# Security model

# Notations

Drand node: a node that is running the drand daemon and participating to the creation of the randomness. Each drand node have a longterm public key and a private share (after running the setup/resharing phase). The drand network is the set of drand nodes connected with each other.

Relay node: a node that is connected to a drand daemon and exposing a Internet-facing interface allowing to fetch the public randomness. The relay network is the set of relay nodes, partially / potentially connected with each other.

When the type of the node is not specified in the document, it is assumed from the context - most often it refers to a drand node.

Corrupted node: a node who is in the control of an attacker. In this case the attacker has access to all the cryptographic material this node posses as well as the networking authorization. For example, if a relay node is corrupted, an attacker has a direct connection to a drand node.

Offline node: a node who is unreachable from an external point of view. It can be offline from the point of view of another drand node or a relay node. The document tries to clarify in which context when relevant.

Online node: a node which is running the binary (drand or relay depending on the context) and sends packets out to the Internet that are correctly received by the endpoint(s).

# Security model

In drand, there are two phases which do not require the same security assumptions. This section highlights both models and the practical realization or assumptions taken.

# Distributed key generation set up

The DKG protocol model follows the one from the Pedersen's protocol. Gennaro's paper explains the protocol and its assumptions.

Synchronous Network: A packet sent from an online node reaches its destination in a bounded amount of time. Drand realizes this assumption by the usage of timeouts during the DKG protocol.

Synchronized Clocks: All nodes must have roughly synchronized clocks (less than one 1s of offset).

Reliable Broadcast Channel: When a node broadcasts a packet to all other nodes, each other node is guaranteed to receive the same exact packet after some bounded amount of time. This assumption is not strictly realized by drand currently. See DKG attacks section to understand the impact.

Authenticated Channel: Every communication between nodes must be authenticated. Drand achieves this by signing every outgoing DKG packets with a BLS signature on the longterm public key of the sender node.

Public Group: Every node willing to run the DKG must know the group formation before starting the DKG, including the longterm public keys of each node. During the DKG, there might be some nodes offline or misbehaving. The set of nodes that successfully passed the DKG are called the qualified set of nodes (QUAL). Only these nodes have valid shares and are able to produce partial beacons that can be successfully validated with respect to the distributed public key.

Malicious parties: The number of malicious parties is strictly less than 50% of the total number of nodes.

DKG's biasability in signatures: Pedersen's DKG is known to exhibit a weakness in the biasability in the distribution of the distributed private key. However, the same authors (Gennaro et al.) that proved the latter also proved this bias is not relevant in the setting of using the DKG to perform digital signatures, which offers other strong properties - paper. In particular, the paper mentions discrete log based systems. However, it is not yet strictly proven that systems using computational Diffie–Hellman assumptions as required for threshold BLS signatures are secure in the model of Gennaro. However, it is believed that this assumptions holds in this context as well and is being worked on. Note that using threshold BLS signatures as a source of randomness is formally proven secure in this paper from Galindo et al.

# Creation of the group

In the distributed key generation protocol, every participants needs to know the public key of every other participants. To ease up the burden of having to create a list of identities manually, and given the permissioned nature of the network, drand introduces a special trust assumption just for the task of creating the list of public keys (i.e. the group file). This follows the TOFU ("Trust On First Use") approach.

The coordinator is a node that gathers, on the wire, all participants's public keys, and that creates the group configuration and sends it back, signed, to other participants. Therefore, the coordinator is considered fully honest in this phase of the setup. Afterwards, each node starts the DKG by themselves independently, i.e. all participants are considered equal.

# Randomness generation model

Network: The randomness generation protocol do not make any assumption on the network bounds. As soon as packet comes in, node processes them and the chain advances if conditions are there (enough partial beacon and time for a new round).

Synchronized Clocks: All nodes must have roughly synchronized clocks to start the rounds at the same time. The accuracy of the synchronicity between clocks only needs to be at the order the round frequency (order of tens of seconds), which is much higher than the reality of the server's clock (NTP-synced servers achieve offsets of under a second over the globe).

