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Proof-of-Stake Bitcoin Sidechains

Matt Bell (@mappum)Nomic Hodlings, Inc.

Version 2.1 - June 22, 2021

Introduction

We present a safe, practical design for a Bitcoin sidechain based on the Tendermint consensus protocol, enabling the development of decentralized networks which coordinate to manage reserves of Bitcoin, allowing for custom application code and smart contracts which use Bitcoin as the native currency. We also avoid the long-range attack problem of proof-of-stake networks by periodically timestamping the sidechain on the Bitcoin blockchain, gaining the security of Bitcoin's proof-of-work in addition to the instant finality of BFT consensus protocols.

Our economic design maintains security guarantees while requiring less amounts of outside capital to be locked as collateral than other designs. Additionally, we describe mechanisms which prevent loss of funds when up to 2/3 of the voting power is malicious, and disincentivize malicious behavior even when 100% of the voting power actively censors fraud proofs on the sidechain.

Technical Overview

A sidechain based on our design exists as its own sovereign network, which we will refer to as the sidechain network. The validators of this network become the signatories of the network's reserves, each with a known Bitcoin-compatible public key and an integer amount of "voting power", representing their signatures' weight in the consensus process and in their control of the reserves as governed by the Bitcoin network.

Reserve Wallet

A reserve of Bitcoin is maintained in a decentralized way through use of a special multisig contract. No individuals in the network are given custody of the Bitcoin in reserves, but instead the collective whole cooperates to hold or disburse funds. The validators of the sidechain network become signatories of the reserve, since their signatures are required to control the funds on the Bitcoin blockchain.

To disburse funds from the reserve, more than two-thirds of the signatory set must sign the Bitcoin transaction (weighted by voting power). This is enforced on the Bitcoin blockchain through the "reserve script". Using the "Taproot" family of features on Bitcoin, we can create a reserve script scheme which only requires the on-chain size of a typical single-signature payment input and lets us support up to 1,000 signatories.

Using a Taproot merklized abstract syntax tree-based output (MAST), we can create a spending condition for the funds in reserve which requires either a signature from a specified public key (the "key path"), or an input to a single script out of a specified set of scripts (the "script path").

In our scheme, we derive the key for the key path by aggregating the keys for the smallest set of signatories which sum to greater than 2/3 of the total voting power (we call this subset the "base signatory set"). Aggregation is done using the Musig2 N-of-N aggregated signature algorithm. We also define a single script for the script path, the "fallback script" which is a large weighted multisig script (defined below).

  • Key Path: Aggregated public key composed of base signatory set (largest 2/3 of signatory set by voting power)
  • Script Paths:
    1. Fallback script - Weighted multisig containing all signatory public keys and voting power

Fallback Script

The fallback script is composed as follows:

<pubkey1> OP_CHECKSIG
OP_IF
  <voting_power1>
OP_ELSE
  0
OP_ENDIF

OP_SWAP
<pubkey2> OP_CHECKSIG
OP_IF
  <voting_power2>
  OP_ADD
OP_ENDIF

OP_SWAP
<pubkey...> OP_CHECKSIG
OP_IF
  <voting_power...>
  OP_ADD
OP_ENDIF

OP_SWAP
<pubkeyN> OP_CHECKSIG
OP_IF
  <voting_powerN>
  OP_ADD
OP_ENDIF

<two_thirds_of_total_voting_power>
OP_GREATERTHAN

The validators in this script are given a canonical ordering: descending by their respective amounts of voting power, and when voting power is equal, ordered ascending lexicographically by public key.

The key path is expected to be taken the vast majority of the time as emperically validators on proof-of-stake networks have been shown to have extremely high uptime. However, if only a single signatory of the base signatory set is offline, the group will be unable to produce valid Musig2 signatures for the aggregated public key, in which case the network will fall back to producing standard signatures for the fallback script path.

The higher Bitcoin network fee cost of the fallback script path can possibly be rectified by forcing the offline signatory (or signatories) of the base set to pay for the increased fee out of their stake, also creating a disincentive for preventing the key path spend.

