npub1lp…c74n4

Last Notes

2023-08-09 18:03:59 CEST

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📅 Original date posted:2023-08-09
🗒️ Summary of this message: The author thanks Johan for their comments and implementation. They discuss the ordering of parameters and the use cases for the deferred output amount check in CCV.
📝 Original message:
Hi Johan,
Thanks a lot for the comments, and the independent implementation!
> - For the opcode parameter ordering, it feels unnatural for the two
> tweaks (data, taptree) to be separated by the internal key. A more
> natural ordering of parameters IMO would be (of course this is all
> subjective):
> <data> <taptree> <internalkey> <index> <flags> OP_CCV.
>
> If you disagree, I would love some rationale for the ordering you
> chose! (looks like you also changed it again after your last post?).
The main concern for the reordering was to put <data> at the bottom,
as that's typically passed via the witness stack.
I put the <index> right next, as I suspect there are use cases for
specifying via the witness what is the input index where a certain
(CCV-encumbered) UTXO is to be found, or which output should funds
be sent to, instead of hard-coding this in the script. This might
help in designing contracts that are more flexible in the way they
are spent, for example by allowing batching their transactions.
Instead, I expect the other parameters to almost always be hardcoded,
or propagated from the current input with the <-1> special values.
I agree that your ordering is more aesthetically pleasing, though.
> I'm wondering what other use cases you had in mind for the deferred
> output amount check? Maybe I have missed something, but if not it
> would perhaps be better to leave out the amount preservation check, or
> go the extra mile and propose a more powerful amount introspection
> machinery.
Yes, the deferred output amount check is not enough for coinpools;
however, it comes at no cost if we have a <flags> parameter anyway,
as OP_2 (value for CCV_IGNORE_OUTPUT_AMOUNT) is a single byte opcode.
The intent of preserving amounts for many-to-one contracts (vaults),
or the one-to-one cases (channels, any 2-party contract, etc.) seems
common enough to deserve 1 bit in the flags, IMHO.
Efforts to define and add explicit introspection to cover your
(exciting!) use cases can proceed independently, but I don't think
they would nullify the advantages of this (optional) feature of CCV.
Best,
Salvatore
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2023-08-08 16:20:52 CEST

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📅 Original date posted:2023-08-07
🗒️ Summary of this message: The sender apologizes for confusion and inconsistent use of plurals. They explain that the opcode is now functionally complete and ready for experimentation.
📝 Original message:
Hi Dave,
I apologize for the confusion and the inconsistent use of plurals.
The reason I called it a "complete proposal" is that the opcode is
now functionally complete, unlike the previous attempt where the
approach for the output amount introspection was not yet specified.
The semantics are informally defined in the previous e-mail, and
implemented in the code [1], which is the only formal specification
at this time. I believe the code is now fairly stable and ready to
experiment with.
My own and (hopefully) others' experimentation will help in writing
a more informed BIP proposal in the next few months.
About the plurals: OP_CHECKCONTRACTVERIFY is indeed now a single
opcode that is useful on its own, but I will also be maintaining a
separate branch [2] that contains both OP_CHECKCONTRACTVERIFY and
OP_CAT, which enables the full generality of the MATT proposal.
Best,
Salvatore
[1] -
https://github.com/bitcoin-inquisition/bitcoin/compare/24.0...Merkleize:bitcoin:checkcontractverify
[2] - https://github.com/Merkleize/bitcoin/tree/matt
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2023-06-08 01:21:09 CEST

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📅 Original date posted:2023-05-28
🗒️ Summary of this message: The author suggests making OP_CICV and OP_COCV symmetrical and exploring the use of OP_CHECKINPUTCONTRACTVERIFY for eltoo-style replacement. They also discuss the possibility of a single OP_CHECK_IN_OUT_CONTRACT_VERIFY opcode for greater flexibility. Additionally, they mention the use of taproot internal pubkey with "dynamic key aggregation" and storing pubkeys of members in embedded data for CoinPools.
📝 Original message:Hi Johan,
Exciting to finally see some merkleization, which was only confined
within the meme, up to this point!
> A simpler way IMO, would be to make OP_CICV and OP_COCV symmetrical:
> Have OP_CICV take an optional taproot and do the same check as is
> done for the output: Q == tweak(tweak(X,D), T).
I think that's an excellent suggestion, which I was already exploring
for a different purpose: bringing externally signed data onto the
stack. My goal there was to allow eltoo-style replacement.
Until recently, I thought that a clean/efficient version of eltoo
would require OP_CHECKSIGFROMSTACK or ANYPREVOUT. However, extending
OP_CHECKINPUTCONTRACTVERIFY to enable introspection of other inputs
allows a reasonable workaround: producing a separate UTXO signed with
ANYONECANPAY, with the required data embedded as usual. Spending that
UTXO together with the channel's UTXO allows one to get that data
on the stack (with its signature already checked by consensus rules).
I drafted this idea in a gist [1].
Remark: it still seems easier (and probably slightly more efficient)
to build eltoo replacement with CSFS or APO in addition to MATT
opcodes.
A possible semantics for OP_CHECKINPUTCONTRACTVERIFY could then be
exactly symmetrical to that of OP_CHECKOUTPUTCONTRACTVERIFY, with
the exception that the special input index -1 would represent the
current input.
Pushing this further, another option that could be be worth exploring
is to have a single OP_CHECK_IN_OUT_CONTRACT_VERIFY opcode, with the
same semantics as OP_CHECKOUTPUTCONTRACTVERIFY from [2], but with an
additional `flags` argument, which is a bitmap where:
- the lowest-significant bit determines if the index refers to inputs
or outputs (where input index -1 refers to the current input)
- the second bit specifies if amounts should be preserved with
deferred checks as described in [2] (only applicable to outputs)
- other bits are OP_SUCCESS and reserved for future behaviors.
This would make the opcodes 1-2 bytes larger, but might allow greater
flexibility, and keep some room for future extensions.
> 2.To make fully functioning CoinPools, one would need functionality
> similar to OP_MERKLESUB[4]: remove some data from the merkle tree,
> and remove a key from the aggregated internal key.
It seems likely that efficient use of the taproot internal pubkey with
"dynamic key aggregation" is not possible with the current semantics
(unless one ventures into the fraud proof machinery, which seems
overkill!).
However, in constructions with MATT opcodes, I would never expect the
need for data to be stored in the taptree. In particular, for the case
of CoinPools, the pubkeys of the members could also be stored in the
embedded data, having a single "unilateral withdrawal" tapleaf.
Removing a key would then amount to replacing it with a fixed NUMS key
and computing the new root (re-using the same Merkle proof).