Broadcast channel: The randomness generation models only needs a regular broadcast channel. It does not need to be reliable given the deterministic nature of a partial beacon and the drand chain: for a given round, a given node can only send one valid partial beacon.

Threshold: The threshold is the amount of nodes that must be online and honest at a given time to broadcast their partial signature in order to create the final random beacon. See the attack section to know what are the consequences when that is not the case.

Determinism of the chain: The chain is deterministic with respect to a fresh DKG phase. This means that if an actor collects over a threshold of private shares, it can generate all future chain beacons. When a resharing occurs, the individual shares of each drand node change but the chain remains the same as well. If the same set of nodes perform a new fresh DKG, it will create a new chain from scratch.

Resharing: During a resharing, a drand network A (with threshold tA)creates new shares for a drand network B (with threshold tB) which can be disjoinct from A, such the drand network B is now responsible to continue creating drand beacons, while that the distributed public key doesn't change. For this to happen, there needs to be at least tA nodes from network A and tB nodes online and honest during the resharing. At the end of the protocol, there are going to be at least tB nodes that are qualified and have private shares to generate randomness.

# Attack vectors

# Randomness generation

There can be multiple ways of attacking the drand network during the randomness generation phase, each with different consequences.

# Front running

  1. Passive Adversary Scenario

    An attacker that is able to listen passively on the traffic between nodes (if TLS is not used - which is not a recommended setup) OR that is able to listen to plaintext traffic from the network of a threshold of nodes might be able to see a threshold number of partial beacons before any other honest nodes.

    Consequence: The attacker in such position is able to aggregate the final beacon of the current round before any other drand nodes. However, the advantage should as most as half of the RTT of the slowest of the link between the honest drand nodes. Drand end users should be using the round number as a marker and not the time accuracy which may not be granular enough for some applications.

  2. Active Adversary Scenario

    Assuming the threshold is 50%+1, an adversary tries to "take down" N/2 drand nodes by either running a DoS on those, or block outgoing traffic from these drand nodes.

    Consequence: The adversary becomes the node that can decide whether to aggregate the final beacon of the current round or not, because the rest of the still alive nodes will send their partal beacons to the adversary but the adversary does not send its, effectively becoming the last "missing piece" to create the final beacon. The adversary has the choice to release now or later the final beacon and the adversary can already use the final beacon for the application while the rest of the network does not know it yet.

# DoS the drand network

Scenario: There is a DoS attacks on multiple drand nodes and at least a threshold of honest drand nodes are now considered offline and can't get other's partial beacons. The attack is substained for a duration X. The threshold of nodes to DoS is the threshold from the group configuration as defined during the DKG phase (threshot must strictly be more than 50% of the nodes).

Consequence: The chain halts for as long as the DoS attack is substained on the drand nodes OR for as long as the drand operators didn't move their drand node to another IP / network not under attacked. That means there will not be any new drand beacon for the number of rounds contained in X.

Criteria for success: The DoS attack must bring completely down the network around a threshold of nodes. Completely means there is not a single outgoing partial beacon that leaves the drand's node network. That is a critical distinction to make since, otherwise, a drand node could still collect the partial beacons of under-attacked drand nodes, one by one. As soon as this node gets a threhsold of them, it can reconstruct the final beacon and broadcast it to the relay network.

Defense mechanism: To counter DoS attacks, the drand nodes must block the incoming traffic as early as possible. To achieve that, allowing traffic only from other drand nodes based on their IP addresses seems the most efficient way to deal with DoS attacks.

Potential additional defense mechanism: Assuming the last criteria is not met (it seems to be quite difficult to put in practice), there still needs to be at least one drand nodes that is not under attack to aggregate the partial beacons. To increase the chance of reconstructing the final random beacon from the partial beacons that "leaks" out from drand nodes under attack, it could also be possible to setup aggregator nodes. Such nodes could be under heavy protection, potentially with a more centralized governance, whose job is only collects the different partial beacons and aggregates them to deliver them to the relay network. There could be many such aggregators nodes such that the chance of getting at least one of these received enough threshold beacon drastically increases.