Limits

An input which spends the key path will use about 30 virtual bytes (the same as a typical payment transaction) for any number of signatories. A spend of the fallback script path will have about 3,000 virtual bytes for 100 signatories.

The Bitcoin consensus rules remove script size limits for Taproot MAST scripts, so teh fallback script can technically be any size. However, there is an added consensus rule which limits the size of the Taproot spend's initial stack to 1,000 elements which means a spend of the fallback script can not include more than 1,000 signatures - limiting us to exactly 1,000 signatories. If there is a 1-to-1 mapping of validators of the sidechain network to signatories, then this limit is more than enough as Tendermint-based networks have on the order of 100 validators. The increased signatory set size limit could also possibly be used to increase security by allowing for other staked nodes to participate as signatories even though they are not Tendermint validators.

Signing Process

For both key-path spends and fallback-path spends, producing a signature for the reserve script will involve a process where signatories submit their individual "signature shares" to the sidechain where the state machine will collect them on the state so valid signatures can be assembled by relayers. For the key-path, the signature is complete once all signatories in the base set have submitted a valid signature share. For the fallback-path, the signature is complete once at least two-thirds of the voting power is represented in valid signature shares.

For the Musig2 aggregated signature used in the Taproot script, a first round must happen where signatories commit to nonces used in the signing process, but this can happen separately before there is a message to be signed.

After a timeout, if the base signatory set has not completed its aggregated signature, the entire signatory set can work to produce a spend of the fallback script. While this could also happen in parallel to reduce latency in the fallback case, it may possibly allow malicious or faulty relayers to broadcast valid fallback-path Bitcoin transactions when their key-path alternative was also signed, causing the transaction to incur more Bitcoin network fees than necessary.

Deposits

To move funds into the reserve pool, depositors send a Bitcoin transaction which pays to the reserve script (derived based on the sidechain network's known signatory set), along with a commitment to the desired destination address in the sidechain network ledger.

There are multiple possible deposit schemes:

Simple OP_RETURN Commitment Scheme

This kind of deposit transaction must have exactly two outputs:

  1. A pay-to-taproot that pays to the hash of the reserve script. All the coins to be deposited into the reserve are paid into this output.
  2. A script which commits to a destination address which will receive the pegged Bitcoin on the sidechain network ledger (OP_RETURN <sidechain address bytes>). This output has an amount of zero.

This scheme is simple for relayer nodes to detect since they can simply filter Bitcoin transactions by checking for outputs which pay to the current reserve script.

However, this scheme faces an issue: currently, no Bitcoin wallet or address scheme will construct transactions with this format. In practice, deposits using this scheme will often be made up of two separate transactions: 1) a standard payment transaction which sends from the user's conventional Bitcoin wallet to a key controlled by their sidechain wallet, and 2) a specialized deposit transaction as described above, constructed by the sidechain wallet.

If sidechain transactions became a common occurence in the future, wallets could possibly adopt a new address scheme which is able to instruct the wallet to create a valid sidechain deposit transaction which pays to a given signatory set and commits to a given address.

Script Path Commitment Scheme

In this scheme the deposit transaction doesn't need a special format. The reserve script is modified to contain an extra script in its script path tree, so a wallet can send a valid deposit transaction with a standard BIP173 address.

The commitment would be a standalone script path which can never be spent: OP_RETURN <sidechain address bytes>.

The Taproot construction for the deposit output would then look like the following:

  • Key Path: Aggregated public key composed of base signatory set (largest 2/3 of signatory set by voting power)
  • Script Paths:
    1. Fallback script - Weighted multisig containing all signatory public keys and voting power
    2. Deposit address commitment - An OP_RETURN to indicate where the pegged BTC should be credited on the sidechain

This scheme doesn't have the issues of the formerly mentioned scheme, however without any advance knowlege, it is impossible for relayer nodes to detect that a transaction is a deposit of this type since the reserve output contains a unique hash due to its unique commitment.

To detect the outputs, depositors will need to broadcast their address to relayers off-chain, and relayers will need to store the address for some reasonable period of time (e.g. hours or days). Then, when scanning for deposits, relayers will need to match every Taproot output they see in Bitcoin transactions against all currently valid signatory sets and possible deposit commitment addresses. Even though they may need to match with a very high number of possible deposit outputs, the operation can be made cheap with hash-based data structures (e.g. a hashmap or Bloom Filter).