Note that this is not a lot costlier than using a tapleaf per user:
instead of paying the cost for the Merkle proof in the control block,
you pay for it explicitly in the Script witness.
Therefore, I would expect there to be reasonable CoinPools designs
without additional opcodes − but I am only moderately confident as
this is beyond the level of sophistication I've been exploring so far.
Best,
Salvatore
[1] - https://gist.github.com/bigspider/041ebd0842c0dcc74d8af087c1783b63
[2] -
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2023-April/021588.html
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2023-06-08 01:21:08 CEST

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📅 Original date posted:2023-05-01
🗒️ Summary of this message: The email discusses oversights in a previous email regarding a contract's embedded data and suggests a solution to store a hash instead. It also proposes a fix for a potential cheating scenario in a game played offline.
📝 Original message:Hi all,
I apologize for a couple of oversights in my last e-mail.
The first is that m_B can't be committed as-is in the contract's
embedded data, with the current semantics of OP_COCV, which
only allows 32-byte values. A solution could be to store its
hash SHA256(m_B), instead.
(I didn't test the Scripts, so there could be other bugs − hopefully the
general idea is clear, anyway)
On Mon, 1 May 2023 at 15:11, Salvatore Ingala <salvatore.ingala at gmail.com>
wrote:
> If the internal_pubkey is a musig-aggregated key of Alice and Bob,
> the game can be settled entirely offline after the first transaction.
> Simply, Bob communicates his move to Alice, Alice reveals her move to
> Bob, and they can settle the bet. The game would be played without
> any script being executed, therefore all transactions could look like
> any other P2TR, with the only possible fingerprinting being due to the
> input amounts.
>
This is incomplete: Alice can't trust Bob by revealing her move, as
he could then cheat on-chain and play a different move.
The fix should be straightforward, after adding the requirement that the
internal pubkey of [S1] is a musig2 of both players.
After Bob reveals his move (say, Rock), Alice will only agree to continue
the game off-chain if Bob pre-signs transactions for the state [S1] (where
m_B = Paper, and m_B = Scissors) that send all the money to Alice.
This guarantees that a cheating Bob is punished.
Best,
Salvatore Ingala
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2023-06-08 01:21:07 CEST

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📅 Original date posted:2023-05-01
🗒️ Summary of this message: The author suggests that games where all possible futures can be enumerated are not ideal to showcase MATT, and proposes rock-paper-scissors as an academic example. They provide a protocol for playing the game and explain how it can be implemented with CICV/COCV.
📝 Original message:Hi Johan,
Thanks for your message.
I think games where all the possible futures can be enumerated are
not ideal to showcase MATT, as one could just fully represent them
with just CTV or COCV, and not use the "data embedding" at all.
Perhaps rock-paper-scissors could be a better academic example. [1]
I'm not sure this will fully address your question; however I think
it's quite an instructive example, and I wanted to work it out for
quite some time.
It would be interesting to explore some contracts where the size
of the embedded data is substantially larger, and that could be
a natural next step to think about.
### Rock paper scissors
We want a protocol between Alice and Bob, where they bet 1 coin each:
1. Alice chooses and publishes her move;
2. Bob chooses his move, and the pot is adjudicated as per the rules.
Of course, if implemented naively, this wouldn't be a very fun game:
Bob would just wait to see Alice's move and play accordingly.
That's easy to fix, though:
1. Alice publishes a commitment to her move
2. Bob publishes his move in clear
3. Alice reveals her move, and the pot is adjudicated.
We can encode Rock = 0, Paper = 1, Scissors = 2. Let m_A, m_B be
Alice's and Bob's move, respectively. Then, it's easy to verify that:
− m_B - m_A == 0 (mod 3) ==> it's a tie
− m_B - m_A == 1 (mod 3) ==> Bob wins
− m_B - m_A == 2 (mod 3) ==> Alice wins
In order to create a hiding commitment for Alice, she can choose a
256-bit random number r_A, and compute:
c_A = SHA256(m_A || r_A)
With that in mind, the full protocol can go like this:
1. Alice chooses her move m_A and a large random number r_A;
she posts c_A computed as above;
2. Bob chooses m_B and publishes it;
3. Alice publishes m_A and r_A, then the winner is adjudicated.
### MATT playing RPS
To implement this with CICV/COCV, we can use just 3 transactions: in
fact, Alice can already compute c_A and share it with Bob before they
both commit their coins into an encumbered UTXO. That also means that
c_A can actually be hardcoded in the Scripts, rather than taking
space in the UTXO's embedded data.
Therefore, they both put one coin each, and they send to an output
whose script is the state S0 described below.
We assume that the keypath in the P2TR defined below is either a NUMS
point, or perhaps a Musig2 aggregate key that can be used to settle
the game collaboratively.
Note that there are 3 possible payout options that are fully known
when the game starts: either Alice takes all the money, or they split
evenly, or Bob takes all the money.
Similarly to the vault implementation [2], this seems to be another
case where CTV fits very well, as it allows to very efficiently
describe the three possible outcomes by their CTV hashes. Let them
be <ctv-alice-wins>, <ctv-split>, <ctv-bob-wins>, respectively.
Therefore, this avoids the need for 64-bit maths, and explicit amount
introspection − at least for these contracts.
[State S0] (Start of the game, Alice moved; Bob's turn)
Spending conditions:
- after <forfait-delay>, Alice takes the money // (Bob forfaits)
- Bob posts m_B (0, 1 or 2); the next output is [S1] with data m_B
The first script is:
// witness: []
<forfait-delay>
OP_CHECKSEQUENCEVERIFY
OP_DROP
<ctv-alice-wins>
OP_CHECKTEMPLATEVERIFY
The second is
// witness: [<bob_sig> <m_B>]
OP_DUP 0 3 OP_WITHIN // check that m_B is 0, 1 or 2
<internal_pubkey> OP_SWAP
<S1's taptree>
OP_CHECKOUTPUTCONTRACTVERIFY // check that the output is correct
<bob_pubkey>
OP_CHECKSIG
[State S1] (Alice reveals m_A and adjudicates)
- after <forfait-timeout>, Bob takes the money // (Alice forfaits)
- Alice posts correct m_A and r_A compatible with c_A;
The first script is symmetric to Bob's forfait script above.
