphis
2. https://github.com/monero-project/research-lab/blob/master/whitepaper/whitepaper.pdf
3. monero-project/meta#299 (comment)
4. https://www.getmonero.org/resources/user-guides/view_only.html
5. https://web.getmonero.org/2019/10/18/subaddress-janus.html
6. monero-project/monero#8138
7. https://github.com/tevador/polyseed
8. monero-project/monero#7889
9. monero-project/research-lab#73
10. https://eprint.iacr.org/2013/322.pdf
11. https://cr.yp.to/ecdh/curve25519-20060209.pdf
12. https://ed25519.cr.yp.to/ed25519-20110926.pdf
13. https://www.schneier.com/wp-content/uploads/2016/02/paper-twofish-paper.pdf
14. http://philzimmermann.com/docs/human-oriented-base-32-encoding.txt
15. https://en.wikipedia.org/wiki/Universally_unique_identifier
16. https://github.com/monero-project/monero/blob/319b831e65437f1c8e5ff4b4cb9be03f091f6fc6/src/common/base58.cpp#L157

Appendix A: Checksum

# Jamtis address checksum algorithm

# cyclic code based on the generator 3BI5PLC1
# can detect 5 errors up to the length of 994 characters
GEN=[0x1ae45cd581, 0x359aad8f02, 0x61754f9b24, 0xc2ba1bb368, 0xcd2623e3f0]

M = 0xffffffffff

def jamtis_polymod(data):
    c = 1
    for v in data:
        b = (c >> 35)
        c = ((c & 0x07ffffffff) << 5) ^ v
        for i in range(5):
            c ^= GEN[i] if ((b >> i) & 1) else 0
    return c

def jamtis_verify_checksum(data):
    return jamtis_polymod(data) == M

def jamtis_create_checksum(data):
    polymod = jamtis_polymod(data + [0,0,0,0,0,0,0,0]) ^ M
    return [(polymod >> 5 * (7 - i)) & 31 for i in range(8)]

# test/example

CHARSET = "xmrbase32cdfghijknpqtuwy01456789"

addr_test = (
    "xmra1mj0b1977bw3ympyh2yxd7hjymrw8crc9kin0dkm8d3"
    "wdu8jdhf3fkdpmgxfkbywbb9mdwkhkya4jtfn0d5h7s49bf"
    "yji1936w19tyf3906ypj09n64runqjrxwp6k2s3phxwm6wr"
    "b5c0b6c1ntrg2muge0cwdgnnr7u7bgknya9arksrj0re7wh")

addr_data = [CHARSET.find(x) for x in addr_test]
addr_enc = addr_data + jamtis_create_checksum(addr_data)
addr = "".join([CHARSET[x] for x in addr_enc])

print(addr)
print("len =", len(addr))
print("valid =", jamtis_verify_checksum(addr_enc))

I'd say my commentary is most relevant toward understanding why a 2 byte view tag would offer basically no privacy advantage at today's tx volume due to its statistical surface, even with Tor and with connecting to 3rd party daemons to submit txs: https://gist.github.com/tevador/50160d160d24cfc6c52ae02eb3d17024?permalink_comment_id=4668705#gistcomment-4668705

I generally agree the idea to add an additional pub key does provide a stronger level of privacy though, which is the primary reason why I'm a proponent of the idea. I agree that when compared to the Jamtis light wallet tier without the additional pub key, this proposal downgrades the statistical attack surface (and the surface could become virtually non-existent with extremely high tx volume).

Still, it's worth keeping in mind that the statistical analysis surface the light wallet tier brings is more significant than Monero's current full wallets.

A while back someone proposed that full wallets only download data necessary to determine which outputs belong to a user, and then once identified, request the transactions of those outputs along with "chaff" (decoy) transactions, in order to minimize data needed to download when scanning. There was pushback on this idea because of the widened statistical surface enabling a node to potentially pinpoint a user's txs: https://www.reddit.com/r/Monero/comments/5wc2th/a_proposal_to_speed_up_wallet_sync_around_5x/de940mj/

It's worth keeping in mind the light wallet tier introduces a similar surface.

It is always possible to construct a transaction and broadcast is to the network directly, and even use a Tor tx proxy, bypassing the light wallet server and obfuscating the user's IP address.

This is what I was getting at in explaining how the optimal privacy profile of a light wallet client would communicate with a 3rd party daemon ideally not colluding with the server. Even with Tor though, if a 3rd party daemon combines logs with a light wallet server, the logs would show e.g. Bob just opened his light wallet client, then 1 person just requested paths in a merkle tree (1 path included one of Bob's view tag matched enotes)/fees/submitted a tx to the network, and Bob has a view tag match in that tx.

Unless there exists significant cover volume where tons of people are trying to construct txs at a specific point in time, then it's fairly trivial to guess Bob's tx, his spent enote, and his change enote.