This scheme is ideal from a user-experience perspective, since a user can generate a deposit address, send to it from their standard Bitcoin wallet, then once the transaction is relayed the funds should show up in their sidechain account - very similar to the process of depositing into a traditional centralized platform. Wallets can also transparently broadcast deposit addresses to relayers in the background without this becoming an explicit extra step.

Timelocked Deposit Reclamation

It may be possible for a deposit to be made to an outdated reserve script - either by the deposit transaction taking a long time to confirm due to underpayment of fees or unexpectedly high load on the Bitcoin network, or possibly by a software issue or user error. Since the sidechain does not honor deposits to outdated reserve scripts (since the signatories are not necessarily available anymore, or may have unbonded their stake), this would by default result in loss of funds.

To solve this, we modify the reserve script slightly to make it possible for the depositor to reclaim the funds after a given time or block height. This is implemented in the Taproot reserve script construction by adding an additional script path, containing the following script:

<locktime> OP_CHECKLOCKTIMEVERIFY OP_DROP
<depositor_pubkey> OP_CHECKSIGVERIFY

Assuming we are using the script path commitment scheme as mentioned above, the Taproot construction for a deposit looks like the following:

  • Key Path: Aggregated public key composed of base signatory set (largest 2/3 of signatory set by voting power)
  • Script Paths:
    1. Fallback script - Weighted multisig containing all signatory public keys and voting power
    2. Deposit address commitment - An OP_RETURN to indicate where the pegged BTC should be credited on the sidechain
    3. Deposit reclamation script - Must be signed by depositor, only valid after timelock has passed

The timelock field should be set to a time or block height in the future significantly past the time it would take for the deposit transaction to be confirmed on the Bitcoin network, relayed to the sidechain network, collected into a checkpoint, and have the checkpoint be confirmed on the Bitcoin network. For example, this could be on the order of 1 day or 144 blocks in the future. The choice of this field can be left up to the depositor, but a minimum value should be enforced by the network to prevent a denial-of-service attack where the depositor reclaims the deposit just before the sidechain signatories are about to broadcast their spend of it (however, this attack is not an issue if the network is able to detect reclaimed deposits and abort spending them).

Note that the funds will still be spendable by the outdated signatory set after the timelock, so the depositor isn't guaranteed to recover their funds and should broadcast a transaction reclaiming the funds as soon as the timelock passes. However, if the stake unbonding period is significantly longer than the time before the reclamation timelock, signatories can be slashed for signing a spend of a deposit which has matured past its timelock. Depositors may also pre-sign a reclamation transaction and send this to "watchtower" nodes who may broadcast it on their behalf for extra assurance that the reclamation happens in a timely fashion.

On-Chain Deposit Process

Once a relayer node detects a valid Bitcoin transaction which has outputs matching the above format, it will broadcast a deposit proof to the sidechain network, which contains:

  • the bytes of the complete deposit transaction data
  • the address bytes committed to in the deposit transaction (when using the script path commitment scheme)
  • the hash of the Bitcoin block which contained the deposit transaction
  • the Merkle branch proving the transaction was included in the Bitcoin block

After the sidechain network receives a valid deposit proof, it will then mint pegged tokens on its ledger, paid out to the destination address committed to by the depositor. These pegged tokens represent claims on the Bitcoin in reserves, which can be transferred, used in smart contracts, or burnt to trigger a withdrawal from the reserves paid to a given destination on the Bitcoin blockchain.

Deposit Finality

Similar to other deposit-accepting systems, such as traditional exchanges and merchants, the sidechain accepts the risk of considering a deposit final (therefore granting pegged tokens) but then having the depositor reverse the transaction through e.g. a reorg of the Bitcoin blockchain. To minimize vulnerability to these kinds of attacks, the system should not consider a deposit final until it has been confirmed sufficiently deep on the Bitcoin blockchain.