The second condition can be split into three leaf scripts, one for
each possible value of m_B - m_A (mod 3):
// witness: [<m_B> <m_A> <r_A>]
OP_OVER OP_DUP OP_TOALTSTACK // save m_A
0 3 OP_WITHIN OP_VERIFY // check that m_A is 0, 1 or 2
// check that SHA256(m_A || r_A) equals c_A
OP_2DUP
OP_CAT OP_SHA256
<c_A>
OP_EQUALVERIFY
OP_DUP
<internal_pubkey>, OP_SWAP
OP_CHECKINPUTCONTRACTVERIFY
OP_FROMALTSTACK
OP_SUB // stack now contains m_B - m_A
OP_DUP // if the result is negative, add 3
0 OP_LESSTHAN
OP_IF
3
OP_ADD
OP_ENDIF
{0, 1, 2} // draw / Bob wins / Alice wins, respectively
OP_EQUALVERIFY
{<ctv-split>, <ctv-bob-wins>, <ctv-alice-wins>} // respectively
OP_CHECKTEMPLATEVERIFY
### Comments
In general, we would have to worry about the possible
malleability of the witness elements, when they are not signatures
or preimages themselves. Here, in particular, it might seem that's
an issue when <m_B> is provided while spending the state [S0].
However, here the value of <m_B> is also committed to in the output
thanks to COCV; therefore, Bob's signature prevents malleability
also for m_B.
In general, it seems to be the case in MATT contracts that one would
want the signature of the authorized party performing a transition to
some other state of the smart contract with contains embedded data;
this makes the malleability issue less of a problem in practice than
I initially thought.
If the internal_pubkey is a musig-aggregated key of Alice and Bob,
the game can be settled entirely offline after the first transaction.
Simply, Bob communicates his move to Alice, Alice reveals her move to
Bob, and they can settle the bet. The game would be played without
any script being executed, therefore all transactions could look like
any other P2TR, with the only possible fingerprinting being due to the
input amounts.
It should be possible to generalize the protocol so that many rounds
can be played off-chain within the same UTXO, but I didn't try to
figure out the details.
Best,
Salvatore Ingala
[1] - https://en.wikipedia.org/wiki/Rock_paper_scissors
[2] -
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2023-April/021588.html
On Fri, 28 Apr 2023 at 10:48, Johan Torås Halseth <johanth at gmail.com> wrote:
> Hi, Salvatore.
>
> I find this proposal very interesting. Especially since you seemingly
> can achieve such powerful capabilities by such simple opcodes.
>
> I'm still trying to grok how this would look like on-chain (forget
> about the off-chain part for now), if we were to play out such a
> computation.
>
> Let's say you have a simple game like "one player tic-tac-toe" with
> only two tiles: [ _ | _ ]. The player wins if he can get two in a row
> (pretty easy game tbh).
>
> Could you give a complete example how you would encode one such state
> transition (going from [ X, _ ] -> [ X, X ] for instance) in Bitcoin
> script?
>
> Feel free to choose a different game or program if you prefer :)
>
> Thanks!
> Johan
>
>
>
> On Tue, Dec 13, 2022 at 2:08 PM Billy Tetrud via bitcoin-dev
> <bitcoin-dev at lists.linuxfoundation.org> wrote:
> >
> > Re Verkle trees, that's a very interesting construction that would be
> super useful as a tool for something like Utreexo. A potentially
> substantial downside is that it seems the cryptography used to get those
> nice properties of Verkle trees isn't quantum safe. While a lot of things
> in Bitcoin seems to be going down the path of quantum-unsafe (I'm looking
> at you, taproot), there are still a lot of people who think quantum safety
> is important in a lot of contexts.
> >
> > On Thu, Dec 1, 2022 at 5:52 AM Salvatore Ingala via bitcoin-dev <
> bitcoin-dev at lists.linuxfoundation.org> wrote:
> >>
> >> Hello Rijndael,
> >>
> >>
> >>
> >> On Wed, 30 Nov 2022 at 23:09, Rijndael <rot13maxi at protonmail.com>
> wrote:
> >>>
> >>> Hello Salvatore,
> >>>
> >>> I found my answer re-reading your original post:
> >>> > During the arbitration phase (say at the i-th leaf node of M_T), any
> party can win the challenge by providing correct values for tr_i = (st_i,
> op_i, st_{i + 1}). Crucially, only one party is able to provide correct
> values, and Script can verify that indeed the state moves from st_i to
> st_{i + 1} by executing op_i. The challenge is over.
> >>
> >> You are correct, the computation step encoded in a leaf needs to be
> simple enough for Script to verify it.
> >>
> >> For the academic purpose of proving completeness (that is, any
> computation can be successfully "proved" by the availability of the
> corresponding fraud proof), one can imagine reducing the computation all
> the way down to a circuit, where each step (leaf) is as simple as what can
> be checked with {OP_NOT, OP_BOOLAND, OP_BOOLOR, OP_EQUAL}.
> >>
> >> In practice, you would want to utilize Script to its fullest, so for
> example you wouldn't compile a SHA256 computation to something else – you'd
> rather use OP_SHA256 directly.
> >>
> >>>
> >>> That raises leads to a different question: Alice initially posts a
> commitment to an execution trace of `f(x) = y`, `x`, and `y`. Bob Disagrees
> with `y` so starts the challenge protocol. Is there a commitment to `f`? In
> other words, the dispute protocol (as I read it) finds the leftmost step in
> Alice and Bob's execution traces that differ, and then rewards the coins to
> the participant who's "after-value" is computed by the step's operation
> applied to the "before value". But if the participants each present valid
> steps but with different operations, who wins? In other words, Alice could
> present [64, DECREMENT, 63] and Bob could present [64, INCREMENT, 65].
> Those steps don't match, but both are valid. Is there something to ensure
> that before the challenge protocol starts, that the execution trace that
> Alice posts is for the right computation and not a different computation
> that yields a favorable result for her (and for which she can generate a
> valid merkle tree)?
> >>
> >>
> >> The function f is already hard-coded in the contract itself, by means
> of the tree of scripts − that already commits to the possible futures.
> Therefore, once you are at state S14, you know that you are verifying the
> 6th step of the computation; and the operation in the 6th step of the
> computation depends solely on f, not its inputs. In fact, you made me
> realize that I could drop op_i from the i-th leaf commitment, and just
> embed the information in the Script of that corresponding state.
> >>
> >> Note that the states S0 to S14 of the 256x game are not _all_ the
> possible states, but only the ones that occurred in that execution of the
> contract (corresponding to a path from the root to the leaf of the Merkle
> tree of the computation trace), and therefore the ones that materialized in
> a UTXO. Different choices made by the parties (by providing different data,
> and therefore choosing different branches) would lead to a different leaf,
> and therefore to different (but in a certain sense "symmetric") states.
> >>
> >> ========
> >>
> >> Since we are talking about the fact that f is committed to in the
> contract, I'll take the chance to extend on this a bit with a fun
> construction on top.
