BIP:
Title: ChillDKG: Distributed Key Generation for FROST
Author: Tim Ruffing <[email protected]>
        Jonas Nick <[email protected]>
Status: Draft
License: CC0-1.0
License-Code: MIT
Type: Informational
Created:
Post-History:
Comments-URI:

ChillDKG: Distributed Key Generation for FROST

Abstract

This Bitcoin Improvement Proposal proposes ChillDKG, a distributed key generation protocol (DKG) for use with the FROST Schnorr threshold signature scheme.

Copyright

This document is made available under CC0 1.0 Universal. The accompanying source code is licensed under the MIT license.

Introduction

Motivation

The FROST signature scheme [KG20, CKM21, BTZ21, CGRS23] enables t-of-n Schnorr threshold signatures, in which some threshold t of a group of n participants is required to produce a signature. FROST remains unforgeable as long as at most t-1 participants are compromised and remain functional as long as t honest participants do not lose their secret key material. Notably, FROST can be made compatible with BIP340 Schnorr signatures and does not put any restrictions on the choice of t and n (as long as 1 <= t <= n).¹

As a result, threshold signatures increase both security and availability, enabling users to escape the inherent dilemma between the contradicting goals of protecting a single secret key against theft and data loss simultaneously. Before being able to create signatures, the participants need to generate a shared threshold public key (representing the entire group with its t-of-n policy), together with n corresponding secret shares (held by the n participants) that allow to sign under the threshold public key. This key generation can, in principle, be performed by a trusted dealer who takes care of generating the threshold public key as well as all n secret shares, which are then distributed to the n participants via secure channels. However, the trusted dealer constitutes a single point of failure: a compromised dealer can forge signatures arbitrarily.

An interactive distributed key generation (DKG) protocol session by all participants avoids the need for a trusted dealer. There exist a number of DKG protocols with different requirements and guarantees in the cryptographic literature. Most suitable for the use with FROST is the PedPop DKG protocol [KG20, CKM21, CGRS23] ("Pedersen DKG [Ped92, GJKR07] with proofs of possession"), which, like FROST, does not impose restrictions on the choice of t and n.

But similar to most DKG protocols in the literature, PedPop has strong requirements on the communication channels between participants, which make it difficult to deploy in practice: First, it assumes that participants have secure (i.e., authenticated and encrypted) channels between each other, which is necessary to avoid man-in-the-middle attacks and to ensure confidentiality of secret shares when delivering them to individual participants. Second, PedPop assumes that all participants have access to some external consensus or reliable broadcast mechanism that ensures they have an identical view of the protocol messages exchanged during DKG. This will, in turn, ensure that all participants eventually reach agreement over the results of the DKG, which include not only parameters such as the generated threshold public key but also whether the DKG has succeeded at all.

To understand the necessity of reaching agreement, consider the example of a DKG to set up a 2-of-3 Bitcoin wallet in which two participants are honest but the third participant is malicious. The malicious participant sends invalid secret shares to the first honest participant, but valid shares to the second honest participant. While the first honest participant cannot finish the DKG, the second honest participant will believe that the DKG has finished successfully and thus may be willing to send funds to the resulting threshold public key. But this constitutes a catastrophic failure: Those funds will be lost irrevocably because the single remaining secret share of the second participant will not be sufficient to produce a signature (without the help of the malicious participant).²

To sum up, there is currently no description of PedPop that does not assume the availability of external secure channels and consensus and thus can be turned into a standalone implementation. To overcome these issues, we propose ChillDKG in this BIP. ChillDKG is a variant of PedPop with "batteries included", i.e., it incorporates minimal but sufficient implementations of secure channels and consensus and thus does not have external dependencies. This makes it easy to implement and deploy, and we provide detailed algorithmic specifications in the form of Python code.

Design

We assume a network setup in which participants have point-to-point connections to an untrusted coordinator. This will enable bandwidth optimizations and is common also in implementations of the signing stage of FROST. Participants are identified and authenticated via long-term public keys.

The basic building block of ChillDKG is the SimplPedPop protocol (a simplified variant of PedPop), which has been proven to be secure when combined with FROST [CGRS23]. Besides external secure channels, SimplPedPop depends on an external equality check protocol. The equality check protocol serves as an abstraction of a consensus mechanism: Its only purpose is to check that, at the end of SimplPedPop, all participants have received identical protocol messages.

Our goal is to turn SimplPedPop into a standalone DKG protocol without external dependencies. We then follow a modular approach that removes one dependency at a time. First, we take care of secure channels by wrapping SimplPedPop in a protocol EncPedPop, which relies on pairwise ECDH key exchanges between the participants to encrypt secret shares. Finally, we add a concrete equality check protocol CertEq to EncPedPop to obtain a standalone DKG protocol ChillDKG.

Our equality check protocol CertEq consists of every participant simply collecting a list of valid signatures on the session transcript from all n participants before finalizing the DKG session with some threshold public key as output. The list of signatures, also called a success certificate, can convince any other honest participant (ultimately at the time of a signing request) that the DKG session has indeed been successful. This is sufficient to exclude the catastrophic failure described in the previous section.

As an additional feature of ChillDKG, the DKG outputs for any signing device can be fully recovered from a backup of a single host secret key specific to the device, (the essential parts of) the public transcripts of the DKG sessions, and the corresponding success certificates. To simplify the interface, we combine the transcript data and the session certificate into a single byte string called the recovery data, which is common to all participants and does not need to be kept confidential. Recovering a device that has participated in a DKG session then requires just the device's host secret key and the recovery data, the latter of which can be obtained from any cooperative participant (or the coordinator) or from an untrusted backup provider.

