random-beacon

Keep Random Beacon v2

The Keep Network requires a trusted source of randomness for the process of trustless group selection. While the network requires that randomness to function correctly, the source of randomness is itself broadly applicable. This trusted source of randomness takes the form of a BLS Threshold Relay.

Table of Contents

• Overview
• Prior Work
• The Mechanism
  • Group Creation
  • Relay Request and Relay Entry
  • Callbacks
  • Timeouts
  • Inactivity notification
  • Rewards
  • Transaction Incentives
• Parameters
• Build
  • Prerequisites
  • Build contracts
  • Test contracts

Overview

The threshold relay is a way of generating verifiable randomness that is resistant to bad actors both in the relay network and on the anchoring Ethereum blockchain. The basic functioning of the relay is:

• Some number of groups exist in the relay.

• An arbitrary seed value v_s counts as the first entry in the relay.

• A request r_i is dispatched to the chain for a new entry.

• The previous entry v_s is used to choose a group to produce the response to the request.

• v_s is signed by at least a subset of the chosen group members, and the resulting signature is the entry generated in response to the request. It is published to the anchoring blockchain as the entry v_i.

• The new entry v_i may trigger the formation of a new group from the set of all members in the relay.

• A group expires after a certain amount of time.

Prior Work

Smart contracts for the first version of the random beacon are available in solidity-v1 directory. The new version uses the same approach for BLS signatures as v1 but replaces ticket-based group selection with an optimistic sortition pool call. It also redesigns staker rewards and offers a more operator-friendly approach for relay entry timeouts. Last but not least, most parameters for the relay are now governable.

The Mechanism

Group Creation

New groups are created with a fixed frequency of relay requests. Instead of a v1 ticket-based approach for a signing group selection, we use a sortition pool. Group creation start transaction is embedded into relay request transaction and locks a sortition pool. From this moment, no operator can enter or leave the pool. Once a new relay entry appears on the chain, all off-chain clients perform group selection by calling RandomBeacon.selectGroup() view function for free. After determining group members, clients should perform off-chain distributed key generation (DKG). One of the group members submits the result to the chain calling RandomBeacon.submitDkgResult(DKG.Result calldata dkgResult) function. Once the result is submitted, a challenge period starts.

During the challenge period, anyone can notify that the submitted DKG result is malicious by calling RandomBeacon.challengeDkgResult(DKG.Result calldata dkgResult) function. A malicious DKG result may contain corrupted data, group members not selected by the pool, or incorrect supporting signatures. If such malicious result is submitted and successfully challenged, the result submitter gets slashed and the malicious result is immediately discarded. The address which notified about malicious DKG result is rewarded. DKG timeout timer is reset, and group members have another chance to submit a valid result.

Once the challenge period passes, and no valid challenge is reported, the DKG result submitter should mark the DKG result as approved calling RandomBeacon.approveDkgResult(DKG.Result calldata dkgResult). This transaction also unlocks the sortition pool. The submitter receives an ETH reimbursement for both submitDkgResult and approveDkgResult transactions as described in Transaction Incentives section. In case the original submitter does not call the approveDkgResult function within a specific number of blocks, anyone can do that and receive the submitter’s reimbursement.

There is a timeout before which a DKG result should be submitted. In case the DKG result was not submitted before the timeout, anyone can notify about the timed out DKG by calling RandomBeacon.notifyDkgTimeout() function and unlock the sortition pool as part of this transaction. DKG timeout includes the situation when no new relay entry was produced and sortition could not be performed.

Off-chain clients are expected to follow the submission order when submitting DKG result to avoid front-running and minimize the cost, but no ordering is enforced on-chain.

The sortition pool weights operators by their authorized stake amount and allows selecting the same operator to the wallet signing group multiple times. Off-chain DKG protocol executes in the same way as for v1 and inactive/disqualified members during the off-chain protocol are marked as ineligible for rewards for a governable period of time when the DKG result is approved.

Each group created in the system remains active for a certain period of time. A group that expired is no longer selected for any new work. Group expiration is performed in the relay request transaction.

Relay Request and Relay Entry

Authorized addresses can request a new relay entry (random number) by calling RandomBeacon.requestRelayEntry(IRandomBeaconConsumer callbackContract) function and providing an optional callback parameter.

In requestRelayEntry transaction, groups that reached their maximum lifetime are getting expired and one of the remaining active groups is tasked with producing a new relay entry. The off-chain clients are expected to monitor the RelayEntryRequested event. If a client is a part of a picked group they should start the off-chain protocol to sign the previous relay entry producing a new one.

Off-chain clients are expected to follow the submission order when submitting relay entry to avoid front-running and minimize the cost, but no ordering is enforced on-chain. New relay entry should be submitted using RandomBeacon.submitRelayEntry(bytes calldata entry) function.

Callbacks

Random Beacon supports simple, low-gas-budget callbacks from a relay entry submit transaction.

When requesting a relay entry, it is possible to pass an optional address parameter - this is the address of a contract implementing IRandomBeaconConsumer interface that should be called when a new relay entry is submitted to the chain.