> >> It is well-known in the academic literature of state channels that you
> can create contracts where even the function ("program", or "contract") is
> not decided when the channel is created.
> >>
> >> Since f is generic, we can choose f itself to be a universal Turing
> machine. That is, we can imagine a function f(code, data) that executes a
> program ("code") on the "data" given to it as input.
> >> Since we can do fraud proofs on statements "f(code, data) == output",
> we could build contracts where the "code" itself is chosen later.
> >>
> >> For example, one could build a universal state channel, where parties
> can enter any contract among themselves (e.g.: start playing a chess game)
> entirely inside the channel. The state of this universal channel would
> contain all the states of the individual contracts that are currently open
> in the channel, and even starting/closing contracts can happen entirely
> off-chain.
> >>
> >> I believe these constructions are practical (the code of universal
> Turing machines is not really complicated), so it might be worth exploring
> further to figure out useful applications of this approach (supercharging
> lightning?).
> >>
> >> We should probably start by implementing testnet rock-paper-scissors in
> MATT, though :)
> >>
> >> Best,
> >> Salvatore Ingala
> >> _______________________________________________
> >> bitcoin-dev mailing list
> >> bitcoin-dev at lists.linuxfoundation.org
> >> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
> >
> > _______________________________________________
> > bitcoin-dev mailing list
> > bitcoin-dev at lists.linuxfoundation.org
> > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>
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2023-06-08 01:16:50 CEST

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📅 Original date posted:2022-11-08
📝 Original message:Hi list,
I have been working on some notes to describe an approach that uses
covenants in order to enable general smart contracts in bitcoin. You can
find them here:
https://merkle.fun
The approach has a number of desirable features:
- small impact to layer 1;
- not application-specific, very general;
- it fits well into P2TR;
- it does not require new cryptographic assumptions, nor any construction
that has not withstood the test of time.
This content was presented at the BTCAzores unconference, where it received
the name of MATT − short for Merkleize All The Things.
In fact, no other cryptographic primitive is required, other than Merkle
trees.
I believe this construction gets close to answering the question of how
small a change on bitcoin's layer 1 would suffice to enable arbitrary smart
contracts.
It is not yet at the stage where a formal proposal can be made, therefore
the proposed specs are only for illustrative purposes.
The same content is reformatted below for the mailing list.
Looking forward to hearing about your comments and improvements.
Salvatore Ingala
==========================================
# General smart contracts in bitcoin via covenants
Covenants are UTXOs that are encumbered with restrictions on the outputs of
the transaction spending the UTXO. More formally, we can define a covenant
any UTXO such that at least one of its spending conditions is valid only if
one or more of the outputs’ scriptPubKey satisfies certain restrictions.
Generally, covenant proposals also add some form of introspection (that is,
the ability for Script to access parts of the inputs/outputs, or the
blockchain history).
In this note, we want to explore the possibilities unleashed by the
addition of a covenant with the following properties:
- introspection limited to a single hash attached to the UTXO (the
“covenant data”), and input/output amounts;
- pre-commitment to every possible future script (but not their data);
- few simple opcodes operating with the covenant data.
We argue that such a simple covenant construction is enough to extend the
power of bitcoin’s layer 1 to become a universal settlement layer for
arbitrary computation.
Moreover, the covenant can elegantly fit within P2TR transactions, without
any substantial increase for the workload of bitcoin nodes.
A preliminary version of these notes was presented and discussed at the
BTCAzores Unconference [1], on 23rd September 2022.
# Preliminaries
We can think of a smart contract as a “program” that updates a certain
state according to predetermined rules (which typically include access
control by authorizing only certain public keys to perform certain
actions), and that can possibly lock/unlock some coins of the underlying
blockchain according to the same rules.
The exact definition will be highly dependent on the properties of the
underlying blockchain.
In bitcoin, the only state upon which all the nodes reach consensus is the
UTXO set; other blockchains might have other data structures as part of the
consensus, like a key-value store that can be updated as a side effect of
transaction execution.
In this section we explore the following concepts in order to set the
framework for a definition of smart contracts that fits the structure of
bitcoin:
- the contract’s state: the “memory” the smart contract operates on;
- state transitions: the rules to update the contract’s state;
- covenants: the technical means that can allow contracts to function in
the context of a bitcoin UTXO.
In the following, an on-chain smart contract is always represented as a
single UTXO that implicitly embeds the contract’s state and possibly
controls some coins that are “locked” in it. More generally, one could
think of smart contracts that are represented in a set of multiple UTXOs;
we leave the exploration of generalizations of the framework to future
research.
## State
Any interesting “state” of a smart contract can ultimately be encoded as a
list, where each element is either a bit, a fixed-size integers, or an
arbitrary byte string.
Whichever the choice, it does not really affect what kinds of computations
are expressible, as long as one is able to perform some basic computations
on those elements.
In the following, we will assume without loss of generality that
computations happen on a state which is a list of fixed length S = [s_1,
s_2, …, s_n], where each s_i is a byte string.
### Merkleized state
By constructing a Merkle tree that has the (hashes of) the elements of S in
the leaves, we can produce a short commitment h_S to the entire list S with
the following properties (that hold for a verifier that only knows h_S):
- a (log n)-sized proof can prove the value of an element s_i;
- a (log n + |x|)-sized proof can prove the new commitment h_S’, where S’
is a new list obtained by replacing the value of a certain leaf with x.
This allows to compactly commit to a RAM, and to prove correctness of RAM
updates.
In other words, a stateful smart contract can represent an arbitrary state
in just a single hash, for example a 32-byte SHA256 output.
### State transitions and UTXOs
We can conveniently represent a smart contract as a finite state machine
(FSM), where exactly one node can be active at a given time. Each node has
an associated state as defined above, and a set of transition rules that
define:
- who can use the rule;
- what is the next active node in the FSM;
- what is the state of the next active node.
It is then easy to understand how covenants can conveniently represent and
enforce the smart contracts in this framework:
- The smart contract is instantiated by creating a UTXO encumbered with a
covenant; the smart contract is in the initial node of the FSM.
- The UTXO’s scriptPubKey specifies the current state and the valid
transitions.
- The UTXO(s) produced after a valid transition might or might not be
further encumbered, according to the rules.
Therefore, what is necessary in order to enable this framework in bitcoin
Script is a covenant that allows the enforcement of such state transitions,
by only allowing outputs that commit to a valid next node (and
corresponding state) in the FSM.
It is not difficult to show that arbitrary computation is possible over the
committed state, as long as relatively simple arithmetic or logical
operations are available over the state.