These features make ChillDKG usable in a wide range of applications. As a consequence of this broad applicability, there will necessarily be scenarios in which specialized protocols need less communication overhead and fewer rounds, e.g., when setting up multiple signing devices in a single location.

In summary, we aim for the following design goals:

• Standalone: ChillDKG is fully specified, requiring no external secure channels or consensus mechanism.
• Conditional agreement: If a ChillDKG session succeeds for one honest participant, this participant will be able to convince every other honest participant that the session has succeeded.
• No restriction on threshold: Like the FROST signing protocol, ChillDKG supports any threshold t <= n, including t > n/2 (also called "dishonest majority").
• Broad applicability: ChillDKG supports a wide range of scenarios, from those where the signing devices are owned and connected by a single individual to those where multiple owners manage the devices from distinct locations.
• Simple backups: The capability of ChillDKG to recover devices from the host secret key together with public recovery data avoids the need for secret per-session backups, enhancing user experience.
• 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 malicious coordinator can force the DKG to fail but cannot negatively affect the security of the DKG.
• Per-participant public keys: When ChillDKG is used with FROST, partial signature verification is supported.

In summary, ChillDKG incorporates solutions for both secure channels and consensus and simplifies backups in practice. As a result, it fits a wide range of application scenarios, and due to its low overhead, we recommend ChillDKG even if secure communication channels or a consensus mechanism (e.g., a BFT protocol or a reliable broadcast mechanism) are readily available.

Why Robustness is Not a Goal

As a consequence of its design goals, ChillDKG does not provide robustness, i.e., the protocol is not guaranteed to succeed in the presence of malicious or faulty participants. In fact, a single participant can cause the protocol to fail, either due to malicious intent, software bugs, or unreliable communication links. In such cases, users must investigate and resolve the issue before the DKG can output key material.

When ChillDKG does not terminate successfully, it is not possible to identify the misbehaving participant unless they misbehave in certain trivial ways. While the ability to identify the misbehaving participant, also called identifiable aborts, is desirable, we keep this goal out of scope for simplicity. (TODO: This may change in a future version of the BIP, but there is no guarantee.)

Adding robustness to ChillDKG would require the coordinator to exclude participants that appear unresponsive or faulty, which degrades the setup already from the beginning from t-of-n to (t-1)-of-(n-1). This approach is undesirable in most scenarios, as a malicious coordinator would have the power to exclude participants at will, and even if ChillDKG's design did not include a coordinator and participants had direct communication links to each other, it would be unclear how to achieve robustness in a dishonest majority setting.

Moreover, we believe that it is preferable to err on the side of caution even in the case of benign failures. For example, consider a key generation ceremony for a threshold cold wallet intended to store large amounts of Bitcoin. If it turns out that one of the devices participating appears non-responsive, e.g., due to a loss of network or a software bug, users will typically prefer security to progress, and abort the protocol instead of forcing successful termination of the ceremony by excluding the device from the DKG session. While warnings can be presented to users in this case, users tend to misunderstand and ignore them.

Even in distributed systems with strict liveness requirements, e.g., a system run by a large federation of nodes of which a majority is trusted, what is typically necessary for the liveness of the system is the continued ability to produce signatures. However, the setup of keys is typically performed in a one-time ceremony at the inception of the system (and possibly repeated in large time intervals, e.g., every few months). In other words, what is primarily required to ensure liveness in these applications is a robust signing protocol (and a solution for FROST exists [RRJSS22], and not a robust DKG protocol.

Structure of this Document

Due to the complexity of ChillDKG, we do not provide both a pseudocode specification and a reference implementation. Instead, the BIP includes only a normative reference implementation in Python 3.12 (see python/chilldkg_ref/chilldkg.py), which serves as an executable specification.

To ease understanding of the design and reference code, we provide a technical overview of the internals of ChillDKG in Section "Internals of ChillDKG". For those who would like to use a ChillDKG implementation in their applications and systems, we explain the external interface and usage considerations of ChillDKG in Section "Usage of ChillDKG".

Internals of ChillDKG

This section provides a detailed technical overview of the internals of ChillDKG, which includes as building blocks the DKG protocols SimplPedPop and EncPedPop, and the equality check protocol CertEq. The contents of this section are purely informational and not strictly required to implement or use ChillDKG, and some details present in the normative Python reference implementation are omitted.

We stress that this document does not endorse the direct use of SimplPedPop or EncPedPop as DKG protocols. While SimplPedPop and EncPedPop may in principle serve as building blocks of other DKG protocols (e.g., for applications that already incorporate a consensus mechanism), this requires careful further consideration, which is not in the scope of this document. Consequently, implementations should not expose the algorithms of the building blocks as part of a high-level API, which is intended to be safe to use.

DKG Protocol SimplPedPop

(See python/chilldkg_ref/simplpedpop.py.)

The SimplPedPop protocol has been proposed by Chu, Gerhart, Ruffing, and Schröder [Section 4, CGRS23]. We make the following modifications as compared to the original SimplPedPop proposal:

• Every participant holds a secret seed, from which all required random values are derived deterministically using a pseudorandom function (based on tagged SHA256).
• Individual participants' public keys are added to the output of the DKG. This allows partial signature verification.
• 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.
• The proofs of knowledge are not included in the data for the equality check. This will reduce the size of the backups in ChillDKG.

