Hi Conduition, hi Fabian, hi all!
If we use
BIP-459 full aggregation for P2MR or P2TRH, we can recover one of the EC keys of a CISA group, solving its equation for that EC key. This saves 32 bytes per group. If a group is small, this actually makes sense.
This is the equation that BIP-459 verifies:
s⋅G = R + Σ c_i⋅P_i
We can solve it for one of the public keys (P_j):
P_j = (c_j^-1 mod n) ⋅ (s⋅G - R - Σ_{i≠j} c_i⋅P_i)
(Here c_j != 0. If c_j ==0, we need to restart the signing session with freshly generated nonces.)
One thing we have to change in BIP-459 to enable this is how coefficients c_i are calculated.
Currently BIP-459 produces them based on EC public keys themselves: roughly c_j = H(L || R || P_j || m_j). This creates a circular dependency at verification time if we don't know the omitted key (for P2MR or P2TRH).
For P2TRH, we need to replace P_j with scriptPubKey_j in the formula (something similar to my
EC recovery proposal). Since it commits to P_j, this should remain secure (need a formal proof). L also depends on public keys in BIP-459 - we need to change it to depend on scriptPubKeys as well. We need to do it at least for the input whose public key is recovered, but can also do for all inputs, for uniformity.
For P2MR
recoverable EC leaf, scriptPubKey is not sufficient as a replacement for a pubkey, since there might be multiple such leaves. To prevent related-key attacks, scriptPubKey must be accompanied with the control block (or its hash) of the leaf. This must be done both in c_j and L formulas.
Then we can recover one of the keys instead of putting it into witness. The natural choice is to recover the key of the input holding the aggregate signature, since it is already a special input in CISA.
Savings:
- P2TRH-CISA: n + 32n + 64 = 33n + 64
- One-key recovery: n + 32(n-1) + 64 = 33n + 32
(This counts the witness payload above, including one marker byte per input, but excludes CompactSize framing, annexes, and explicit sighash bytes.)
Inputs P2TRH-CISA One-key recovery Saved Saving
1 97 bytes 65 bytes 32 32.99%
2 130 bytes 98 bytes 32 24.62%
3 163 bytes 131 bytes 32 19.63%
4 196 bytes 164 bytes 32 16.33%
5 229 bytes 197 bytes 32 13.97%
7 295 bytes 263 bytes 32 10.85%
10 394 bytes 362 bytes 32 8.12%
20 724 bytes 692 bytes 32 4.42%
100 3,364 bytes 3,332 bytes 32 0.95%
One additional nice effect of this is that no separate ordinary mode is needed for basic single-input spending. A one-input full-aggregation group has the same 65-byte payload as a marker-based non-CISA single-input spend.
The price is the loss of batch verification across CISA groups. Inside-group verification efficiency is preserved: EC workload inside group is almost the same, just one additional scalar inversion.
Best,
Boris
On Saturday, July 18, 2026 at 1:50:35 PM UTC-5 conduition wrote:
Sending this again because I think the first time didn't work.
Thanks Fabian, this is very cool. I haven't read the entire BIP in detail yet, but first thing I notice on a quick skim is that reserving segwit version 2 conflicts with BIP-360 which proposes to use the same.
I'm particularly interested in how to dovetail this proposal with PQ migration efforts. I have two questions:
- Can the framework you use for verifying aggregated sigs be generalized to support future aggregated PQ signatures in the future? (assuming we someday have a PQ sig algorithm that admits aggregation)
- How do you see this proposal mixing with BIP360? The major hurdle I see is that your proposed output type puts a bare EC pubkey on-chain in the script-pubkey. Unfortunately Boris' EC recovery trick does not seem to work in this context: Because signatures are aggregated we can't recover pubkeys, so we can't hide them behind a hash. We either have to put them in the SPK, or the witness. So at face value, it seems there are two options:
- Couple CISA tightly with P2TRv2. On one hand this would be good because it would provide a concrete incentive for users to migrate to a wallet that supports PQC. This also seems like the easier option from an engineering perspective. However it comes with all the baggage of P2TRv2 (not actually quantum-safe by default, need to solve the Q-day timing problem).
- Hide the EC pubkeys behind a hash in the SPK (e.g. P2MR or P2TRH), and attach the EC pubkey in the witness of every aggregated TX input, so that the verifier can run the aggregated sig-verify algorithms. This would be more secure and relaxes the Q-day timing constraints, but we don't get as much relative savings.
Napkin math of the witness weight of an aggregated input, assuming full-aggregation is used:
- with P2TRv2:
- 1 byte for the marker
- total: 1 byte
- with P2TRH:
- 1 byte for the marker
- 32 bytes for the EC pubkey
- total: 33 weight units
- with P2MR:
- 1 byte for the marker (witness)
- 32 bytes for the merkle sibling node (witness)
- 32 bytes for the EC pubkey (witness)
- total: 65 weight units
regards,
conduition
Hi list,
I would like to share a BIP draft for transaction-wide cross-input
signature aggregation (CISA). It introduces a new witness version,
which enables Taproot-style key path spending where inputs can
aggregate their signatures.
Each input chooses between half-aggregation, full-aggregation, or an
explicit opt-out via a marker byte in its witness.
The aggregation schemes themselves are specified in the previously
shared BIP 458 (half-aggregation) and BIP 459 (full-aggregation)
drafts. Script path spending follows BIP 341/342 unchanged.
The BIP draft text can be found here:
For inline comments, I have opened a mock pull request on my BIPs
repo fork:
Feedback of any kind is much appreciated.
Best,
Fabian
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