Remark: using an acyclic FSM does not reduce the expressivity of the smart
contracts, as any terminating computation on bounded-size inputs which
requires cycles can be unrolled into an acyclic one.
### Merkleized state transitions
Similarly to how using Merkle trees allows to succinctly represent
arbitrary data with a short, 32-byte long summary, the same trick allows to
succinctly represent arbitrary state transitions (the smart contract’s
code) with a single 32-byte hash. Each of the possible state transitions is
encoded as a Script which is put in a leaf of a Merkle tree; the Merkle
root of this tree is a commitment to all the possible state transitions.
This is exactly what the taptree achieves in Taproot (see BIP-0341 [2]).
Later sections in this document will suggest a possible way of how both the
contract’s state and valid transition rules could be represented in UTXOs.
## On-chain computation?!
Should the chain actually do computation?
If naively designed, the execution of a contract might require a large
number of transactions, which is not feasible.
While the covenant approach does indeed enable a chain of transactions to
perform arbitrary computation, simple economic considerations will push
protocol designers to perform any non-trivial computation off-chain, and
instead use the blockchain consensus only to verify the computation; or, if
possible, skip the verification altogether.
The fundamental fact that a blockchain’s layer 1 never actually needs to
run complex programs in order to enable arbitrary complex smart contracting
was observed in the past, for example in a 2016 post by Greg Maxwell [3].
Vitalik Buterin popularized the concept of "functionality escape velocity"
[4] to signify the minimum amount of functionality required on layer 1 in
order to enable anything else to be built on top (that is, on layer 2 and
beyond).
In the following section, we will argue that a simple covenant construction
suffices to achieve the functionality escape velocity in the UTXO model.
# Commitments to computation and fraud challenges
In this section, we explore how a smart contract that requires any
non-trivial computation f : X --> Y (that is too expensive or not feasible
with on-chain Script state transitions) can be implemented with the simple
covenants described in the previous section.
The ideas in this section appeared in literature; the reader is referred to
the references for a more comprehensive discussion.
We want to be able to build contracts that allow conditions of the type
"f(x) = y"; yet, we do not want layer 1 to be forced to perform any
expensive computation.
In the following, we assume for simplicity that Alice and Bob are the only
participants of the covenant, and they both locked some funds bond_A and
bond_B (respectively) inside the covenant’s UTXO.
1. Alice posts the statement “f(x) = y”.
2. After a challenge period, if no challenge occurs, Alice is free to
continue and unlock the funds; the statement is true.
3. At any time before the challenge period expires, Bob can start a
challenge: “actually, f(x) = z”.
In case of a challenge, Alice and Bob enter a challenge resolution
protocol, arbitrated by layer 1; the winner takes the other party’s bond
(details and the exact game theory vary based on the type of protocol the
challenge is part of; choosing the right amount of bonds is crucial for
protocol design).
The remainder of this section sketches an instantiation of the challenge
protocol.
## The bisection protocol for arbitrary computation
In this section, we sketch the challenge protocol for an arbitrary
computation f : X --> Y.
### Computation trace
Given the function f, it is possible to decompose the entire computation in
simple elementary steps, each performing a simple, atomic operation. For
example, if the domain of x and y is that of binary strings of a fixed
length, it is possible to create a boolean circuit that takes x and
produces y; in practice, some form of assembly-like language operating on a
RAM might be more efficient and fitting for bitcoin Script.
In the following, we assume each elementary operation is operating on a
RAM, encoded in the state via Merkle trees as sketched above. Therefore,
one can represent all the steps of the computation as triples tri = (st_i,
op_i, st_{i + 1}), where st_i is the state (e.g. a canonical Merkle tree of
the RAM) before the i-th operation, st_{i + 1} is the state after, and op_i
is the description of the operation (implementation-specific; it could be
something like “add a to b and save the result in c).
Finally, a Merkle tree M_T is constructed that has as leaves the values of
the individual computation steps T = {tr_0, tr_1, …, tr_{N - 1}} if the
computation requires N steps, producing the Merkle root h_T. The height of
the Merkle tree is log N. Observe that each internal node commits to the
portion of the computation trace corresponding to its own subtree.
Let’s assume that the Merkle tree commitments for internal nodes are
further augmented with the states st_{start} and st_{end}, respectively the
state before the operation of in the leftmost leaf of the subtree, and
after the rightmost leaf of the subtree.
### Bisection protocol
The challenge protocol begins with Alice posting what she claims is the
computation trace h_A, while Bob disagrees with the trace h_B != h_A;
therefore, the challenge starts at the root of M_T, and proceeds in steps
in order to find a leaf where Alice and Bob disagree (which is guaranteed
to exist, hence the disagreement). Note that the arbitration mechanism
knows f, x and y, but not the correct computation trace hash h_T.
(Bisection phase): While the challenge is at a non-leaf node of M_T, Alice
and Bob take turns to post the two hashes corresponding to the left and
right child of their claimed computation trace hash; moreover, they post
the start/end state for each child node. The protocol enforces that Alice’s
transaction is only valid if the posted hashes h_{l; A} and h_{r; A}, and
the declared start/end state for each child are consistent with the
commitment in the current node.
(Arbitration phase): If the protocol has reached the i-th leaf node, then
each party reveals (st_i, op_i, st_{i + 1}); in fact, only the honest party
will be able to reveal correct values, therefore the protocol can
adjudicate the winner.
Remark: there is definitely a lot of room for optimizations; it is left for
future work to find the optimal variation of the approach; moreover,
different challenge mechanisms could be more appropriate for different
functions f.
### Game theory (or why the chain will not see any of this)
With the right economic incentives, protocol designers can guarantee that
playing a losing game always loses money compared to cooperating.
Therefore, the challenge game is never expected to be played on-chain. The
size of the bonds need to be appropriate to disincentivize griefing attacks.
### Implementing the bisection protocol's state transitions
It is not difficult to see that the entire challenge-response protocol
above can be implemented using the simple state transitions described above.
Before a challenge begins, the state of the covenant contains the value of
x, y and the computation trace computed by Alice. When starting the
challenge, Bob also adds its claim for the correct computation trace, and
the covenant enters the bisection phase.
During the bisaction phase, the covenant contains the claimed computation
trace for that node of the computation protocol, according to each party.
In turns, each party has to reveal the corresponding computation trace for
both the children of the current node; the transaction is only valid if the
hash of the current node can be computed correctly from the information
provided by each party about the child nodes. The protocol repeats on one
of the two child nodes on whose computation trace the two parties disagree
(which is guaranteed to exist). If a leaf of M_T is reached, the covenant
enters the final arbitration phase.