Our variant of the SimplPedPop protocol then works as follows:

1. Every participant i creates a t-of-n sharing of a random secret scalar using Feldman Verifiable Secret Sharing (VSS), a variant of Shamir Secret Sharing. This involves generating random coefficients a_i[0], ..., a_i[t-1] of a polynomial f_i of degree t-1 in the scalar group:

   f_i(Z) = a_i[0] + a_i[1] * Z + ... a_i[t-1] * Z^(t-1)
   

   Here, f_i(0) = a_i[0] acts as the secret scalar to be shared. Participant i computes a VSS share shares[j] = f_i(j+1) for every participant j (including j = i), which is supposed to be sent to participant j in private. (This will be realized in EncPedPop using encryption.)

   Participant i then sends a VSS commitment, which is a vector com = (com[0], ..., com[t-1]) = (a_i[0] * G, ..., a_i[t-1] * G) of group elements, where G is the base point of the secp256k1 elliptic curve, and a BIP340 Schnorr signature pop on message "i" with secret key a_i[0] to the coordinator. (The Schnorr signature acts as a proof of possession, i.e., it proves knowledge of the discrete logarithm of com[0] = a_i[0] * G. This avoids rogue-key attacks, also known as key cancellation attacks.)

2. Upon receiving coms[j] = (coms[j][0], ..., coms[j][t-1]) and pops[j] from every participant j, the coordinator aggregates the commitments by computing the component-wise sum of all coms[j] vectors except for their first components coms[j][0], which are simply concatenated (because the participants will need them to verify the proofs of possession):

   sum_coms_to_nonconst_terms = (coms[0][1] + ... + coms[n-1][1], ..., coms[0][t-1] + ... + coms[n-1][t-1])
   coms_to_secrets = (coms[0][0], ..., com[n-1][0])
   

   The coordinator sends the vectors coms_to_secrets, sum_coms_to_nonconst_terms, and pops to every participant.

3. Upon receiving coms_to_secrets, sum_coms_to_nonconst_terms, and pops from the coordinator, every participant i verifies every signature pops[j] using message j and public key coms_to_secret[j]. If any signature is invalid, participant i aborts.

   Otherwise, participant i sums the components of coms_to_secrets, and prepends the sum to the sum_coms_to_nonconst_terms vector, resulting in a vector sum_coms. (Assuming the coordinator performed its computations correctly, the vector sum_coms is now the complete component-wise sum of the coms[j] vectors from every participant j. It acts as a VSS commitment to the sum f = f_0 + ... + f_{n-1} of the polynomials of all participants.)

   Participant i computes the public share of every participant j as follows:

   pubshares[j] = (j+1)^0 * sum_coms[0] + ... + (j+1)^(t-1) * sum_coms[t-1]
   

   Let secshare be the sum of VSS shares privately obtained from each participant. Participant i checks the validity of secshare against sum_coms by checking if the equation secshare * G = pubshares[i] holds. (Assuming secshare is the sum of the VSS shares created by other participants, it will be equal to f(i+1).)

   If the check fails, participant i aborts. Otherwise, participant i sets the DKG output consisting of this participant's secret share secshare, the threshold public key threshold_pubkey = sum_coms[0], and all participants' public shares pubshares.

   As a final step, participant i enters a session of an external equality check protocol to verify that all participants agree on the transcript, i.e., common data produced during the session, and that none of them has aborted the session due to an invalid VSS share or an invalid proof of possession. The transcript of SimplPedPop, constructed in a variable eq_input, is simply the concatenation (of serializations) of t and the sum_coms vector. Upon the equality protocol returning successfully, participant i returns successfully with the DKG outputs as computed above. Details of the interface of the equality check protocol will be described further below in Subsection "Background on Equality Checks".

DKG Protocol EncPedPop

(See python/chilldkg_ref/encpedpop.py.)

EncPedPop is a thin wrapper around SimplPedPop that takes care of encrypting the VSS shares so that they can be sent over an insecure communication channel.

As in SimplPedPop, every EncPedPop participant holds a long-term secret seed. Every participant derives from this seed a static, long-term ECDH key pair consisting of a secret decryption key and a public encryption key. It is assumed that every participant has an authentic copy of every other participant's encryption key.

The encryption relies on ephemeral-static ECDH key exchange. Every participant derives from fresh randomness an ephemeral encryption nonce pair consisting of a secret nonce and the corresponding public nonce. This will enable every pair of sending participant i and recipient participant j != i to perform an ECDH key exchange between the ephemeral encryption nonce pair of participant i and the static encryption key pair of participant j in order to establish a shared secret pad pad_ij only known to participants i and j. The derivation of pad_ij from the raw ECDH output uses tagged SHA256 and includes the static encryption key and the index j of the recipient.³

Every participant derives an ephemeral session seed passed down to SimplPedPop from their long-term seed and their public encryption nonce. Moreover, all encryption keys of all participants is included in the derivation to ensure that different sets of participants will have different SimplPedPop sessions, even in the case that the randomness for deriving the encryption nonce pair is accidentally reused.

EncPedPop then works like SimplPedPop with the following differences: Participant i will additionally transmit their public encryption nonce and an encrypted VSS share shares[j] + pad_ij for every other participant j as part of the first message to the coordinator. The coordinator collects all encrypted VSS shares, and computes the sum enc_secshare[j] of all shares intended for every participant j. The coordinator sends all public encryption nonces along with this sum to participant j who stores the sum as enc_secshare, derives the pads pad_0j, ..., pad_nj as described above, and obtains the value secshare = enc_secshare - (pad_0j + ... + pad_nj) required by SimplPedPop.⁴

EncPedPop appends to the transcript eq_input of SimplPedPop the n public encryption nonces, and also all the n static encryption keys to ensure that the participants agree on their identities. The inclusion of the latter excludes man-in-the-middle attacks if Eq authenticates participants, e.g, if the Eq protocol messages are signed under long-term public keys of the participants.