Typical deposit-acceptors simply wait for a transaction to be N blocks deep, however this can still leave the system vulnerable to attacks, especially when transfers are allowed (in contrast to merchant platforms, where a double-spend has limited damage since an administrator can simply cancel the attacker's pending orders and remove the balance from their account).

A safe heuristic would be to wait for at least the pending quantity of Bitcoin to be mined for a deposit to progress from "pending" to "final". For instance, if 8 BTC is deposited, and 6.25 BTC is mined per block on mainnet, then waiting for 2 confirmations is a safe depth since a miner would likely consume more costs in a chain reorg than in gains they made from the fraudulent deposit.

The finality heuristic should also not make the assumption that every depositor is a separate party - if deposit confirmations simply depended on the amount of BTC in the UTXO then a Sybil attack would be possible where the deposit is split into many smaller-sized transactions which are all double-spent together. A conservative solution would be to keep a network-wide counter of the total BTC quantity currently being deposited, then scaling confirmation block counts for all deposits regardless of size based on this total, confirming the individual deposits in a FIFO ordering.

Since these very conservative confirmation heuristics create a degraded user experience compared to traditional centralized platforms which often only wait for 1 or 2 block confirmations, we can create a market for speculation on transaction confirmations so that users can have instant access to their funds minus some premium, and nodes with advanced knowlege of the Bitcoin network can earn revenue by modelling the risk of double-spends. We expand on this more in the Deposit Confirmation Derivatives section in the appendix of this document.

Deposits to Outdated Signatory Sets

The signatory set may have changed after a deposit was sent but before confirmation, so deposits to slightly-outdated signatory sets must still be considered valid. If the unbonding period is sufficiently long (on the order of days), we can ensure deposits to stale signatory sets are safe and process them up to some maximum age which is significantly less than the unbonding period.

Deposits which are not processed can be reclaimed based on the timelocked reclamation process, and can still be considered safe until the signatory set is older than the unbonding period. If the unbonding period is significantly longer than the deposit reclamation period then depositors should be able to reclaim without risk.

Checkpoints

Periodically, the network will make transactions on the Bitcoin blockchain which spend from the reserve wallet. These transactions are called checkpoints, and serve the purpose of (1) collecting deposits, (2) updating the reserve script to reflect the latest signatory set, (3) disbursing pending withdrawals, (4) providing a way for light clients to verify the state of the sidechain network secured by the Bitcoin network's proof-of-work, and (5) invalidating the previous "emergency disbursal" transaction (mentioned later in this document).

Each checkpoint is made up of 3 connected Bitcoin transactions, the deposit collection transaction, the checkpoint transaction, and the disbursal transaction.

Deposit Collection Transaction

A deposit collection transaction spends all sufficiently confirmed unspent deposit outputs and joins them into a single output. It has a variable number of inputs, depending on the number of pending deposits. It always has exactly one output, paying all funds minus some fee to the reserve script. If no deposits have been made, no deposit collection transaction will be made.

Checkpoint Transaction

A checkpoint transaction spends from the latest deposit collection output, and the output of the previous checkpoint transaction. It will have the following structure:

Inputs:

  1. The reserve output of the previous checkpoint transaction.
  2. (If there have been deposits) The deposit collection transaction output.

Outputs:

  1. The reserve output, equal to the amount of Bitcoin which are to be held in reserve. Paid to the updated reserve script based on the most recent signatory set.
  2. (If there are pending withdrawals) The disbursal output, equal to the total amount of Bitcoin to be disbursed. Paid to the updated reserve script based on the most recent signatory set.

Disbursal Transaction

Disbursal transactions spend the second output of the most recent checkpoint transaction, and pay to various outputs to settle any pending withdrawals. Each output pays its respective amount to the script specified in its withdrawal request. If no withdrawals are pending, this transaction is not created.

"Follow-the-Money" Proof-of-Stake Verification

A known issue of proof-of-stake consensus is the so-called long-range attack, where a client verifying the blockchain cannot safely sync if their most recent knowledge about the network is out of date (e.g. the validator set they last knew about may now have nothing at stake and would be able to trick the client into accepting an alternate ledger, while suffering no risk of having their stake taken away).