During the arbitration phase (say at the i-th leaf node of M_T), any party
can win the challenge by providing correct values for tr_i = (st_i, op_i,
st_{i + 1}). Crucially, only one party is able to provide correct values,
and Script can verify that indeed the state moves from st_i to st_{i + 1}
by executing op_i. The challenge is over.
At any time, the covenant allows one player to automatically win the
challenge after a certain timeout if the other party (who is expected to
“make his move”) does not spend the covenant. This guarantees that the
protocol can always find a resolution.
### Security model
As for other protocols (like the lightning network), a majority of miners
can allow a player to win a challenge by censoring the other player’s
transactions. Therefore, the bisection protocol operates under the honest
miner majority assumption. This is acceptable for many protocols, but it
should certainly be taken into account during protocol design.
# MATT covenants
We argued that the key to arbitrary, fully general smart contracts in the
UTXO model is to use Merkle trees, at different levels:
1. succinctly represent arbitrary state with a single hash. Merkleize the
state!
2. succinctly represent the possible state transitions with a single hash.
Merkleize the Script!
3. succinctly represent arbitrary computations with a single hash.
Merkleize the execution!
(1) and (2) alone allow contracts with arbitrary computations; (3) makes
them scale.
Merkleize All The Things!
In this section we sketch a design of covenant opcodes that are
taproot-friendly and could easily be added in a soft fork to the existing
SegWitv1 Script.
## Embedding covenant data in P2TR outputs
We can take advantage of the double-commitment structure of taproot outputs
(that is, committing to both a public key and a Merkle tree of scripts) to
compactly encode both the covenant and the state transition rules inside
taproot outputs.
The idea is to replace the internal pubkey Q with a key Q’ obtained by
tweaking Q with the covenant data (the same process that is used to commit
to the root of the taptree). More precisely, if d is the data committed to
the covenant, the covenant-data-augmented internal key Q’ is defined as:
Q’ = Q + int(hashTapCovenantData(Q || h_{data}))G
where h_{data} is the sha256-hash of the covenant data. It is then easy to
prove that the point is constructed in this way, by repeating the
calculation.
If there is no useful key path spend, similarly to what is suggested in
BIP-0341 [5] for the case of scripts with no key path spends, we can use
the NUMS point:
H =
lift_x(0x0250929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0).
TODO: please double check if the math above is sound.
## Changes to Script
The following might be some minimal new opcodes to add for taproot
transactions in order to enable the construction above. This is a very
preliminary proposal, and not yet complete nor correct.
- OP_SHA256CAT: returns the SHA256 hash of the concatenation of the second
and the first (top) element of the stack. (redundant if OP_CAT is enabled,
even just on operands with total length up to 64 bytes)
- OP_CHECKINPUTCOVENANTVERIFY: let x, d be the two top elements of the
stack; behave like OP_SUCCESS if any of x and d is not exactly 32 bytes;
otherwise, check that the x is a valid x-only pubkey, and the internal
pubkey P is indeed obtained by tweaking lift_x(x) with d.
- OP_INSPECTNUMINPUTS, OP_INSPECTNUMOUTPUTS, OP_INSPECTINPUTVALUE and
OP_INSPECTOUTPUTVALUE - opcodes to push number on the stack of
inputs/outputs and their amounts.
- OP_CHECKOUTPUTCOVENANTVERIFY: given a number out_i and three 32-byte hash
elements x, d and taptree on top of the stack, verifies that the out_i-th
output is a P2TR output with internal key computed as above, and tweaked
with taptree. This is the actual covenant opcode.
TODO:
- Many contracts need parties to provide additional data; simply passing it
via the witness faces the problem that it could be malleated. Therefore, a
way of passing signed data is necessary. One way to address this problem
could be to add a commitment to the data in the annex, and add an opcode to
verify such commitment. Since the annex is covered by the signature, this
removes any malleability. Another option is an OP_CHECKSIGFROMSTACK opcode,
but that would cost an additional signature check.
- Bitcoin numbers in current Script are not large enough for amounts.
Other observations:
- OP_CHECKINPUTCOVENANTVERIFY and OP_CHECKOUTPUTCOVENANTVERIFY could have a
mode where x is replaced with a NUMS pubkey, for example if the first
operand is an empty array of bytes instead of a 32 byte pubkey; this saves
about 31 bytes when no internal pubkey is needed (so about 62 bytes for a
typical contract transition using both opcodes)
- Is it worth adding other introspection opcodes, for example
OP_INSPECTVERSION, OP_INSPECTLOCKTIME? See Liquid's Tapscript Opcodes [6].
- Is there any malleability issue? Can covenants “run” without signatures,
or is a signature always to be expected when using spending conditions with
the covenant encumbrance? That might be useful in contracts where no
signature is required to proceed with the protocol (for example, any party
could feed valid data to the bisection protocol above).
- Adding some additional opcodes to manipulate stack elements might also
bring performance improvements in applications (but not strictly necessary
for feasibility).
Remark: the additional introspection opcodes available in Blockstream
Liquid [6] do indeed seem to allow MATT covenants; in fact, the opcodes
OP_CHECKINPUTCOVENANTVERIFY and OP_CHECKOUTPUTCOVENANTVERIFY could be
replaced by more general opcodes like the group {OP_TWEAKVERIFY,
OP_INSPECTINPUTSCRIPTPUBKEY, OP_PUSHCURRENTINPUTINDEX,
OP_INSPECTOUTPUTSCRIPTPUBKEY }.
### Variant: bounded recursivity
In the form described above, the covenant essentially allows fully
recursive constructions (an arbitrary depth of the covenant execution tree
is in practice equivalent to full recursion).
If recursivity is not desired, one could modify the covenants in a way that
only allows a limited depth: a counter could be attached to the covenant,
with the constraint that the counter must be decreased for
OP_CHECKOUTPUTCOVENANTVERIFY. That would still allow arbitrary fraud proofs
as long as the maximum depth is sufficient.
However, that would likely reduce its utility and prevent certain
applications where recursivity seems to be a requirement.
The full exploration of the design space is left for future research.
# Applications
This section explores some of the potential use cases of the techniques
presented above. The list is not exhaustive.
Given the generality of fraud proofs, some variant of every kind of smart
contracts or layer two construction should be possible with MATT covenants,
although the additional requirements (for example the capital lockup and
the challenge period delays) needs to be accurately considered; further
research is necessary to assess for what applications the tradeoffs are
acceptable.
## State channels
A state channel is a generalization of a payment channel where,
additionally to the balance at the end of each channel, some additional
state is stored. The state channel also specifies what are the rules on how
to update the channel’s state.