However, yes, it's still a "guess" which I agree is stronger privacy than the current Jamtis light wallet tier's "100% certainty in some cases" and would improve with higher tx volume.

@UkoeHB I've been thinking about the slowness of the self-send tau checks under the new addressing scheme, and yes you are right, they are slower since there are no address tag hints. However, since you can now do 3-bytes of view tag checks BEFORE doing the self-send tau checks vs 1-byte of view tags checks, under the the new scheme, the process of self-send tau checks will be done ~65536 times less (more often if one's self-sends is a larger portion of total on-chain enote volume). Hopefully, this amortizes out to be slightly faster overall for most users.

Too many view tag bytes hurts privacy AFAIUI, @j-berman to properly state what I'm thinking of so we're all on the same page.

To be clear, I say 3 bytes of view tags, but it is split into two view tags, a 1-byte and a 2-byte tag, which are each computed from two independent DH secrets. You can give access to compute just one view tag (presumably the 1-byte view tag) to a light wallet server. However, if you are the client with the whole view-balance key, you can compute both view tags and check against both before trying self-send tau checks.

@j-berman Was making the point that without huge increases to transaction volume and the assumption that the third-party daemon and light wallet server are not colluding, the privacy of giving a light wallet server the ability to compute 2-byte view tags is very bad.

Ah, sorry. Thanks for clarifying.

For the base32 encoding, instead of using a custom alphabet, why not use an existing standard that meets our requirements like Crockford base32? Spec here: https://www.crockford.com/base32.html. There's an existing C++ implementation here: https://github.com/tplgy/cppcodec/blob/master/cppcodec/base32_crockford.hpp.

After considering the pros and cons, the biggest concern for me is that combining the view tags gives you a scan tier that can almost definitively identify all owned enotes (normal and self-send). The combined tier would be an ultra-efficient scan tier with high visibility into user transaction graphs. I expect that in the long run, someone will implement that tier to the detriment of user privacy.

So the trade-off is: A) improve privacy for the recommended remote scanning tier, B) expose an unrecommended remote scanning tier that is materially superior to the recommended tier and greatly weakens user privacy.

Tbf, this was already possible by combining Find-Received + Cipher-Tag. You could give a third-party s_ct and k_fr, and then they could decrypt and decipher address tags, whittling down the probability that a scanned enote is a false negative to 1:16777216.

Tbf, this was already possible by combining Find-Received + Cipher-Tag.

Not quite. With k_fr and s_ct you can only identify normal enotes. You still need to send all view tag matches to the client so they can scan for self-sends, which means a remote scanner with k_fr and s_ct is not materially more efficient than one with just k_fr. However, with the dual view tags this changes because now you can rule out many more self-send candidates using the second view tag, greatly reducing the amount of data that needs to be sent to the client.

We can fix this issue by keeping the prior jamtis design (with the address tag hint). The only change is to add the second key derivation to s^sr_1 for normal scans only. This way a remote scanner with k_fr and k_rs (receive-secret key for the second key derivation) is equivalent to the current remote scanner, while a remote scanner with just k_fr has the benefits of your original proposal. This is actually much better overall, because now it is feasible for someone to offload both k_fr and k_rs to a remote scanner in order to offload computation of the second key derivation to that scanner (in your proposal it would not be feasible due to the self-send identification issue), which may be a beneficial trade-off if tx volume becomes very large (e.g. if tx volume increases 256x, then your proposal would leave light wallet clients with the same scanning perf normal clients have today).

On the other hand, I do wonder if all these scanning optimizations and tweaks would/will make sense in the long run. If there comes a time when remote scanning only makes sense by offloading both derivations, then we are back to the original jamtis proposal at the cost of a uselessly larger jamtis address and bloated spec.

We can fix this issue by keeping the prior jamtis design (with the address tag hint). The only change is to add the second key derivation to s^sr_1 for normal scans only. This way a remote scanner with k_fr and k_rs (receive-secret key for the second key derivation) is equivalent to the current remote scanner, while a remote scanner with just k_fr has the benefits of your original proposal.

I like this solution. The cost would be slightly longer addresses (247 vs 244 characters), but there would be much stronger protection of self-sends from the remote scanning services. See this comment to understand why hiding self-sends is vital to protect the privacy properties of the whole network.

On the other hand, I do wonder if all these scanning optimizations and tweaks would/will make sense in the long run. If there comes a time when remote scanning only makes sense by offloading both derivations, then we are back to the original jamtis proposal at the cost of a uselessly larger jamtis address and bloated spec.

If tx volume increases 256x, we'd be at ~40 MB blocks with a blockchain growth of >10 TB/year. If the network can handle that, I think it's safe to assume that CPU performance and network bandwidth have also increased so that light clients can easily keep up using 1/256 view tags.