# Corruption of the drand network

Scenario #1: Corruption of less than threshold of nodes

In this scenario, the attacker corrupts less than a threshold of drand nodes. Consequence: The attacker is not able to derive any meaningful information with respect to beacon chain (i.e. he can't derive future beacons). However, it is assumed it has now access to the long term private key of each compromised node.

Scenario #2: Corruption of more than a threshold of nodes

In this scenario, the threat model of drand is now violated and thus is the scenario to avoid at all costs: the attacker corrupts at least a threshold of drand nodes. Consequence: The attacker is now able to derive the whole chain, i.e. it can derive any given random beacon of the chain. The drand randomness is not unpredictable anymore from the point of view of the attacker. However, the drand randomness stays unbiasable: attacker is not able to change the randomness in any way.

Mitigation: Proactive resharing allows both to:

  1. Let a new group of nodes take over the randomness generation, potentially with more nodes and higher threshold.
  2. Refresh shares for nodes that participate in the resharing in the new group: partial beacons created from an old share is not validated by the members of the new group.

Given a "periodical" resharing with more nodes, it makes it harder for the attacker to maintain the grasp on the shares of the drand nodes since he must have continuous control over the drand node itself. If the operator of a corrupted drand node recovers from the attacker's intrusion, after a resharing, the attacker's share is invalid. Moreover, a resharing with more nodes highers the bar for the attacker to attain the second scenario both because of the previous argument and because attacker needs now to corrupts more nodes than in the initial group now.

As such, it is recommended to reshare often, even if between the same nodes, as it creates new shares.

# Distributed key generation ceremony

# DoS attacks

If during the DKG, some nodes are DoS attacked, then these nodes might not be able to receive the deals (shares) in time and / or reply in the second phase in time. Given the necessity of time for achieving the synchronous network assumption, that means these nodes risk getting excluded from the final group that gets shares at the end.

Practical Remediation: At the end of a DKG, the nodes that successfully ran the DKG are the one listed on the final configuration file, noted as "qualified". Given the low frequency of drand nodes having to run a DKG, manual observation of which node is in the final group can lead to decide whether to re-run a DKG / resharing or not.

# Corruption attacks

Scenario 1: An attacker only "controls" less than a threshold of nodes. The attacker can choose the private polynomial used to create the shares. Attacker can influence the distribution of the private share but is believed to not being able to bias the distribution of the randomness later on.

Scenario 2: An attacker controls more than a threshold of nodes during the DKG. This scenario is similar to the scenario 2 for the randomness generation since even before the DKG: attacker can know before the end of the DKG the whole randomness chain (since he can see the honest shares before sending them).

# Broadcast channel assumption

Attacker is at least one node in the group and broadcasts inconsistent shares and public polynomial to different parties. Given drand does not use a reliable broadcast channel, the attacker is able to send any shares over different polynomials for example - see here for one example of such an attack. Note attacker could try to partition the set of honest nodes in two such that each half would have consistent shares within itself but inconsistent with respect to the other half.

Consequence: Shares can be inconsistent with each other, and in such cases, nodes will not be able to verify partial beacons during the randomness generation phase. Another more subtil scenario is that nodes finish the DKG with half of the honest nodes having a distributed public key different than the other half, a "split".

Practical Observation: After a DKG is setup, nodes (1) publish the distributed public key they have and (2) start the randomness generation rounds. The first step enables any third party to verify the distributed public keys are the same (it is in fact sufficient to verify a threshold of them have the same). In (2), the chain will not be able to advance and therefore it becomes clear that the DKG step went wrong. Given the DKG phase is run once in a while, it is reasonable to assume nodes can restart the DKG phase in case things have gone wrong.

Remediation to keep assumption true - (not implemented yet): A practical step towards ensuring non equivocation during the DKG phase is to move to a libp2p pubsub overlay to be close to the reliable broadcast assumption. Indeed, an attacker that would send different public polynomials is likely to end up as not a qualified dealer since honest nodes would relay its packet and find the inconsistency.