Smart contract consuming new relay entry needs to implement IRandomBeaconConsumer interface. The gas limit for __beaconCallback is initially set to 56k gas which is enough to SSTORE new relay entry, SSTORE block height in which the entry was submitted, and to emit an event. Failure in the callback function does not revert the relay entry transaction.

interface IRandomBeaconConsumer {
    /// @notice Receives relay entry produced by Keep Random Beacon. This function
    /// should be called only by Keep Random Beacon.
    ///
    /// @param relayEntry Relay entry (random number) produced by Keep Random
    ///                   Beacon.
    /// @param blockNumber Block number at which the relay entry was submitted
    ///                    to the chain.
    function __beaconCallback(uint256 relayEntry, uint256 blockNumber) external;
}

Timeouts

There are two timeouts for a relay entry to be provided by a group: soft timeout and hard timeout.

Soft Relay Entry Timeout

If no entry was provided within the soft timeout, all operators in the group start bleeding and losing their stake. The bleeding increases linearly from 0 to the slashing amount per operator over time, until the hard timeout is reached or until a relay entry is submitted by the group.

The soft timeout is a governable parameter. This gives a chance to start with more forgiving penalties and increase them over time. In general, the slashing penalty should be proportional to rewards and the frequency of relay requests and associated risk.

Hard Relay Entry Timeout

When the hard timeout is reached, anyone can notify about this fact by calling RandomBeacon.reportRelayEntryTimeout() function and receive a notifier reward . The group which failed to submit a relay entry is terminated, group members are slashed, and if there are still active groups in the beacon, another group is selected and tasked with producing a relay entry for the given relay request.

DKG Timeout

There is a governable timeout for DKG to complete and for the result to be submitted. DKG timeout includes the time it takes to execute off-chain protocol to generate a key, and the time it takes to submit the result. When DKG timeout is exceeded, anyone can call RandomBeacon.notifyDkgTimeout(). This function unlocks the sortition pool and clears up DKG data, but no slashing for DKG timeout is executed and no one is marked as ineligible for rewards.

Inactivity notification

Off-chain clients are free to execute any heartbeat protocol they want to ensure group member key material is still available and nodes are operating properly.

💡

One example of a heartbeat protocol is signing some piece of information every n-th block and making sure this piece of information cannot be used for RandomBeacon.reportUnauthorizedSigning(). Specifically, the signed piece of information can not become msg.sender for reportUnauthorizedSigning call.

Group members can agree to punish members who are permanently inactive and issue an operator inactivity claim. If the required threshold of group members signed the operator inactivity claim, they can submit it to RandomBeacon.notifyOperatorInactivity(Inactivity.Claim calldata claim, uint256 nonce, int32[] calldata groupMembers) function and have the group members who are inactive excluded from the sortition pool rewards for a governable time period.

This approach is theoretically susceptible to group members colluding together, but because a reasonably high number of operators is needed to sign a claim and operators signing the claim receive nothing in return, we consider this approach safe and good enough. An important advantage of this approach is that honest players can decide off-chain when it makes sense to submit an operator inactivity claim and mark someone as ineligible for rewards. For example, marking an operator ineligible for rewards for the next two weeks has a higher impact than prolonging reward ineligibility for 10 minutes for an operator that was already marked as ineligible for rewards. This approach does not increase the gas cost of a happy path and leaves some freedom to group members. They can mark as ineligible operators who turned off their nodes, operators whose nodes never participate in signing because they are misconfigured, or operators who notoriously miss their turn in submitting relay entries.

Rewards

T rewards are allocated to all operators registered in the beacon sortition pool, excluding operators who were marked as ineligible for rewards as a result of being reported by other group members as inactive or as a result of being inactive or disqualified during the DKG. Rewards are allocated proportionally to the operator’s weight in the pool.

Transaction Incentives

There are three types of transactions: Operator-Only, Public-Knowledge, and Punishment.

Operator-Only

Operator-Only transactions are where only the operators have access to the information required to assemble the transaction with the right input parameters.

In order to avoid all operators racing to submit the transaction at the same time, we have an off-chain informal agreement to submit based on the operator’s position in the group (can use the hash of the group’s pubkey).

If the designated operator does not submit their transaction before a timeout expires, the duty moves to the next operator and the group can sign a transaction to mark that operator as inactive. Since there is no slashing reward, and since this transaction can only be submitted by an operator, this transaction is also Operator-Only.

In order to compensate the operator for posting the transaction, the gas spent will be reimbursed by a DAO-funded ETH pool in the same transaction. It is important to note, that the system has a governable cap for the gas price to protect against malicious operators trying to drain the pool (see Reimbursable and ReimbursementPool smart contracts).

Operator-only transactions are submitDkgResult, submitRelayEntry, notifyOperatorInactivity, and approveDkgResult for a certain number of blocks, before a timeout for the original DKG result submitter to call this function elapses.

Public-Knowledge

Public-Knowledge transactions are where anyone has access to the information required to assemble the transaction and the transaction does not lead to punishment.

In order to prevent wasting gas on racing to submit, such transactions need to be executed rarely, and off-chain clients should follow the informal agreement about the submission order.