Background on Equality Checks

As explained in the "Motivation" section, it is crucial for security that participants reach agreement over the results of a DKG session. SimplPedPop, and consequently also EncPedPop, ensure agreement during the final step of the DKG session by running an external equality check protocol Eq. The purpose of Eq is to verify that all participants have received an identical transcript, which is a byte string constructed by the respective DKG protocol.

Eq is assumed to be an interactive protocol between the n participants with the following abstract interface: Every participant can invoke a session of Eq with an input value eq_input. Eq may not return at all to the calling participant, but if it returns successfully to some participant, then all honest participants agree on the value eq_input. (However, it may be the case that not all honest participants have established this fact yet.) This means that the DKG session was successful, and the resulting threshold public key can be returned to the participant, who can use it, e.g., by sending funds to some Bitcoin address derived from it.

More formally, Eq must fulfill the following properties [CGRS23]:

• Integrity: If Eq returns successfully to some honest participant, then for every pair of input values eq_input and eq_input' provided by two honest participants, we have eq_input = eq_input'.
• Conditional Agreement: Assuming all messages are delivered eventually, if Eq returns successfully to some honest participant, then Eq will eventually return successfully to all honest participants.

Depending on the application scenario, different approaches may be suitable to implement Eq, such as a consensus protocol already available as part of a federated system or out-of-band communication. For example, in a scenario where a single user employs multiple signing devices to set up a threshold wallet, every device could display its value eq_input (or a hash of eq_input under a collision-resistant hash function) to the user. The user could manually verify the equality of the values by comparing the values shown on all displays, and confirm their equality by providing explicit confirmation to every device, e.g., by pressing a button on every device. Similarly, if signing devices are controlled by different organizations in different geographic locations, agents of these organizations could meet and compare the values. A detailed treatment of these out-of-band methods is out of scope of this document.

DKG Protocol ChillDKG

(See python/chilldkg_ref/chilldkg.py.)

Instead of performing an out-of-band check as the last step of the DKG, ChillDKG relies on a more direct approach: It is a wrapper around EncPedPop, which instantiates the required equality check protocol with a concrete in-band protocol CertEq. CertEq assumes that each participant holds a long-term key pair of a signature scheme, called the host key pair. ChillDKG repurposes the host key pairs as the ECDH key pairs required by EncPedPop,⁵ and it repurposes the host secret key as the seed required by EncPedPop.

ChillDKG requires that all participants have authentic copies of the other participants' host public keys.⁶ Authenticity of the host public keys can be verified through pairwise out-of-band comparisons between every pair of participants. This verification can occur at any time before the DKG session is finalized, in particular before the start of the session.

Equality Check Protocol CertEq

The CertEq protocol is straightforward:⁷ Every participant sends a signature on their input value eq_input to every other participant (via the untrusted coordinator), and expects to receive valid signatures on eq_input from the other participants. A participant terminates successfully as soon as the participant has collected what we call a success certificate, i.e., a full list of valid signatures from all n participants (including themselves).⁸

This termination rule immediately implies the integrity property: Unless a signature has been forged, if some honest participant with input eq_input terminates successfully, then by construction, all other honest participants have sent a signature on eq_input and thus received eq_input as input.

The key insight to ensuring conditional agreement is that any participant terminating successfully obtains a success certificate cert consisting of the collected list of all n signatures on eq_input. This certificate will, by the above termination rule, convince every other honest participant (who, by integrity, has received eq_input as input) to terminate successfully. Crucially, this other honest participant will be convinced even after having received invalid or no signatures during the actual run of CertEq, due to unreliable networks, an unreliable coordinator, or malicious participants signing more than one value.

Thus, the certificate does not need to be sent during a normal run of CertEq, but can instead be presented to other participants later, e.g., during a request to participate in a FROST signing session.

Facilitating Backup and Recovery

ChillDKG constructs a transcript eq_input by appending to the transcript of EncPedPop the vector enc_secshare. This ensures that all participants agree on all encrypted shares, and as a consequence, the entire DKG output of a successful ChillDKG participant can be deterministically reproduced from a per-participant host secret key and the transcript.

This property is leveraged to offer a backup and recovery functionality: ChillDKG outputs a string called recovery data which is the concatenation of the transcript eq_input and the success certificate cert. The recovery data, which is the same for every participant, can be used by any participant together with the host secret key to recover the full output of the DKG session.

Crucially, the recovery data carries proof that the DKG session took place: any recovering participant can extract their own valid signature on the transcript from the success certificate. This valid signature proves that the participant, or more precisely, their former instance, had successfully reached the state at which this signature is sent to the coordinator. In particular, this implies that the proofs of possession from all participants, which are omitted in recovery data for succinctness, had been checked successfully.

In fact, the recovery procedure subsumes the handling of a valid success certificate which is presented to the participant only after the session (in case an invalid or no certificate was received during the session). As a result, ChillDKG does not provide a dedicated method for providing a success certificate after the session, and callers can simply use the recovery functionality instead.

Usage of ChillDKG

The purpose of this section is to provide a high-level overview of the interface and usage of ChillDKG, aimed at developers who would like to use a ChillDKG implementation in their applications and systems.

Detailed API documentation of the reference implementation is provided in Subsection "API Documentation". Developers who would like to implement ChillDKG or understand ChillDKG's internals and reference implementation should also read Section "Internals of ChillDKG".