For example, two people might play a chess game, where the state encodes
the current configuration of the board. The valid state transitions
correspond to the valid moves; and, once the game is over, the winner takes
a specified amount of the channel’s money.
With eltoo-style updates, such a game could be played entirely off-chain,
as long as both parties are cooperating (by signing the opponent’s state
update).
The role of the blockchain is to guarantee that the game can be moved
forward and eventually terminated in case the other party does not
cooperate.
In stateful blockchain, this is simply achieved by publishing the latest
state (Merkleized or not) and then continuing the entire game on-chain.
This is expensive, especially if the state transitions require some complex
computation.
An alternative that avoids moving computations on-chain is the use of a
challenge-response protocol, as sketched above.
Similarly to the security model of lightning channels, an honest party can
always win a challenge under the honest-majority of miners. Therefore, it
is game-theoretically losing to attempt cheating in a channel.
## CoinPool
Multiparty state channels are possible as well; therefore, constructions
like CoinPool [7] should be possible, enabling multiple parties to share a
single UTXO.
## Zero knowledge proofs in L2 protocols
Protocols based on ZK-proofs require the blockchain to be the verifier; the
verifier is a function that takes a zero-knowledge proof and returns
true/false based on its correctness.
Instead of an OP_STARK operator in L1, one could think of compiling the
OP_STARK as the function f in the protocol above.
Note that covenants with a bounded “recursion depth” are sufficient to
express OP_STARK, which in turns imply the ability to express arbitrary
functions within contracts using the challenge protocol.
One advantage of this approach is that no new cryptographic assumptions are
added to bitcoin’s layer 1 even if OP_STARK does require it; moreover, if a
different or better OP_STARK2 is discovered, the innovation can reach layer
2 contracts without any change needed in layer 1.
## Optimistic rollups
John Light recently posted a research report on how Validity Rollups could
be added to bitcoin’s layer 1 [8]. While no exact proposal is pushed
forward, the suggested changes required might include a combination of
recursive covenants, and specific opcodes for validity proof verification.
Fraud proofs are the core for optimistic rollups; exploring the possibility
of implementing optimistic rollups with MATT covenants seems a promising
direction. Because of the simplicity of the required changes to Script,
this might answer some of the costs and risks analyzed in the report, while
providing many of the same benefits. Notably, no novel cryptography needs
to become part of bitcoin’s layer 1.
Optimistic Rollups would probably require a fully recursive version of the
covenant (while fraud proofs alone are possible with a limited recursion
depth).
# Acknowledgments
Antoine Poinsot suggested an improvement to the original proposed covenant
opcodes, which were limited to taproot outputs without a valid key-path
spend.
The author would also like to thank catenocrypt, Antoine Riard, Ruben
Somsen and the participants of the BTCAzores unconference for many useful
discussions and comments on early versions of this proposal.
# References
The core idea of the bisection protocol appears to have been independently
rediscovered multiple times. In blockchain research, it is at the core of
fraud proof constructions with similar purposes, although not focusing on
bitcoin or covenants; see for example:
- Harry Kalodner et al. “Arbitrum: Scalable, private smart contracts.” −
27th USENIX Security Symposium. 2018.
https://www.usenix.org/system/files/conference/usenixsecurity18/sec18-kalodner.pdf
- Jason Teutsch and Christian Reitwiessner. “A scalable verification
solution for blockchains” − TrueBit protocol. 2017.
https://people.cs.uchicago.edu/~teutsch/papers/truebit.pdf
The same basic idea was already published prior to blockchain use cases;
see for example:
Ran Canetti, Ben Riva, and Guy N. Rothblum. “Practical delegation of
computation using multiple servers.” − Proceedings of the 18th ACM
conference on Computer and communications security. 2011.
http://diyhpl.us/~bryan/papers2/bitcoin/Practical%20delegation%20of%20computation%20using%20multiple%20servers.pdf
# Footnotes
[1] - https://btcazores.com
[2] - https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki
[3] -
https://bitcointalk.org/index.php?topic=1427885.msg14601127#msg14601127
[4] - https://vitalik.ca/general/2019/12/26/mvb.html
[5] -
https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki#constructing-and-spending-taproot-outputs
[6] -
https://github.com/ElementsProject/elements/blob/master/doc/tapscript_opcodes.md
[7] - https://coinpool.dev/v0.1.pdf
[8] - https://bitcoinrollups.org
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2023-06-08 00:55:20 CEST

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📅 Original date posted:2021-06-28
📝 Original message:Hi Andrew,
I just have a small suggestion on this proposal.
On Tue, 22 Jun 2021 at 23:29, Andrew Chow via bitcoin-dev <
bitcoin-dev at lists.linuxfoundation.org> wrote:
> | Taproot Leaf Script
> | <tt>PSBT_IN_TAP_LEAF_SCRIPT = 0x15</tt>
> | <tt><control block></tt>
> | The control block for this leaf as specified in BIP 341. The control
> block contains the merkle tree path to this leaf.
> | <tt><script> <8-bit uint></tt>
> | The script for this leaf as would be provided in the witness stack
> followed by the single byte leaf version.
>
So far, all the defined PSBT types had a relatively short keydata (not much
bigger than a couple of pubkeys).
I think that is a desirable property to keep, as it is often a reasonable
assumption that dictionary keys are not very large.
The control block as per BIP 341 can be up to 33 + 32*128 = 4129 bytes long.
Perhaps it would be better to split this into PSBT_IN_TAP_LEAF_SCRIPT
and PSBT_IN_TAP_LEAF_CONTROL_BLOCK (both with no keydata)?
Best,
Salvatore Ingala
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2023-06-08 00:51:21 CEST

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📅 Original date posted:2021-04-12
📝 Original message:Hi Hugo,
First of all, thank you for the impressive work on leading the
standardization efforts!
I believe one ought to more clearly distinguish the "Signer" (as in: one of
the parties in the multisig setup), from the "*Signing device*" (which is
likely a hardware wallet). BSMS defines a "Signer" as "a participating
member in the multisig", therefore a person/entity who is likely using
both a hardware wallet and some BSMS-friendly software wallet (e.g. the
next version of Specter Desktop). It is therefore relevant to discuss which
parts of the BSMS mechanism are implemented in the Signer's software
wallet, and which should be in the Signer's hardware wallet.
>From the discussion, it appears to me that different people might have
different expectations on what the signing device/HWW should do, so I would
like to comment on this point specifically (while I reckon that it mostly
falls within the realm of concerns #4 and #5 of the motivation paragraph,
which are explicitly left out of scope).