This kind of issue can be solved out-of-band from the proof-of-stake network, e.g. by receiving new knowledge about the network from a trusted third party. However, our Bitcoin checkpointing mechanism allows clients to prevent long-range attacks by utilizing the proof-of-work security of the Bitcoin blockchain.

To securely sync through history to get the latest state of the proof-of-stake sidechain network, a client will first SPV-verify the headers of the Bitcoin blockchain, ensuring they are on the highest-work chain. After this, the client only needs to possess each checkpoint transaction and its Merkle branch proving its membership in the containing Bitcoin block. The client can securely verify that a checkpoint transaction is the successor of another by ensuring it spends the reserve output of the previous checkpoint transaction. By following this chain of checkpoint transactions, the client can ensure that a signatory set is the correct one by deriving its reserve script and comparing to the one in the latest reserve UTXO.

While the three transaction types described (deposit collection, checkpoint, and disbursal) could be combined into one for simplicity and space savings, we separate these for the purpose of reducing the amount of data for a light client to follow the chain of checkpoints. If all deposits and withdrawals were also contained in the checkpoints, the light client would need to download all this data just to sync through history (Bitcoin transaction and not Merklized - all inputs and outputs are required to calculate a transaction's hash). On a large-scale sidechain network, this data could be a significant size to a light-client.

Interval

To keep the signatory set as reflected on the Bitcoin blockchain as close as possible to its current state on the sidechain, a checkpoint should be created every time the signatory set changes by a certain threshold, or on a certain time interval. A faster checkpoint interval has higher Bitcoin fee cost, but also decreases the processing time for deposits and withdrawals. For a large-scale network, we expect the network's transaction fee cost to be negligible compared to its reserves, so it's feasible for the network to aim to produce the ideal of one checkpoint per Bitcoin block.

Relaying

Whenever a new Bitcoin block is mined, or a deposit transaction is broadcast to the Bitcoin network, the data will need to be carried to the sidechain network. Conversely, when a transaction is signed by the signatory set in the checkpointing process, it will need to be carried to the Bitcoin network. This job is done by relayer nodes, which can be any node with knowledge of both networks running software to broadcast the relayed data.

Note that no trust is placed in the relayer nodes and the system operates correctly as long as at least a single relayer node is active. In practice a significant amount of sidechain full nodes will likely opt to run relayers.

Relayed from Bitcoin to sidechain:

  • Bitcoin block mined - header is relayed to sidechain
  • Deposit transaction is confirmed - transaction and Merkle proof are relayed to sidechain

Relayed from sidechain to Bitcoin:

  • Checkpoint signed by signatory set - assembled transaction is broadcasted to Bitcoin network

Security Features

Since sidechain networks may one day hold large reserves of Bitcoin, security needs to be carefully considered. In contrast with many blockchain projects, a security incident resulting in the loss of funds can not be reverted through consensus of the sidechain network, and appealing to Bitcoin governance for a bailout is considered impossible.

Sidechains backed by decentralized custody like the one described in this document inherently suffer from risk of failure, where signatories take the money from the reserve (by collusion among at least 2/3 of the voting power, an endemic software vulnerability, or some other reason). While this mechanism offers many improvements over a centralized party who may act arbitrarily, it makes sense to make efforts toward reducing all possible risk of sidechain failure.

We reduce risk of failure of the sidechain through a staked token which acts as collateral for signatories, an emergency disbursal process which protects against liveness failures, and a stake-locking mechanism which ensures that signatories are economically disincentivized from stealing from the reserves even when they are able to censor fraud proofs on the sidechain.

Staking Token

Native to the sidechain network is a token which may be locked or "staked" to gain voting power as a validator in the network's consensus process in addition to voting power as a signatory in the network's decentralized custody of its Bitcoin reserves. As with all modern proof-of-stake networks, the staked tokens are "slashed" when fraud is proven, for instance in a "double-signing" attack.