Not quite. With k_fr and s_ct you can only identify normal enotes.

Fair enough

You still need to send all view tag matches to the client so they can scan for self-sends, which means a remote scanner with k_fr and s_ct is not materially more efficient than one with just k_fr. However, with the dual view tags this changes because now you can rule out many more self-send candidates using the second view tag, greatly reducing the amount of data that needs to be sent to the client.

If the user is this hell-bent on revealing their transaction graph for the sake of efficiency, why doesn't the user also send his self-send TXIDs to the light wallet server? IIRC, current light wallet servers already know which users are tied to which outgoing transactions by virtue of helping them construct that transaction. Heck, all of these changes still don't keep the user from sending their view balance key, which would constitute the most efficient light wallet server. If they wanted to dance around the fact that this isn't private, they could even add some ad-hoc tech to randomly request other data so they can claim its private, or an infinite amount of other things that degrade privacy but make it more efficient. To me, this argument falls under the same category of criticism at the announcement of view-balance keys, because someone else could force them to reveal their view balance keys. It isn't cryptographically possible to prevent people from revealing secret keys willy-nilly, so I don't know how productive it is to talk about potential future scenarios in which the tier system is willingly abused. What we should design are the tiers that we want to see, because users will use them and gain certain trade-offs, while minimizing risk to the planned tiers.

but there would be much stronger protection of self-sends from the remote scanning services

Same point here: It isn't stronger if we don't assume the user won't abuse the wallet tiers, which is what brought this discussion on.

See this comment to understand why hiding self-sends is vital to protect the privacy properties of the whole network.

I agree that hiding self-sends is important, but unless you have a protocol that forces users' self-send privacy, I think that point is moot here.

After considering the pros and cons, the biggest concern for me is that combining the view tags gives you a scan tier that can almost definitively identify all owned enotes (normal and self-send).

One thing about prevents this using actual incentives is the existence of the the 2-byte view tag "sparse" tier in the original proposal. 2-bytes of view tag, for people like us, is complete overkill in efficiency/privacy balance as of current tx volume. But potentially in the future, if there are users who don't want to even scan 1/256 of the enotes on the chain, because they value convenience over privacy 10-fold, they can scan 256x times less than that: 1/65536 (about ~1 enote every day on mainnet today). I think it's not unreasonable that tx volume could 256x sometime in the distant future, which would mean that an enote hit every 10 minutes or so for people using the 2-byte view tag tier. (@j-berman did a great analysis of timing attacks against 2-byte view tags against current tx volume in this thread)

But here's the big thing: this tier doesn't have the deterministic drawbacks of a third-party wallet knowing your nominal address tags: identifying incoming normal enotes to known addresses and incoming normal enotes sent to addresses more than once with ~100% certainty. The privacy of the 2-byte view tag tier scales up with volume, and it is much more detrimental to privacy than the proposed "dense" view tag tier, but if we're planning for very desperate users like we're doing here, we need a bigger jump for light wallet scanning than replacing DH ops with Twofish ops; we need to have the option to cut bandwidth without deterministic attacks.

On the other hand, I do wonder if all these scanning optimizations and tweaks would/will make sense in the long run. If there comes a time when remote scanning only makes sense by offloading both derivations, then we are back to the original jamtis proposal at the cost of a uselessly larger jamtis address and bloated spec.

Here again is the beauty of a 2-byte view tag tier being available. Since we're planning for huge tx volume which displaces users who simply can't keep up with chain data, a 2-byte view tag tier will actually cut bandwidth hugely w/o deterministic downsides.

I think it's safe to assume that CPU performance and network bandwidth have also increased so that light clients can easily keep up using 1/256 view tags

If it's safe to assume this, then why have the modifications in the first place? If it's so easy to keep up with bandwidth and computation, why would users feel the need to jump ship to worse privacy trade-offs en masse?

why doesn't the user also send his self-send TXIDs to the light wallet server

Rational users have exactly zero incentive to do this.

Here again is the beauty of a 2-byte view tag tier being available. Since we're planning for huge tx volume which displaces users who simply can't keep up with chain data, a 2-byte view tag tier will actually cut bandwidth hugely w/o deterministic downsides.

Do we really need two view tags for this from the start? Why can't the bitsize of the "standard" view tag scale with volume to keep the false positive rate roughly constant? E.g. when tx volume doubles, one bit is added to the view tag deterministically. That would react much more smoothly and provide plausible deniability under all conditions.

Why can't the bitsize of the "standard" view tag scale with volume to keep the false positive rate roughly constant? E.g. when tx volume doubles, one bit is added to the view tag deterministically. That would react much more smoothly and provide plausible deniability under all conditions.

This can be abused by a malicious remote scanning service to reduce the anonymity of users by spamming the chain.

Malicious actors can reduce the anonymity of users by spamming the chain right now.

