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nit: Don't use citation tags as words
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README.md

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@@ -122,10 +122,10 @@ which is common to all participants and does not need to be kept confidential.
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Recovering a device that has participated in a DKG session then requires just the device's host secret key and the recovery data,
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the latter of which can be obtained from any cooperative participant (or the coordinator) or from an untrusted backup provider.
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ChillDKG outputs a threshold public key that can be safely used in [[BIP 341](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki)] Taproot outputs.
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In contrast, a standard PedPop implementation would allow a malicious participant to secretly embed a Taproot commitment to a BIP 341 script path within the threshold public key.
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ChillDKG outputs a threshold public key that can be safely used in Taproot outputs [[BIP 341](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki)].
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In contrast, a standard PedPop implementation would allow a malicious participant to secretly embed a Taproot commitment to a script path within the threshold public key.
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If such a key was used directly in a Taproot output, the malicious participant could spend the output through their hidden script path, bypassing the requirement for `t - 1` additional signatures.
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While BIP 341 outlines special precautions for using threshold public keys generated by standard PedPop, ChillDKG eliminates this vulnerability entirely, providing built-in protection against accidental misuse.
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While [BIP 341](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki) outlines special precautions for using threshold public keys generated by standard PedPop, ChillDKG eliminates this vulnerability entirely, providing built-in protection against accidental misuse.
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If a ChillDKG session fails due to the participants or the coordinator deviating from the protocol,
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any aborting party will be able to identify and blame a single party responsible for the failure
@@ -144,7 +144,7 @@ In summary, we aim for the following design goals:
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- **Simple backups**: ChillDKG allows recovering the DKG output using the host secret key and common recovery data shared among all participants and the coordinator. This eliminates the need for session-specific backups, simplifying user experience.
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- **Untrusted coordinator**: Like FROST, ChillDKG uses a coordinator that relays messages between the participants. This simplifies the network topology, and the coordinator additionally reduces communication overhead by aggregating some of the messages. A faulty coordinator can force the DKG to fail but cannot negatively affect the security of the DKG.
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- **Per-participant public shares**: ChillDKG supports partial signature verification in FROST signing sessions.
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- **Taproot-safe threshold public key**: ChillDKG prevents malicious participants from embedding a hidden [[BIP 341]](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki) Taproot commitment to a script path in the threshold public key.
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- **Taproot-safe threshold public key**: ChillDKG prevents malicious participants from embedding a hidden Taproot commitment to a script path [[BIP 341]](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki) in the threshold public key.
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- **Blame functionality**: If a ChillDKG session aborts, it is possible to identify and blame a single party responsible for the failure (assuming the network, and, depending on the circumstances, the coordinator, is reliable).
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In summary, ChillDKG incorporates solutions for both secure channels and consensus and simplifies backups in practice.
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- Every participant holds a secret seed, from which all required random values are derived deterministically using a pseudorandom function (based on tagged hashes as defined in [[BIP 340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki)]).
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- Individual participants' public shares are added to the output of the DKG. This allows partial signature verification.
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- The participants send VSS commitments to an untrusted coordinator instead of directly to each other. This lets the coordinator aggregate VSS commitments, which reduces communication costs. Nevertheless, if a session fails, participants are able to investigate who provided invalid secret shares by asking the coordinator for the other participants' individual contributions to their public share.
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- To prevent a malicious participant from embedding a [[BIP 341](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki)] Taproot script path in the threshold public key, the participants tweak the VSS commitment such that the corresponding threshold public key has an unspendable BIP script path.
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- To prevent a malicious participant from embedding a Taproot script path [[BIP 341](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki)] in the threshold public key, the participants tweak the VSS commitment such that the corresponding threshold public key has an unspendable script path.
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- ~The proofs of knowledge are not included in the data for the equality check. This will reduce the size of the backups in ChillDKG.~ (TODO: This will be fixed in an updated version of the paper.)
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Our variant of the SimplPedPop protocol then works as follows:
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Participant `i` blames this participant `j` .
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Otherwise, i.e., in the successful case that the equation `secshare * G = pubshare` holds, participant `i` proceeds as follows.
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In order to obtain a threshold public key with an unspendable [[BIP 341](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki)] Taproot script path,
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In order to obtain a threshold public key with an unspendable Taproot script path [[BIP 341](https://github.com/bitcoin/bips/blob/master/bip-0341.mediawiki)],
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participant `i` computes a Taproot tweak `tweak` for an unspendable script path,
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and adds the point `tweak * G` to `sum_coms[0]`, resulting in a new VSS commitment called `sum_coms_tweaked`.
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Participant `i` computes the public share of every participant as

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