In our case, proof of an unexpected signature for a Bitcoin transaction which spends from the reserves is also a slashable offense since signatories should only ever sign transactions which spend the reserves for the network's checkpointing process. This can be proven to the network by submitting a fraud proof transaction which contains the (partially) signed Bitcoin transaction - the network state machine should be able to parse the Bitcoin transaction, verify that it is an unexpected spend of the reserves, and verify that one or more signatories signed it, and then slash those signatories' stake accordingly.

Many designs exist to define how the staking token comes into circulation. In order to maintain a fair and decentralized distribution, for instance, tokens could be minted based on a submitted proof of burned BTC, or to Bitcoin miners as a secondary block reward.

Reserve Demurrage

In common with other decentralized Bitcoin custody projects backed by collateral such as tBTC and XCLAIM, a simple heuristic exists where the signatories must be overcollateralized relative to the quantity of Bitcoin reserves they are managing. We'll call the ratio between the signatories' total staked collateral and the reserves the "collateralization ratio". If the collateralization ratio was less than 1.5, a rational 2/3 subset of signatories would simply steal the reserves (they would benefit even if they lose all of their collateral). However, this requirement is typically very capital inefficient - for a network to safely hold $1B in its reserves, signatories would need to invest more than $1.5B in other outside capital as collateral. This requirement is also assumed to have prevented adoption of these decentralized custody projects in favor of centralized trusted custodian-based projects such as Wrapped Bitcoin.

To reduce the amount of outside capital required to satisfy this security heuristic, our native staking token earns recurring revenue by charging demurrage (negative interest) from all accounts holding claims to BTC on the sidechain. Based on this revenue, the value of the staking token can be valued relative to the size of the reserves based on the discounted cash flow - as more Bitcoin is deposited into the system, the value of the stake should increase proportionally.

The demurrage rate paid by BTC claim-holders is called the reserve rate and is continuously paid to holders of staked staking tokens.

The reserve rate and collateralization ratio can be set by various different schemes, for example:

  • Collateralization-Adjusted Rate: If we assume we have some oracle that gives us the price between the staking token and Bitcoin (e.g. a TWAP automated market maker hosted on the sidechain), we can calculate the collaterization ratio. We can choose some target collateralization ratio, then if the staked value is too low the reserve rate can be increased, and if the staked value is higher than necessary the reserve rate can be decreased (e.g. with a simple control algorithm such as a PID controller).
  • Capped Collateralization: Another scheme would require all Bitcoin claim-holders to choose a maximum reserve rate. Then, if the collateralization ratio falls below its target, BTC-claims would be removed from the network through a forced disbursal, with priority for keeping the claims with higher maximum reserve rates. When the collateralization ratio is in its target range, the effective reserve rate paid can be given by the lowest chosen maximum out of the BTC-claim accounts on the chain.

If these schemes are based simply on the price of the stake, then they are not factoring in liquidity - the stake may be less valuable than the reserves since it cannot be effectively liquidated for a high enough value. Because of this, the collateralization ratio should possibly be higher than 1.5.

It should be noted that any complementary added source of value for the staking token, such as its potential revenue for participation in the consensus process, should decrease the effective reserve rate paid by claim-holders. The reserve rate can be thought of as a fee paid to maintain security (similar to the dilutive block reward in Bitcoin), where the staked signatories of the chain are the ones providing the security and taking on operational risk with their captial.

Emergency Disbursal Process

In the case of an extended liveness failure, all deposited funds would be frozen in place on the Bitcoin blockchain with no recourse other than manually resolving the situation with the signatories.

To protect against this case, as part of the checkpointing process signatories also sign an "emergency disbursal" transaction which spends the entire reserve and pays out each individual claim-holder on the Bitcoin blockchain. Signatories publish these signatures to the network at the time of the checkpoint so that relayers may assemble them.

These transactions are timelocked at some future date, e.g. 2 weeks past the checkpoint, so that the emergency disbursal only happens if a checkpoint has not been created for an extended period of time. Since Bitcoin signatures commit to the inputs they spend, signed emergency disbursals will automatically be invalidated as soon as a newer checkpoint happens since it will spend the same reserve UTXO and become confirmed before the emergency disbursal unlocks.