Yes but a dynamic view tag would make spam more damaging.

The options are:

1. Fixed-size view tag: Either good plausible deniability now and possibly inadequate filtering later, or vice versa (or somewhere in between).
2. Multiple view tags of various sizes: coarse tuning of the false positive rate; susceptible to spam attacks (an attacker can spam for a while to make users subscribe with the larger tag); retroactive privacy loss when switching to a larger tag.
3. Dynamic-size view tag: fine tuning of the false positive rate, no retroactive privacy loss, susceptible to spam attacks.

Choose your poison.

The fourth option, which is what @UkoeHB was proposing, is a fixed-size view tag but optionally enable third parties to compute nominal address tags, which reduces light-side single-core compute time by about 100x, but increases the bandwidth by ~10%.

optionally enable third parties to compute nominal address tags

This is orthogonal, can be added to any of the above 3 options. The important point is that it does not reduce the bandwidth requirements for light clients.

I don't know if this idea has ever been floated before, and I'm making this up right now, but we could do dynamic view tags that 1) aren't susceptible to spam attacks, 2) scale as the receiver wishes and 3) all look uniform on-chain while keeping transaction size the same. They would have an absolute maximum size set by consensus (say 2-bytes, or 3-bytes if we're pushing it, but 2-bytes is probably fine for a maximum). All tags on-chain will show up as this constant length. Let's call this number of bits b_max. The actual length of view tag/the amount of filtering that a receiver desires is encoded in the address. Let's call this value b_addr. We shouldn't give users too many options, else they will partition themselves too finely and addresses could be attempted to be correlated. Let's say that we give the users 8 (could be any number and 4 might be better) choices, which means the size of integer b_addr is fixed at 3 bits (which we could actually fit into an address in my proposal without expanding the address size since there's 4 unused bits). Let's say that our 8 choices for b_addr (the utilized bit length of the view-assist tag) are 1, 2, 4, 6, 8, 10, 12, or 16 bits wide. The higher b_addr is, the more efficient scanning is, but the smaller the anonymity pool is. Full wallets would likely set this value as high as it will go (since they lose no privacy either way if they are giving up that private key). Light wallets would select a good value for them, then send k_va (view-assist) and b_addr to their light wallet server.

Senders, when sending to an address, will extract b_addr from the address and encode b_addr number of bits into the view-assist tag, and whatever bits are left in the view tag space (b_max - b_addr), they will fill with random noise (this part is important to not miss otherwise we might accidentally filter using more bits than intended).

Light wallet servers, who know b_addr for each user, when doing DH exchanges against k_va, will match b_addr bits and send those records to the light wallet client, who scans them as usual.

Cons: 1) Partitioning on receive addresses can happen. 2) Malicious senders can use more bits than requested (b_addr) to signal probabilistically to someone's light wallet server that an incoming normal enote belongs to said receiver. 3) If a receiver creates a recieve address with b_addr1, then gives that address to a sender, then wants to increase b_addr1 to b_addr2>b_addr1, the receiver might not properly scan a transaction sent with the old b_addr1, and will need the sender to tell the receiver the transaction ID. Not too worried about point 2 since its already possible to construct a transaction then blab about it. Point 1 is a little trickier.

Pros: 1) Many options for users so they are incentivized to not completely bomb their privacy even with incredibly high transaction volume and bad connectivity, 2) on-chain uniformity, 3) view tags not susceptible to spam attacks 4) no retroactive loss of privacy when increasing b_addr (moving to less private, more efficient tier) 5) There are options to do less than 1:256 view filter, e.g. 1:64 filtering.

What do you think?

In the context of a Jamtis protocol where we do 2 DH operations for normal enotes anyways (to guard the sender-receiver secret from light wallet servers), all txs could also still include the independent fixed-size view tag for the second key (like the "sparse view tag" in my original proposal). Full wallets could use this fixed-size view tag as they first tag they scan against, allowing them to generate random values of b_addr for their addresses to help mitigate partitioning, while not affecting their scan time by more than fractions of a percent.

Interesting idea, but:

1. Users of remote scanning services might be coerced or tricked into using the longest possible tag, getting zero privacy, while costing the malicious service nothing.
2. Any address with fewer than the maximum number of bits would immediately leak the fact that the user is using a remote scanner.
3. Horrible UX when changing the tag size. Payments sent to old addresses would not be recognized and asking the sender for the TXID is not always possible (e.g. donations).

Compare that with a dynamic tag size calculated from the running average tx volume over the last 100 000 blocks so that the mean false positive rate is about 256 tag matches per day:

1. Malicious services would have to spam constantly at least 50% of the transaction volume to add 1 bit to the tag size (reducing the effective false positive rate to 128 matches per day). This attack is not free, the attacker is paying transaction fees.
2. Neither addresses nor transactions leak anything.
3. No UX problems because there is always agreement about the tag size that was used in a transaction.