To compensate these transactions, whoever posts them will have the gas spent reimbursed by a DAO-funded ETH pool in the same transaction.

The only public knowledge transaction is notifyDkgTimeout.

approveDkgResult turns into a public knowledge transaction in case the original submitter has not approved the result before the timeout.

Punishment

Punishment transactions are where anyone has access to the information required to assemble the transaction (like Public-Knowledge) and the transaction leads to slashing.

In these transactions, maintaining system health is more important than optimizing gas via preventing racing, so we offer up bounties in the form of a notifier reward from slashed tokens to whichever submitter submits first. We do not compensate gas. Notification rewards are distributed by Threshold Network TokenStaking contract.

Punishment transactions are: challengeDkgResult, reportRelayEntryTimeout, and reportUnauthorizedSigning.

Parameters

Property Name	Description	Governable	Default Value
DKG
groupSize	Size of a group in the threshold relay.	No	64
groupThreshold	The minimum number of group members needed to interact according to the protocol to produce a signature	No	33
activeThreshold	The minimum number of active and properly behaving group members during the DKG needed to accept the result.	No	58 90% of groupSize
singnatureByteSize	Size in bytes of a single signature produced by operator supporting DKG result.	No	65
resultChallengePeriodLength	Time in blocks during which the submitted DKG result can be challenged.	Yes	11_520 blocks ~48h assuming 15s block time
resultSubmissionTimeout	Time in blocks during which a DKG result is expected to be submitted.	Yes	1280 blocks 64 members * 20 blocks = 1280 blocks
submitterPrecedencePeriodLength	Time in blocks during which only the DKG result submitter is allowed to approve it.	Yes	20 blocks
Groups
groupLifetime	Group lifetime in blocks.	Yes	259_200 blocks ~30 days assuming 15s block time
groupCreationFrequency	The number of relay requests needed to kick off a new group creation process.	Yes	2
Relay Entry
relayEntrySoftTimeout	Time in blocks during which a result is expected to be submitted.	Yes	1280 blocks 64 members * 20 blocks = 1280 blocks
relayEntryHardTimeout	Hard timeout in blocks for a group to submit the relay entry.	Yes	5760 blocks ~24h assuming 15s block time
callbackGasLimit	Relay entry callback gas limit.	Yes	64_000
Slashing
maliciousDkgResultSlashingAmount	Slashing amount for submitting malicious DKG result.	Yes	400e18 400 T
dkgMaliciousResultNotificationRewardMultiplier	Percentage of the staking contract malicious behavior notification reward which will be transferred to the notifier reporting about a malicious DKG result.	Yes	100
relayEntrySubmissionFailureSlashingAmount	Slashing amount for not submitting relay entry.	Yes	400e18 400 T
relayEntryTimeoutNotificationRewardMultiplier	Percentage of the staking contract malicious behavior notification reward which will be transferred to the notifier reporting about relay entry timeout.	Yes	100
unauthorizedSigningSlashingAmount	Slashing amount when an unauthorized signing has been proved.	Yes	400e18 400 T
unauthorizedSigningNotificationRewardMultiplier	Percentage of the staking contract malicious behavior notification reward which will be transferred to the notifier reporting about unauthorized signing.	Yes	100
sortitionPoolRewardsBanDuration	Duration of the sortition pool rewards ban imposed on operators who were inactive/disqualified during off-chain DKG or were voted by the group as inactive for other reasons.	Yes	2 weeks
Random Beacon
dkgResultSubmissionGas	Calculated gas cost for submitting a DKG result. This will be refunded as part of the DKG approval process.	Yes	235_000
dkgResultApprovalGasOffset	Gas that is meant to balance the DKG result approval’s overall cost.	Yes	41_500
notifyOperatorInactivityGasOffset	Gas that is meant to balance the operator inactivity notification cost.	Yes	54_500
relayEntrySubmissionGasOffset	Gas that is meant to balance the relay entry submission cost.	Yes	11_250
authorizedRequesters	Authorized addresses that can request a relay entry.	Yes
Authorization
minimumAuthorization	The minimum authorization amount required so that operator can participate in the Random Beacon.	Yes	40_000e18 40 000 T
authorizationDecreaseDelay	Delay in seconds that needs to pass between the time authorization decrease is requested and the time that request gets approved.	Yes	3_888_000 seconds 45 days
authorizationDecreaseChangePeriod	Time period in seconds before the authorization decrease delay end, during which the authorization decrease request can be overwritten.	Yes	3_888_000 seconds 45 days

Build

Random beacon contracts use Hardhat development environment. To build and deploy these contracts, please follow the instructions presented below.

Prerequisites

Please make sure you have the following prerequisites installed on your machine:

• Node.js >=14.18.2

• Yarn >=1.22.17

Build contracts

To build the smart contracts, install node packages first:

yarn install

Once packages are installed, you can build the smart contracts using:

yarn build

Compiled contracts will land in the build/ directory.

Test contracts

There are multiple test scenarios living in the test directory. You can run them by doing:

yarn test