Use ChillDKG only for FROST

ChillDKG is designed for usage with the FROST Schnorr signature scheme, and its security depends on the specifics of FROST. We stress that ChillDKG is not a general-purpose DKG protocol,⁹ and combining it with other threshold cryptographic schemes, e.g., threshold signature schemes other than FROST, or threshold decryption schemes requires careful further consideration, which is not endorsed or in the scope of this document.

Protocol Parties and Network Setup

There are n >= 2 participants, t of which will be required to produce a signature. Each participant has a point-to-point communication link to the coordinator (but participants do not have direct communication links to each other).

If there is no dedicated coordinator, one of the participants can act as the coordinator.

Inputs and Output

The inputs of a session consist of a long-term host secret key (individual to each participant, not provided by the coordinator) and public session parameters (common to all participants and the coordinator).

If a session ChillDKG returns an output to a participant or the coordinator, then we say that this party deems the protocol session successful. In that case, the DKG output is a triple consisting of a secret share for participating in FROST signing sessions (individual to each participant, not returned to the coordinator), the threshold public key representing the t-of-n policy of the group (common to all participants and the coordinator), and a list of n public shares for verification of individual contributions to a FROST signing session (common to all participants and the coordinator). Moreover, all parties obtain recovery data (common to all participants and the coordinator), whose purpose is detailed in the next subsection.

Backup and Recovery

Losing the secret share or the threshold public key, e.g., after the loss of a participant device, will render the participant incapable of participating in signing sessions. As these values depend on the contributions of the other participants to the DKG session, they can, unlike deterministically derived secret keys [BIP32] as typically used for single-signer Schnorr signatures [BIP340] or MuSig [BIP327], not be rederived solely from the participant's seed.

To facilitate backups of a DKG session, ChillDKG offers the possibility to recover a participant's DKG output from the participant's host secret key and the recovery data of the specific session, As a result, a full backup of a participant consists of the host secret key as well as the recovery data of all DKG sessions the participant has successfully participated in.

Since the recovery data is the same for all participants, if a participant loses the backup of the recovery data of the DKG session, they can request it from any other participants or the coordinator. Moreover, the recovery data contains secrets only in encrypted form and is self-authenticating so that it can, in principle, be stored with an untrusted third-party backup provider. Users should, however, be aware that the session parameters (the threshold and the host public keys) and public parts of the DKG output (the threshold public key and the public shares) can be inferred from the recovery data, which may constitute a privacy issue.

Keeping backups of the secret key accessible and secure is hard (typically similarly hard as keeping the participant devices themselves). As a consequence, it may not be an unreasonable strategy in a threshold setup not to perform backups of host secret keys at all, and simply hope that t honest and working participants will remain available. As soon as one or more participants are lost or broken, a new DKG session can be performed with the lost participants replaced. The obvious drawback of this method is that it will result in a change of the threshold public key, and the application will, therefore, need to transition to the new threshold public key, e.g., funds stored under the current threshold public key need to be transferred to the new key.

Whether to perform backups of host secret keys and how to manage them ultimately depends on the requirements of the application, and we believe that a general recommendation is not useful.

Recovering Stuck Participants

The mere fact that the coordinator or a participant deems a ChillDKG session successful does not imply that other participants deem it successful yet. Indeed, due to failing network links or invalid messages sent by malicious participants, it is possible that a party has deemed the DKG session successful, but others have not (yet) and thus are stuck in the DKG session. In that case, the successful parties can eventually convince the stuck participants to consider the DKG session successful by presenting the recovery data to them. The recovery data can, e.g., be attached to the first request to initiate a FROST signing session.

An important implication of the above is that anyone who uses the threshold public key, and thereby relies on the participants' ability to participate in signing sessions, is responsible for ensuring that the participants have already deemed the DKG session successful, or at least, that the recovery data will be available to convince any stuck participants of the success of the DKG session.

For an example of what could go wrong, assume that some participant deems the DKG session successful and uses the threshold public key by sending funds to some Bitcoin address derived from it. Even though everything looks fine from the perspective of this participant, it is entirely possible that this participant is the only one who has deemed the DKG session successful, and thus (besides the untrusted coordinator) the only one who knows the recovery data. If the recovery data is lost now because this participant's permanent storage crashes, the other participants cannot be convinced to deem the DKG session successful (without the help of the untrusted coordinator) and so the funds will be lost.

Thus, anyone who intends to use the threshold public key should first obtain explicit confirmations from all participants that they have deemed the DKG session successful, which will also imply that all participants have a redundant copy of the recovery data. One simple method of obtaining confirmation is to collect signed confirmation messages from all participants. (TODO Implement this in the code.)

Depending on the application, other methods may be appropriate. For example, in a scenario where a single user employs multiple signing devices in the same room to set up a threshold wallet, the user could check that all n devices signal confirmation via its display. Alternatively, the user could check all n devices when generating a receiving address for the first time, which constitutes the first use of the threshold public key.

If a recovering party (see Backup and Recovery) cannot (re-)obtain confirmations, this simply means they should stop using the threshold public key going forward, e.g., stop sending additional funds to addresses derived from it. (But, in contrast to the bad example laid out above, it will still be possible to spend the funds, and even recovered participants can participate in signing sessions.)

Threat Model and Security Goals

Some participants, the coordinator, and all network links may be malicious, i.e., controlled by an attacker. We expect ChillDKG to provide the following informal security goals when it is used to set up keys for the FROST threshold signature scheme.