In the case an emergency disbursal actually happens, the remaining stake becomes valueless and the signatories have all effectively been entirely slashed - so it is expected that the signatories will do everything in their power to prevent extended periods of liveness failure.

Bitcoin has default policies to limit transactions to 100K virtual bytes, so for a large-scale sidechain this would be structured as a tree of multiple transactions in order to scale to contain 1 output per account. Assuming there are 100,000 accounts on the sidechain, and each of these accounts receive a pay-to-pubkey-hash UTXO (34 bytes each), this would require over 3.4M vbytes of transaction data (a small amount of additional space is required for the base transaction fields and the inputs). This structure could then be made up of about 36 transactions, 1 intermediate transaction which directly spends the reserve output and has 35 outputs, and 35 transactions which spend outputs from the intermediate transaction and pay out to many P2PKH outputs (one for each account).

Stake-Locking

On-chain slashing mechanisms rely on honest nodes submitting fraud proofs to the network. However, in a scenario where more than 2/3 of the voting power is executing an attack (e.g. stealing from the reserves), the attackers also control the consensus for the sidechain network and are able to censor fraud proofs to avoid losing any of their stake. To prevent this, we introduce a simple rule where signatories who request to unbond do not receive their stake until after proof of a checkpoint committed to the Bitcoin blockchain which reflects the unbonding in its updated signatory set.

This means that even if the attackers control 100% of the voting power and have the power to censor fraud proofs against themselves, they are unable to receive their stake without actually removing their own control from the reserves on the Bitcoin blockchain. In a scenario where attackers successfully commit an unexpected spend from the reserves, all stake would be forfeited - it would be impossible to unlock as now a valid checkpoint is impossible to produce.

Appendix

Deposit Confirmation Derivatives

Once a deposit transaction on the Bitcoin blockchain is considered final and the depositor has been paid out in BTC-claim tokens, the process cannot be reversed on the sidechain even if the deposit is reversed on the Bitcoin blockchain since the tokens may have been transferred to other parties.

This means the sidechain should only grant BTC-claim tokens when it is entirely certain the Bitcoin transaction cannot be reversed, which is why we use conservative heuristics for considering a deposit final. Because of this, depositors are required to wait for longer confirmation periods than they may be used to on centralized platforms.

To give depositors the ability to access their funds instantly without requiring the network to take on risk of double-spends, we can create a market where traders may speculate on the likelihood of a deposit being confirmed.

To implement this market, we can allow for relaying of deposits which have not yet been confirmed based on the sidechain's finality conditions - including deposits which have not yet been mined in a Bitcoin block at all. Once one of these non-final deposits are relayed, a new token specific to this deposit UTXO is minted to the depsitor, with an equivalent quantity to what will be granted in BTC-claim tokens once the deposit is confirmed. Upon confirmation of the deposit, these tokens are convertible at a 1-to-1 ratio for newly-minted BTC-claim tokens from the network.

In order to access the funds without waiting for the confirmation, a depositor may sell these unconfirmed-deposit tokens to traders who have beliefs about the deposit's likelihood to eventually be confirmed (through data such as the deposit's prevalence in BTC miners' mempools, whether the deposit opts into replace-by-fee, network hashrate conditions indicating likelihood of a reorg, knowlege about the depositor, etc.). Tokens will trade at a market price less than 1, with the difference depending on factors such as perceived risk, the time-value of money until the deposit is confirmed, and liquidity in the unconfirmed deposit market. Depositors are essentially paying a premium for access to instant funds and traders are earning the premium for taking on the double-spend risk.

Liveness Failure Swaps

We can separate BTC-claim tokens into two components, 1) withdrawal-claims which grant the holder the right to withdraw for an equal amount of BTC on the Bitcoin main chain via the disbursal process, and 2) emergency-disbursal-claims which converts to main chain BTC for the holder in the event of a liveness failure via the emergency disbursal. If there exists a market between the two, traders can speculate on the likelihood of an emergency disbursal happening. This market can serve as an important indicator to the rest of the network by measuring the risks of a catastrophic failure.

However, it should be noted that this market will not factor in the risk of theft of the reserves by the signatories since this will spend the reserve output and invalidate the emergency disbursal.

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