Full wallets could use this fixed-size view tag as they first tag they scan against, allowing them to generate random values of b_addr for their addresses to help mitigate partitioning, while not affecting their scan time by more than fractions of a percent.

You have to look at it from a game-theoretic perspective. If users can make a choice that improves their experience regardless of what other users do, you have to assume they will make that choice (see prisoner's dilemma). Full wallet users will use the full tag size if they can speed up their scan time by a fraction of a percent.

Yeah the downsides are kinda weird and hard to reason about/plan OPSEC for. If there was a way to allow someone to encode a certain level of entropy to be received by someone else without the sender knowing what the level of entropy is, I think that'd be the way to go, but I don't know if that's possible.

I'm much less sure than before, but I still think that a mix of a 1-byte and a 2-byte fixed-size view tag is the best option (assuming we're doing 2 DH options to get q). I think we should put a ton of effort into plan A, making sure the scanning compute process is as optimized as possible, and uses as much processors as available for any given machine. The performance tests show that even doing 1 DH op (instead of 1 Twofish op) for every received record on the light wallet client-side keeps up with modern, middle-of-the-road bandwidth speed, even using just a single core.

The fact that the view tags options are so coarse might hopefully incentivize us developers in the future to push hard for plan A for light wallet users so that they don't switch to option B, the 2-byte view tags, but if they do, at least they won't have deterministic downsides and will more-or-less know what they're getting into: 256x smaller anonymity set.

I don't think we should allow users to select the view tag size. There should be only one view tag and I'm more in favor of the dynamic size as it's a more future-proof solution and I'm not convinced that spam attacks are a real problem compared to the alternatives.

I'm proposing the following:

Jamtis with dynamic view tags

Pros

• Third-parties who compute view tags on behalf of users can no longer strongly identify incoming normal enotes to known public addresses. (same as the proposal by @jeffro256)
• Third-parties who compute view tags on behalf of users can no longer strongly identify incoming normal enotes sent to a public address that is used more than once. (same as the proposal by @jeffro256)
• Third-parties can now compute view tags and generate public addresses on behalf of users without the ability to learn any additonal balance recovery information. (same as the proposal by @jeffro256)
• Light wallets have a fixed bandwidth (about 200KB/day) and CPU (about 100 ms/day) cost regardless of the transaction volume. These costs are so low that no third party provider should be able to successfully argue for users to hand over higher tier private keys.
• Users cannot shoot themselves in the foot by selecting a view tag size that doesn't have enough false-positive matches.

Cons

• Public address length is increased from 196 to 244 characters. (same as the proposal by @jeffro256)
• Third-parties who compute view tags on behalf of users can spam the network to reduce the effective number of false-positive matches of their users.
• Additional ~40 ms of CPU time per day for users who scan the blockchain locally, but this is negligible.
• Additional complexity in the specs

Changes

Private keys and wallet tiers

The number of private keys stays the same, but some keys have a different function and have been renamed:

• d_ua "unlock-amounts" -> d_vr "view-received"
• d_fr "find-received" -> "filter-received"

k_m (master key)
 |
 |
 |
 +- k_vb (view-balance key)
     |
     |
     |
     +- d_vr (view-received key)
         |
         |
         |
         +- d_fr (filter-received key)
         |
         |
         |
         +- s_ga (generate-address secret)
             |
             |
             |
             +- s_ct (cipher-tag secret)

This cleanly maps to the supported wallet tiers:

Tier	Knowledge	Off-chain capabilities	On-chain capabilities
Master	k_m	all	all
ViewBalance	k_vb	all	view all
ViewReceived	d_vr	all	view all received except of change and self-spends
FilterReceived	d_fr	recognize all public wallet addresses	calculate view tags
GenAddr	s_ga	generate public addresses	none

GenAddr + FilterReceived can be safely combined. The key hierarchy ensures that no additional tiers can be constructed.

Addresses

Addresses consist of 4 public keys:

1. K^j_1 = K_s + k^j_u U + k^j_x X + k^j_g G (unchanged)
2. D^j_2 = (1 / d^j_a) * d_fr * B
3. D^j_3 = (1 / d^j_a) * d_vr * B
4. D^j_4 = (1 / d^j_a) * B

B is the Curve25519 base point. Note the inverted usage of d^j_a, which simplifies enote recovery.

There is no tag hint, so only j' = BlockEnc(s_ct, j) is part of the address. The total address length in base32 is 244 characters including the prefix and checksum.

Key exchange

The sender generates an ephemeral private key d_e and calculates D_e = d_e * D^j_4.