If a participant deems a protocol session successful (see above), then this participant is assured that:

• A coalition of at most t - 1 malicious participants and a malicious coordinator cannot forge a signature under the returned threshold public key on any message m for which no signing session with at least one honest participant was initiated. (Unforgeability)¹⁰
• All honest participants who deem the protocol session successful will have correct and consistent protocol outputs. In particular, they agree on the threshold public key, the list of public shares, and the recovery data. Moreover, any t of them have secret shares consistent with the threshold public key.¹¹ This means that any t participants have all the necessary inputs to run FROST signing sessions which produce signatures valid under the threshold public key.
• The success certificate will, when presented to any other (honest) participant, convince that other participant to deem the protocol successful.

Overview of a ChillDKG Session

(See also python/example.py.)

The following figure shows an example execution of the participants and the coordinator. Arrows indicate network messages between the participants. For simplicity, only one participant is depicted; all participants run the identical code and send messages in the same steps.

A participant can run multiple sessions with the same hostseckey, provided that the session state as output from any of the "step" functions is not reused. Multiple sessions may be run concurrently. Whenever a function call fails, the corresponding party will not continue the session.

API Documentation

This subsection is an export of the API documentation generated from the docstrings in the reference implementation (see python/chilldkg_ref/chilldkg.py.)

hostpubkey_gen

def hostpubkey_gen(hostseckey: bytes) -> bytes

Compute the participant's host public key from the host secret key.

The host public key is the long-term cryptographic identity of the participant.

This function interprets hostseckey as big-endian integer, and computes the corresponding "plain" public key in compressed serialization (33 bytes, starting with 0x02 or 0x03). This is the key generation procedure traditionally used in Bitcoin, e.g., for ECDSA. In other words, this function is equivalent to IndividualPubkey as defined in [BIP327]. TODO Refer to the FROST signing BIP instead, once that one has a number.

Arguments:

• hostseckey - This participant's long-term secret key (32 bytes). The key must be 32 bytes of cryptographically secure randomness with sufficient entropy to be unpredictable. All outputs of a successful participant in a session can be recovered from (a backup of) the key and per-session recovery data.

  The same host secret key (and thus the same host public key) can be used in multiple DKG sessions. A host public key can be correlated to the threshold public key resulting from a DKG session only by parties who observed the session, namely the participants, the coordinator (and any eavesdropper).

Returns:

The host public key (33 bytes).

Raises:

• SecretKeyError - If the length of hostseckey is not 32 bytes.

SessionParams Tuples

class SessionParams(NamedTuple):
    hostpubkeys: List[bytes]
    t: int

A SessionParams tuple holds the common parameters of a DKG session.

Attributes:

• hostpubkeys - Ordered list of the host public keys of all participants.

• t - The participation threshold t. This is the number of participants that will be required to sign. It must hold that 1 <= t <= len(hostpubkeys) and t <= 2^32 - 1.

  Participants must ensure that they have obtained authentic host public keys of all the other participants in the session to make sure that they run the DKG and generate a threshold public key with the intended set of participants. This is analogous to traditional threshold signatures (known as "multisig" in the Bitcoin community), [BIP383], where the participants need to obtain authentic extended public keys ("xpubs") from the other participants to generate multisig addresses, or MuSig2 [BIP327], where the participants need to obtain authentic individual public keys of the other participants to generate an aggregated public key.

  All participants and the coordinator in a session must be given an identical SessionParams tuple. In particular, the host public keys must be in the same order. This will make sure that honest participants agree on the order as part of the session, which is useful if the order carries an implicit meaning in the application (e.g., if the first t participants are the primary participants for signing and the others are fallback participants). If there is no canonical order of the participants in the application, the caller can sort the list of host public keys with the KeySort algorithm specified in BIP327 to abstract away from the order.

params_id

def params_id(params: SessionParams) -> bytes

Return the parameters ID, a unique representation of the SessionParams.

In the common scenario that the participants obtain host public keys from the other participants over channels that do not provide end-to-end authentication of the sending participant (e.g., if the participants simply send their unauthenticated host public keys to the coordinator, who is supposed to relay them to all participants), the parameters ID serves as a convenient way to perform an out-of-band comparison of all host public keys. It is a collision-resistant cryptographic hash of the SessionParams object. As a result, if all participants have obtained an identical parameters ID (as can be verified out-of-band), then they all agree on all host public keys and the threshold t, and in particular, all participants have obtained authentic public host keys.

Returns:

• bytes - The parameters ID, a 32-byte string.

Raises:

• FaultyParticipantOrCoordinatorError - If hostpubkeys[i] is not a valid public key for some i, which is indicated in the exception.
• DuplicateHostpubkeyError - If hostpubkeys contains duplicates.
• ThresholdError - If 1 <= t <= len(hostpubkeys) does not hold.
• OverflowError - If t >= 2^32 (so t cannot be serialized in 4 bytes).

DKGOutput Tuples

class DKGOutput(NamedTuple):
    secshare: Optional[bytes]
    threshold_pubkey: bytes
    pubshares: List[bytes]

Holds the outputs of a DKG session.

Attributes:

• secshare - Secret share of the participant (or None for coordinator)
• threshold_pubkey - Generated threshold public key representing the group
• pubshares - Public shares of the participants

participant_step1

def participant_step1(hostseckey: bytes, params: SessionParams, random: bytes) -> Tuple[ParticipantState1, ParticipantMsg1]

Perform a participant's first step of a ChillDKG session.

Arguments:

• hostseckey - Participant's long-term host secret key (32 bytes).
• params - Common session parameters.
• random - FRESH random byte string (32 bytes).

Returns:

• ParticipantState1 - The participant's session state after this step, to be passed as an argument to participant_step2. The state must not be reused (i.e., it must be passed only to one participant_step2 call).
• ParticipantMsg1 - The first message to be sent to the coordinator.

