This is based on how much an attacking miner stands to lose in block
rewardy by mining a private chain which double spends a payment.
This is not foolproof, since mining is based on luck, and breaks
down as the attacking miner nears 50% of the network hash rate,
and the estimation is based on a constant block reward.
Scheme by luigi1111:
Multisig for RingCT on Monero
2 of 2
User A (coordinator):
Spendkey b,B
Viewkey a,A (shared)
User B:
Spendkey c,C
Viewkey a,A (shared)
Public Address: C+B, A
Both have their own watch only wallet via C+B, a
A will coordinate spending process (though B could easily as well, coordinator is more needed for more participants)
A and B watch for incoming outputs
B creates "half" key images for discovered output D:
I2_D = (Hs(aR)+c) * Hp(D)
B also creates 1.5 random keypairs (one scalar and 2 pubkeys; one on base G and one on base Hp(D)) for each output, storing the scalar(k) (linked to D),
and sending the pubkeys with I2_D.
A also creates "half" key images:
I1_D = (Hs(aR)+b) * Hp(D)
Then I_D = I1_D + I2_D
Having I_D allows A to check spent status of course, but more importantly allows A to actually build a transaction prefix (and thus transaction).
A builds the transaction until most of the way through MLSAG_Gen, adding the 2 pubkeys (per input) provided with I2_D
to his own generated ones where they are needed (secret row L, R).
At this point, A has a mostly completed transaction (but with an invalid/incomplete signature). A sends over the tx and includes r,
which allows B (with the recipient's address) to verify the destination and amount (by reconstructing the stealth address and decoding ecdhInfo).
B then finishes the signature by computing ss[secret_index][0] = ss[secret_index][0] + k - cc[secret_index]*c (secret indices need to be passed as well).
B can then broadcast the tx, or send it back to A for broadcasting. Once B has completed the signing (and verified the tx to be valid), he can add the full I_D
to his cache, allowing him to verify spent status as well.
NOTE:
A and B *must* present key A and B to each other with a valid signature proving they know a and b respectively.
Otherwise, trickery like the following becomes possible:
A creates viewkey a,A, spendkey b,B, and sends a,A,B to B.
B creates a fake key C = zG - B. B sends C back to A.
The combined spendkey C+B then equals zG, allowing B to spend funds at any time!
The signature fixes this, because B does not know a c corresponding to C (and thus can't produce a signature).
2 of 3
User A (coordinator)
Shared viewkey a,A
"spendkey" j,J
User B
"spendkey" k,K
User C
"spendkey" m,M
A collects K and M from B and C
B collects J and M from A and C
C collects J and K from A and B
A computes N = nG, n = Hs(jK)
A computes O = oG, o = Hs(jM)
B anc C compute P = pG, p = Hs(kM) || Hs(mK)
B and C can also compute N and O respectively if they wish to be able to coordinate
Address: N+O+P, A
The rest follows as above. The coordinator possesses 2 of 3 needed keys; he can get the other
needed part of the signature/key images from either of the other two.
Alternatively, if secure communication exists between parties:
A gives j to B
B gives k to C
C gives m to A
Address: J+K+M, A
3 of 3
Identical to 2 of 2, except the coordinator must collect the key images from both of the others.
The transaction must also be passed an additional hop: A -> B -> C (or A -> C -> B), who can then broadcast it
or send it back to A.
N-1 of N
Generally the same as 2 of 3, except participants need to be arranged in a ring to pass their keys around
(using either the secure or insecure method).
For example (ignoring viewkey so letters line up):
[4 of 5]
User: spendkey
A: a
B: b
C: c
D: d
E: e
a -> B, b -> C, c -> D, d -> E, e -> A
Order of signing does not matter, it just must reach n-1 users. A "remaining keys" list must be passed around with
the transaction so the signers know if they should use 1 or both keys.
Collecting key image parts becomes a little messy, but basically every wallet sends over both of their parts with a tag for each.
Thia way the coordinating wallet can keep track of which images have been added and which wallet they come from. Reasoning:
1. The key images must be added only once (coordinator will get key images for key a from both A and B, he must add only one to get the proper key actual key image)
2. The coordinator must keep track of which helper pubkeys came from which wallet (discussed in 2 of 2 section). The coordinator
must choose only one set to use, then include his choice in the "remaining keys" list so the other wallets know which of their keys to use.
You can generalize it further to N-2 of N or even M of N, but I'm not sure there's legitimate demand to justify the complexity. It might
also be straightforward enough to support with minimal changes from N-1 format.
You basically just give each user additional keys for each additional "-1" you desire. N-2 would be 3 keys per user, N-3 4 keys, etc.
The process is somewhat cumbersome:
To create a N/N multisig wallet:
- each participant creates a normal wallet
- each participant runs "prepare_multisig", and sends the resulting string to every other participant
- each participant runs "make_multisig N A B C D...", with N being the threshold and A B C D... being the strings received from other participants (the threshold must currently equal N)
As txes are received, participants' wallets will need to synchronize so that those new outputs may be spent:
- each participant runs "export_multisig FILENAME", and sends the FILENAME file to every other participant
- each participant runs "import_multisig A B C D...", with A B C D... being the filenames received from other participants
Then, a transaction may be initiated:
- one of the participants runs "transfer ADDRESS AMOUNT"
- this partly signed transaction will be written to the "multisig_monero_tx" file
- the initiator sends this file to another participant
- that other participant runs "sign_multisig multisig_monero_tx"
- the resulting transaction is written to the "multisig_monero_tx" file again
- if the threshold was not reached, the file must be sent to another participant, until enough have signed
- the last participant to sign runs "submit_multisig multisig_monero_tx" to relay the transaction to the Monero network
- refactoring: proof generation/checking code was moved from simplewallet.cpp to wallet2.cpp
- allow an arbitrary message to be signed together with txid
- introduce two types (outbound & inbound) of tx proofs; with the same syntax, inbound is selected when <address> belongs to this wallet, outbound otherwise. see GitHub thread for more discussion
- wallet RPC: added get_tx_key, check_tx_key, get_tx_proof, check_tx_proof
- wallet API: moved WalletManagerImpl::checkPayment to Wallet::checkTxKey, added Wallet::getTxProof/checkTxProof
- get_tx_key/check_tx_key: handle additional tx keys by concatenating them into a single string
Transactions in the txpool are marked when another transaction
is seen double spending one or more of its inputs.
This is then exposed wherever appropriate.
Note that being marked with this "double spend seen" flag does
NOT mean this transaction IS a double spend and will never be
mined: it just means that the network has seen at least another
transaction spending at least one of the same inputs, so care
should be taken to wait for a few confirmations before acting
upon that transaction (ie, mostly of use for merchants wanting
to accept unconfirmed transactions).