Shared secrets

There are 3 DH shared secrets:

1. DH_1 = d_e * D^j_2 = d_fr * D_e
2. DH_2 = d_e * D^j_3 = d_vr * D_e
3. DH_3 = d_e * B = d^j_a * D_e

• DH_1 is used to calculate the view tag.
• DH_2 is used to derive the first high-level shared secret: s^sr_1 = H(DH_2 || D_e || input_context)
• DH_3 is used to derive the second high-level shared secret: s^sr_2 = H(DH_3)

Self-send enotes use a different construction for the high-level secrets (unchanged).

View tags

The view tag is calculated by hashing DH_1 together with K_o (both for normal and self-send enotes).

View tag filter target

The view tag size is dynamic and is automatically adjusted based on the transaction volume so that the false positive rate (the number of view tag matches) is 480 enotes/day. Because the view tag filter rate must be a power of 2, this will actually result in a range from 480 to 960 enotes per day depending on the tx volume. If we "average the averages" over all possible values of tx volume, this will give a mean of 720 enote matches per day, or roughly 1 match per block, which is what was suggested by @jeffro256. I think this is close to the upper limit of what is acceptable for light wallet clients (~200 KB/day) and should provide a good number of false positives even if there was a short term drop in tx volume.

The fomula to calculate the view tag size in bits is:

tag_size = trunc(log2(3 * num_outputs_100k / 200000))

where num_outputs_100k is the total number of outputs in the last 100 000 blocks. The trunc(log2(x)) function can be easily calculated using only integer operations (it's basically the position of the most significant bit).

As an example, the value of num_outputs_100k is currently about 7.9 million, which results in a view tag size of 6 bits when plugged into the formula. With around 56000 daily outputs, there will be about 880 matches per day. If the long-term daily volume increases to about 62000 ouputs, the view tag size will be increased to 7 bits and the number of matches will drop to 480 per day.

View tag size encoding

The view tag size must be encoded explicitly to avoid UX issues with missed transactions at times when the view tag size changes. This can be done with a 1-byte field per transaction (all outputs will use the same tag size).

I'm proposing a range of valid values for the tag size between 1 and 16 bits.

A 1-bit view tag requires num_outputs_100k > 133333. Since there are always at least 100k coinbase outputs, the 1-bit view tag would be "too large" only if there were fewer than 120 transactions per day, which hasn't happened on mainnet except for a few weeks shortly after launch in 2014.

A 17-bit view tag that would overflow the supported range would require num_outputs_100k > 8738133333, an increase of more than 1000x over the current tx volume. If this somehow happened, the number of false positives would exceed 960 per day, which would only have performance implications for light wallets, but would not cause any privacy problems.

So the proposed range of 1-16 bits is sufficient.

Complementary view tag

Regardless of the tag_size, the view tag is always encoded in 2 bytes as a 16-bit integer per enote. The remaining bits are filled with a "complementary" view tag calculated from s^sr_1, which needs a different private key.

For example, with tag_size = 6, the 16 bits would be CCCCCCCCCCTTTTTT, where T is a view tag bit and C is a complementary view tag bit.

Third-party scanning

The intended use is to provide d_fr to a third party, who can then calculate the "T" bits of the view tag and filter out non-matching enotes. There will always be a sufficient number of false positives so that the third party cannot learn with certainty which enotes are owned by the user. The light wallet can then calculate the "C" bits and further filter out enotes. On average, the light wallet will need to recompute K_o for 1 enote out of 65536.

Users might be tempted to provide the view-received key d_vr to the third party to speed up scanning. However, this does not save any bandwidth in practice because the server can't calculate s^sr_1 for self-send enotes. It only saves a minuscule amount of CPU time (~100 ms/day at best) in exchange for a loss of privacy for all incoming payments (including amounts).

Similarly, users might be tempted to provide the view-balance key k_vb to the third party to speed up scanning. This would save about 200 KB/day in exchange for a complete loss of privacy.

These unintended use cases are sufficiently unfavorable to restrict third party scanners to the FilterReceived wallet tier.

Scanning speed

The following table shows the cryptographic operations needed to recognize owned enotes for different types of wallets (assuming the wallet does not receive more than a few payments per day). I'm ignoring symmetric crypto operations for simplicity (they are negligible).

Wallet type	For each enote	For ~720 enotes/day	For 1/65536 enotes
Full wallet (ViewBalance)	1x DH	1x DH	3x recompute K_o
Full wallet (ViewReceived)	1x DH	1x DH	1x recompute K_o
Light wallet (ViewBalance)	-	1x DH	3x recompute K_o
Light wallet (ViewReceived)	-	1x DH	1x recompute K_o

Here "Light wallet" refers to a wallet that downloads data from a FilterReceived wallet service. The ViewBalance tiers need to recompute each K_o three time to detect self-send enotes.

To get an idea about the required bandwidth and CPU time, I'm estimating 256 bytes of data per view tag match, 50 μs of CPU time for DH and 50 μs of CPU time to recompute K_o (recomputing K_o needs 3 fixed-base scmults, which are about 3-4x faster than variable-base scmults for DH).