Raises:

• ValueError - If the participant's host public key is not in argument hostpubkeys.
• SecretKeyError - If the length of hostseckey is not 32 bytes.
• FaultyParticipantOrCoordinatorError - If hostpubkeys[i] is not a valid public key for some i, which is indicated in the exception.
• DuplicateHostpubkeyError - If hostpubkeys contains duplicates.
• ThresholdError - If 1 <= t <= len(hostpubkeys) does not hold.
• OverflowError - If t >= 2^32 (so t cannot be serialized in 4 bytes).

participant_step2

def participant_step2(hostseckey: bytes, state1: ParticipantState1, cmsg1: CoordinatorMsg1) -> Tuple[ParticipantState2, ParticipantMsg2]

Perform a participant's second step of a ChillDKG session.

Arguments:

• hostseckey - Participant's long-term host secret key (32 bytes).
• state1 - The participant's session state as output by participant_step1.
• cmsg1 - The first message received from the coordinator.

Returns:

• ParticipantState2 - The participant's session state after this step, to be passed as an argument to participant_finalize. The state must not be reused (i.e., it must be passed only to one participant_finalize call).
• ParticipantMsg2 - The second message to be sent to the coordinator.

Raises:

• SecKeyError - If the length of hostseckey is not 32 bytes. FIXME

• FaultyParticipantOrCoordinatorError - If cmsg1 is invalid. This can happen if another participant has sent an invalid message to the coordinator, or if the coordinator has sent an invalid cmsg1.

  Further information is provided as part of the exception, including a hint about which party might be to blame for the problem. The hint should not be trusted and should be used only for debugging. In particular, the hint may point at the wrong party, e.g., if the coordinator is malicious or network connections are unreliable, and as a consequence, the caller should not conclude that the party hinted at is malicious.

• UnknownFaultyPartyError - TODO

participant_finalize

def participant_finalize(state2: ParticipantState2, cmsg2: CoordinatorMsg2) -> Tuple[DKGOutput, RecoveryData]

Perform a participant's final step of a ChillDKG session.

If this function returns properly (without an exception), then this participant deems the DKG session successful. It is, however, possible that other participants have received a cmsg2 from the coordinator that made them raise a SessionNotFinalizedError instead, or that they have not received a cmsg2 from the coordinator at all. These participants can, at any point in time in the future (e.g., when initiating a signing session), be convinced to deem the session successful by presenting the recovery data to them, from which they can recover the DKG outputs using the recover function.

Warning: Changing perspectives, this implies that even when obtaining a SessionNotFinalizedError, you MUST NOT conclude that the DKG session has failed, and as a consequence, you MUST NOT erase the hostseckey. The underlying reason is that some other participant may deem the DKG session successful and use the resulting threshold public key (e.g., by sending funds to it). That other participant can, at any point in the future, wish to convince us of the success of the DKG session by presenting recovery data to us.

Arguments:

• state2 - The participant's state as output by participant_step2.

Returns:

• DKGOutput - The DKG output.
• bytes - The serialized recovery data.

Raises:

• SessionNotFinalizedError - If finalizing the DKG session was not successful from this participant's perspective (see above).

participant_blame

def participant_blame(blame_state: ParticipantBlameState, cblame: CoordinatorBlameMsg) -> NoReturn

Perform a participant's blame step of a ChillDKG session. TODO

coordinator_step1

def coordinator_step1(pmsgs1: List[ParticipantMsg1], params: SessionParams) -> Tuple[CoordinatorState, CoordinatorMsg1]

Perform the coordinator's first step of a ChillDKG session.

Arguments:

• pmsgs1 - List of first messages received from the participants.
• params - Common session parameters.

Returns:

• CoordinatorState - The coordinator's session state after this step, to be passed as an argument to coordinator_finalize. The state is not supposed to be reused (i.e., it should be passed only to one coordinator_finalize call).

Raises:

• FaultyParticipantOrCoordinatorError - If hostpubkeys[i] is not a valid public key for some i, which is indicated in the exception.
• DuplicateHostpubkeyError - If hostpubkeys contains duplicates.
• ThresholdError - If 1 <= t <= len(hostpubkeys) does not hold.
• OverflowError - If t >= 2^32 (so t cannot be serialized in 4 bytes).

coordinator_finalize

def coordinator_finalize(state: CoordinatorState, pmsgs2: List[ParticipantMsg2]) -> Tuple[CoordinatorMsg2, DKGOutput, RecoveryData]

Perform the coordinator's final step of a ChillDKG session.

Arguments:

• state - The coordinator's session state as output by coordinator_step1.
• pmsgs2 - List of second messages received from the participants.

Returns:

• CoordinatorMsg2 - The second message to be sent to all participants.
• DKGOutput - The DKG output. Since the coordinator does not have a secret share, the DKG output will have the secshare field set to None.
• bytes - The serialized recovery data.

Raises:

• SessionNotFinalizedError - If finalizing the DKG session was not successful from the perspective of the coordinator. In this case, it is, in principle, possible to recover the DKG outputs of the coordinator using the recovery data from a successful participant, should one exist. Any such successful participant would need to have received messages from other participants via a communication channel beside the coordinator (or be malicious).

coordinator_blame

def coordinator_blame(pmsgs: List[ParticipantMsg1]) -> List[CoordinatorBlameMsg]

Perform the coordinator's blame step of a ChillDKG session. TODO

recover

def recover(hostseckey: Optional[bytes], recovery_data: RecoveryData) -> Tuple[DKGOutput, SessionParams]

Recover the DKG output of a session from the hostseckey and recovery data.