I fully agree that a *Signer* must persist the full wallet's description,
and should also create physical backups which include the full descriptor
and the cosigner's information. I would disagree, however, if any standards
were to force *hardware wallets* to persist any substantial amount of state
other than the seed, as I believe that it gives no substantial advantage
over externally stored signed data for many use cases.
The following is the *wallet registration flow* I am currently working on
(in the context of adding support to multisig wallets at Ledger). The goal
is to allow a *Signer* (the person) to persist a multisig setup in its
storage, while achieving a similar level of security you would have if you
were storing it on the hardware wallet itself (note that the following flow
would happen as part of Round 2):
1) The desktop wallet of the requests the HWW to register a new multisig
wallet. The request includes the full multisig wallet description, and some
extra metadata (e.g.: a name to be associated to this multisig wallet).
2) The HWW validates the wallet and verifies it with the user with the
trusted screen (as per BSMS Round 2); on confirmation, it returns a wallet
id (which is a vendor-specific hash of all the wallet description +
metadata) and signature
3) The desktop wallet stores the full wallet description/id/signature.
(Optionally, a backup could be stored elsewhere).
Whenever an operation related to the multisig wallet is required (verifying
a receiving address, or signing a spending transaction), the HWW first
receives and verifies all the data stored at step 3 above (without any user
interaction). Then it proceeds exactly the same way as if it had always
stored the multisig wallet in their own storage. I think this is basically
the same flow Michael Flaxman is suggesting here:
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2021-April/018775.html
(Note that none of this is flow specific to Multisig wallet, as the same
flow would be unchanged for any arbitrary supported script that needs to be
"registered" on a stateless device, and can be generalized for MPC
protocols)
The only caveat I can think of is that the script registration is never
revocable if a signing key derived from the seed is used in step (2), which
might or might not be desirable. One could instead prefer to use a
different signing key that is destroyed if the device is wiped, which would
therefore need to be stored on the device. Note that the only thing that is
lost is the on-device multisig wallet registration, which could easily be
repeated from a backup.
On Sun, 11 Apr 2021 at 19:11, Hugo Nguyen via bitcoin-dev <
bitcoin-dev at lists.linuxfoundation.org> wrote:
> I reiterate that I strongly disagree that going stateless is the direction
> we want to pursue when it comes to multisig.
>
> In a multisig or any type of MPC smart contract, any Signer in the
> contract must know who the other co-Signers are at all times. You can
> choose to do this verification once at setup and persist this info on the
> Signer, or you'd have to re-do the verification for every single
> transaction. There is no other choice.
>
>
Signing the descriptor record is insufficient, while also introducing a
> great deal of complexity. Here are the problems:
> 1) The signature needs to be stored somewhere. Who stores it if it's not
> the Signer itself? What if it gets lost? (If the Signer stores its own
> signature, then the scheme is no longer stateless. You might as well store
> the full descriptor).
>
In the flow I describe above, the desktop wallet would indeed store the
signed descriptor record and wallet metadata. So yes, the *Signer* as in *the
party in the protocol* stores it, but not the signing device*. *The same
method could be used to store state temporarily between round 1 and 2,
where the only *state* on the hardware wallet would be the TOKEN, while
everything else is stored (encrypted and signed) on the Signer's desktop.
> 2) When the signature is "played back" to the Signer, a copy of the
> original descriptor must be included. Who stores the descriptor? What if it
> gets lost? This is an under-appreciated aspect of the stateful approach:
> every participant in the multisig has a full copy of the original contract,
> which adds resilience to the wallet backup / recovery process.
>
"Playing back" the signature and wallet's setup data to the hardware wallet
would indeed happen transparently from the Signer's wallet software. If the
Signer lost this data due to malware, faulty hardware, etc., the user would
indeed have to recover from backup, which seems ok to me.
> 3) Because the full descriptor must be "played back" for every single
> transaction, this means every detail of the contract must be shared again
> and again, indefinitely. Not only does this add overhead (engineering and
> cognitive) to the spending process, it has massive privacy implications,
> since the descriptor contains everything you need to know about the wallets
> and its participants.
>
I agree with some of these concerns, but I observe:
- The engineering overhead in handling externally-stored-signed-data is
paid once, and would mostly fall on the hardware wallet vendor. External
software only cares about storing certain data and sending it back later.
- Storing xpubs/descriptors in the desktop software that interacts with
the HWW is already common practice, and necessary for using any watch-only
wallet.
Summarizing, I argue that the stateful/stateless characteristic of a
hardware wallet does not really affect (modulo some extra work) the ability
to participate in the BSMS ceremony, whose *Signers* should indeed be
stateful.
Some more clarifications on the trust assumptions might help at clarifying
the best possible software/hardware implementation tradeoffs, either in
this or a follow-up BIP.
Best,
Salvatore Ingala
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2023-06-07 20:31:17 CEST

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2023-06-07 20:25:19 CEST

- reply

📅 Original date posted:2020-06-08
📝 Original message:Dear all,
I have been working on some constructions for cryptographic accumulators
that optimise for quick insertion.
As a brief background, an accumulator is a data structure that maintains
compact commitments to a potentially very large (and dynamic) set, while
keeping proofs of membership short. Unsurprisingly, they are getting more
popular, and one notable application in Bitcoin is to create light-weight
full nodes that do not need to store the UTXO set (Utreexo accumulator[1]).
In this work, I focus on additive accumulators that supports adding new
elements, but not removing them. My motivation is to support extending
Script with access to an arbitrarily large portion of the blockchain
history and state (e.g., past blocks, txids, or any more complex state
obtained from them - with all due care). The additional storage and
computation cost for nodes is small, and the cost (in additional bytesize)
for any transaction that wishes to access state committed in the
accumulator should be just slightly bigger than typical Merkle proofs.
I have focused on:
- An accumulator with insertion time O(1) and proof size O(log^2 n)
- A construction with insertion time O(log log n) and proof size O(log n
log log n)
All the performance metrics above are in "number of hashes".
You can find:
- draft writeup:
https://github.com/bigspider/accumulator/blob/master/docs/paper-draft.pdf
- sample python code (only for the first construction at this time):
https://github.com/bigspider/accumulator
While this is still an unfinished work, the ideas in the draft are
hopefully clear enough and easy to understand. I wanted to share it at this
stage as it can benefit from comments to improve the constructions, to
cover any related work or to find potential applications in Bitcoin (e.g.
Script, layer2, side chains, etc).
Best,
Salvatore Ingala
[1] - Thaddeus Dryja, Utreexo: A dynamic hash-based accumulator optimized
for the Bitcoin UTXO set - https://eprint.iacr.org/2019/611.pdf
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