Wallet type	bandwidth/day	CPU/day
Full wallet (ViewBalance)	depends on tx volume	depends on tx volume
Full wallet (ViewReceived)	depends on tx volume	depends on tx volume
Light wallet (ViewBalance)	180 KB	<144 ms
Light wallet (ViewReceived)	180 KB	<72 ms

So even when opening a light wallet after 1 month, sync times should be on the order of a few seconds regardless of future transaction volumes.

Practical issues

How does the sending wallet figure out what view tag size to use?

Current Monero wallets already have that information. Wallets call the RPC function get_output_distribution when constructing a tx to pick decoys. This distribution contains enough information (the number of outputs in each block) to calculate the number of bits the view tag should have.

With full-chain membership proofs, wallets will still have to make a RPC call to get the current fee estimate, so that could also be used to get the current view tag size. A rough estimate could be made from the knowledge of the number of leaf nodes in the output tree.

What if a malicious sender purposely selects a shorter view tag (to cause more computation for all wallets) or a longer view tag (to reduce the recipient's light wallet privacy)?

There could be a relay rule that rejects transactions that use a view tag size other than the current or the previous one (i.e. 1 bit shorter if tx volume is growing or 1 bit longer if tx volume is dropping). It could also be enforced by consensus, but that seems like an overkill.

Shouldn't the calculation be DH_3 = d_e * G = 1/(d^j_a * b) * D_e?

I personally think we should set the target to 1 enote false positive per blocktime (2 minutes) to confound timing attacks. If there's a view tag hit almost every single time that a block is submitted, I imagine this would mitigate a lot of timing attacks for low wallet usage. That's about 2.8x what you're proposing, but that's still very doable today, and since its a constant throughput, compute and bandwidth will quickly catch up.

I'm liking this proposal, and just have one more modification: a three byte fixed-size view tag for DH_2. This 1) makes full wallet scanning faster and not dependent on sender-submitted fields (the view tag width), 2) also speeds up light-wallet client side scanning as a byproduct, and 3) most importantly, completely nukes the incentive for a light wallet user to hand over their "filter-received key" else they will have no normal enote privacy. Con: enotes are 3 bytes bigger.

Also shouldn't it be DH_3 = d_e * G = 1/(d^j_a * b) * D_e?

I'm using B to denote the Curve25519 base point. B = ed25519_pk_to_curve25519(G).

Second, I personally think we should set the target to 1 enote false positive per blocktime (2 minutes) to confound timing attacks. If there's a view tag hit almost every single time that a block is submitted, I imagine this would mitigate a lot of timing attacks for low wallet usage. That's about 2.8x what you're proposing, but that's still very doable today, and since its a constant throughput, compute and bandwidth will quickly catch up.

Yes, the target could be higher than 256. I chose 256/day as it matches an 8-bit view tag with the current tx volume. The lower bound for the target is 144/day to hide when an output is spent soon after the 10 block lock time. The upper bound is only limited by the bandwidth cost for light wallets.

a three byte fixed-size view tag for DH_2. This 1) makes full wallet scanning faster and not dependent on sender-submitted fields (the view tag width), 2) also speeds up light-wallet client side scanning as a byproduct.

I'm not really sure if this is worth the ~25-70 ms of CPU time per day it would save.

3. most importantly, completely nukes the incentive for a light wallet user to hand over their "filter-received key" else they will have no normal enote privacy

Did you mean "view-received key"?

I'm not really sure if this is worth the ~25-70 ms of CPU time per day it would save.

Here "Light wallet" refers to a wallet that downloads data from a FilterReceived wallet service. The ViewAll tiers need to recompute each K_o twice to detect self-send enotes.

You actually need to try 1 + <number of self-send types> times. For the current Jamtis code in seraphis_lib with PLAIN, DUMMY, CHANGE, & SELFSPEND enote types, this is 4 total K_o re-computations per filter-received enote hit, which might end of being not insignificant for total scan-time. However, since this cost doesn't scale up over time with dynamic view tags, I guess that I'm more okay with it as long as there's no address tag hint to tempt people to disclose the view-received private key.

I'm using B to denote the Curve25519 base point. B = ed25519_pk_to_curve25519(G)

Ah okay I thought B was D^j_ua (AKA DH Base).

Did you mean "view-received key"?

Yes I did, sorry.

Note the inverted usage of d^j_a, which simplifies enote recovery.

I do really like this feature, and AFAIK, inverting the address private key in the address, not in balance recovery, is orthogonal to all of the previous discussed changes, which is nice.