This function serves two different purposes:

1. To recover from a SessionNotFinalizedError after obtaining the recovery data from another participant or the coordinator (see participant_finalize).
2. To reproduce the DKG outputs on a new device, e.g., to recover from a backup after data loss.

Arguments:

• hostseckey - This participant's long-term host secret key (32 bytes) or None if recovering the coordinator.
• recovery_data - Recovery data from a successful session.

Returns:

• DKGOutput - The recovered DKG output.
• SessionParams - The common parameters of the recovered session.

Raises:

• InvalidRecoveryDataError - If recovery failed due to invalid recovery data or recovery data that does not match the provided hostseckey.

FaultyParticipantOrCoordinatorError Expection

class FaultyParticipantOrCoordinatorError(ProtocolError)

Raised when another participant appears faulty.

This is raised when another participant appears to have sent an invalid protocol message. This error does not necessarily imply that the suspected participant is faulty. It is always possible that the coordinator is faulty instead and has misrepresented the suspected particant's protocol messages. It is also possible that protocol message was simply not transmitted correctly.

Attributes:

• participant int - Index of the suspected participant.

FaultyCoordinatorError Expection

class FaultyCoordinatorError(ProtocolError)

Raised when the coordinator appears faulty.

This is raised when the coordinator appears to have sent an invalid protocol message. This error does not necessarily imply that the coordinator is faulty. It is also possible that a protocol message from the coordinator was simply not transmitted correctly.

UnknownFaultyPartyError Expection

class UnknownFaultyPartyError(ProtocolError)

TODO

Changelog

To help the reader understand updates to this document, we attach a version number that resembles "semantic versioning" (MAJOR.MINOR.PATCH). The MAJOR version is incremented if changes to the BIP are introduced that are incompatible with prior versions. An exception to this rule is MAJOR version zero (0.y.z) which is for development and does not need to be incremented if backwards-incompatible changes are introduced. The MINOR version is incremented whenever the inputs or the output of an algorithm changes in a backward-compatible way or new backward-compatible functionality is added. The PATCH version is incremented for other noteworthy changes (bug fixes, test vectors, important clarifications, etc.).

• 0.1.0 (2024-07-08): Publication of draft BIP on the bitcoin-dev mailing list

Acknowledgments

We thank Lloyd Fournier for their contributions to this document.

Footnotes

1. While t = n and t = 1 are in principle supported, simpler alternatives are available in these cases. In the case of t = n, using a dedicated n-of-n multi-signature scheme such as MuSig2 (see BIP327) instead of FROST avoids the need for an interactive DKG. The case t = 1 can be realized by letting one participant generate an ordinary BIP340 key pair and transmitting the key pair to every other participant, who can check its consistency and then simply use the ordinary BIP340 signing algorithm. Participants still need to ensure that they agree on a key pair. A detailed specification is not in the scope of this document. ↩

2. A very similar attack has been observed in the implementation of a resharing scheme [AS20, Section 3]. ↩

3. This implements a multi-recipient multi-key key encapsulation mechanism (MR-MK-KEM) secure under the static Diffie-Hellman assumption [Theorem 2, PPS14]. ↩

4. We use additively homomorphic encryption to enable the coordinator to aggregate the shares, which saves communication. Note that this emulates a Dining Cryptographer's Network [Cha88], though anonymity is an anti-feature in our case: If a SimplPedPop participant receives an invalid secshare, it is impossible for this participant to identify another participant who has sent wrong contributions, even if the coordinator is trusted. This is the price we pay for the communication optimization. ↩

5. Schnorr signatures and ECDH-based KEMs are known to be jointly secure [Theorem 2, DLPSS11] under the combination of the gap-DH and gap-DL assumptions, and this result can be adapted to the MR-KEM used in EncPedPop. ↩

6. No protocol can prevent man-in-the-middle attacks without this or a comparable assumption. Note that this requirement is implicit in other schemes as well. For example, setting up a multi-signature wallet via non-interactive key aggregation in MuSig2 [BIP327] also requires the assumption that all participants have authentic copies of each other's individual public keys. ↩

7. CertEq can be viewed as a signed variant of the Goldwasser-Lindell echo broadcast protocol [GL05, Protocol 1], or alternatively, as a unanimous variant of Signed Echo Broadcast [Rei94, Section 4], [CGR11, Algorithm 3.17].) ↩

8. Abstractly, the required primitive is a multi-signature scheme, i.e., n participants signing the same message eq_input. We have chosen the naive scheme of collecting a list of n individual signatures for simplicity. Other multi-signatures schemes, e.g., MuSig2 [BIP327] or a scheme based on Schnorr signature half aggregation [Halfagg-BIP-Draft, CGKN21, CZ22], could be used instead to reduce the size of the success certificate. These methods are out of scope of this document. (TODO: Half-agg may be included in a future version of the BIP, but no guarantee.) ↩

9. As a variant of Pedersen DKG, ChillDKG does not provide simulation-based security GJKR07. Roughly speaking, if ChillDKG is combined with some threshold cryptographic scheme, the security of the combination is not automatically implied by the security of the two components. Instead, the security of every combination must be analyzed separately. The security of the specific combination of SimplPedPop (as the core building block of ChillDKG) and FROST has been analyzed CGRS23. ↩

10. See Chu, Gerhart, Ruffing, and Schröder [Definition 3, CGRS23] for a formal definition. ↩

11. See Ruffing, Ronge, Jin, Schneider-Bensch, and Schröder [Definition 2.5, RRJSS22] for a formal definition. ↩