D^j_4 = (1 / d^j_a) * B

I like the simplicity of this, but if we're missing some sort of d_ua unlock-amounts factor, then we can't have tier(s) which identify transactions that we're involved in (by recomputing K_o) without knowing the amounts, which makes cold/hot/hardware wallet separation more private, but just as convenient. And since we're using the x25519 curve for this portion of the protocol, we can cache the value of d_ua * B and then multiply by d^j_a to get s^sr_2, and it's all just as performant.

To expand on the last point, we could have all secret keys (besides cipher-tag) below the view-balance secret in the derivation tree: view-received, view-sent (new key explained below), unlock-amounts, generate-address (moved out from under view-received), and filter-involved (basically the same as filter-received but the name needs an update since we use it also for outgoing). Then we can mix and match the unlock-amounts key with/without view-received and view-sent keys to create different tiers while keeping the number of operations in balance recovery the same. The new derivation tree would look like:

Private Keys

k_m (private master key)
 |
 |
 |
 +- k_vb (private view-balance key)
     |
     |
     |
     +- d_fi (private filter-involved key)
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     +- d_ua (private unlock-amounts key)
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     +- s_vs (secret view-sent key)
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     +- d_vr (private view-received key)
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     +- s_ga (secret generate-address key)
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             +- s_ct (secret cipher-tag key)

Addresses

Addresses consist of 4 public keys (just added in a factor of d_ua):

1. K^j_1 = K_s + k^j_u U + k^j_x X + k^j_g G (unchanged)
2. D^j_2 = 1 / (d^j_a * d_ua) * d_fi * B (filter-received -> filter-involved)
3. D^j_3 = 1 / (d^j_a * d_ua) * d_vr * B
4. D^j_4 = 1 / (d^j_a * d_ua) * B

Shared Secrets

There are 3 DH shared secrets:

1. DH_1 = d_e * D^j_2 = d_fi * D_e (filter-received -> filter-involved)
2. DH_2 = d_e * D^j_3 = d_vr * D_e (unchanged from @tevador's last post)
3. DH_3 = d_e * B = d^j_a * d_ua * D_e (added in factor of d_ua)

The DH exchanges are used for the same normal enote high-level secrets in @tevador's post.

However, self-send enotes use a different construction for the high-level secrets (and different from before). For self-send higher level secrets, we use a combination of s_vs (view-sent secret) and d_ua (unlock-amounts key) instead of only k_vb (view-balance):

1. s^sr_1 = H_[tau]1(s_vs || D_e || input_context)
2. s^sr_2 = H_[tau]2(d_ua || s^sr_1)

Wallet Tiers

Tier	Knowledge	Off-chain capabilities	On-chain capabilities
GenAddr	s_ga	generate public addresses	none
FilterInvolved	d_fi	recognize all public wallet addresses	calculate view tags
ViewReceived	d_vr, d_fi, s_ga	all	view all received enotes (w/o amounts) except for change and self-spends
ViewSent	s_vs, d_fi, s_ga	all	view all change and self-spends enotes (w/o amounts)
HotWallet	s_vs, d_vr, d_fi, s_ga,	all	view all received, change, and self-spends enotes (w/o amounts)
PaymentValidator	d_fi, d_vr, d_ua, s_ga,	all	view all received enotes with amounts
ViewBalance	k_vb	all	view all enotes, calculate key images
Master	k_m	all	all

Sorry, this post strayed away from the view tag balancing discussion, but changing the derivation tree and self-send higher-level secrets calculations in this manner can be added to the current Jamtis proposal orthogonally to make better hot/cold wallet setups for little to no extra cost.

For the current Jamtis code in seraphis_lib with PLAIN, DUMMY, CHANGE, & SELFSPEND enote types

What is the reasoning for these types? AFAICS we only need 2 types to tell the wallet if the enote should be displayed in history or not (this could also be achieved with a 1-bit flag encrypted with s^sr_2, so only 1 extra K_o recomputation is needed).

To expand on the last point, we could have all secret keys (besides cipher-tag) below the view-balance secret in the derivation tree: view-received, view-sent (new key explained below), unlock-amounts, generate-address (moved out from under view-received), and filter-involved (basically the same as filter-received but the name needs an update since we use it also for outgoing). Then we can mix and match the unlock-amounts key with/without view-received and view-sent keys to create different tiers while keeping the number of operations in balance recovery the same.

I don't like the additional tiers between "FilterInvolved" and "ViewBalance". They give more arguments for third-party scanners to request additional private keys. Especially the "HotWallet" tier sounds very dangerous as light wallet users might be satisfied with not revealing amounts, but it actually allows the third party to identify spent outputs in the blockchain.

The missing d_ua key and the key hierarchy in my proposal was intentional to prevent any wallet tiers that could be useful for 3rd party scanning other than "FilterReceived".

Here is a comment by @UkoeHB speaking against your "HotWallet" tier: https://gist.github.com/tevador/50160d160d24cfc6c52ae02eb3d17024?permalink_comment_id=4274612#gistcomment-4274612