# WorkLock¶

## Overview¶

WorkLock is a novel, permissionless network node setup mechanism, developed at NuCypher, which requires participants to temporarily stake ETH and operate NuCypher network threshold cryptography nodes in order to be allocated NU, the native token of the NuCypher network that enables node operation.

The NuCypher team designed the WorkLock to onboard threshold cryptography nodes to the live NuCypher network using a process that selects participants who are most likely to strengthen the network by committing to staking and running nodes.

The WorkLock begins with an escrow period, during which anyone seeking to operate a NuCypher network threshold cryptography node can send ETH to the WorkLock contract to be temporarily escrowed on-chain. At any time during the escrow period, WorkLock participants can cancel their participation to forgo NU and recoup their escrowed ETH immediately. Once the escrow period closes, the WorkLock contract does not accept more ETH, but it will still accept cancellations during an additional time window. At the end of this cancellation period, the allocation period opens and stake-locked NU are allocated to participants in non-transferable stakes designed for the limited purpose of running threshold cryptography nodes on the live NuCypher network. Stake-locked NU will be allocated at network launch according to the following principles:

• All of the NU held by WorkLock will be allocated to network nodes in non-transferable stakes designed to enable node operation.

• All ETH escrows must be greater than or equal to the minimum allowed escrow.

• For each escrow, the surplus above the minimum allowed escrow is called the bonus; all escrows are composed of a base escrow (fixed minimum) and a bonus escrow (variable amount).

• Each participant will receive at least the minimum amount of staked NU needed to operate a network node.

• Once all participants have been allocated the minimum amount of NU, each participant with a bonus will be allocated a portion of the remaining NU, allocated pro rata across all participants, taking into consideration only their bonus ETH amounts.

• If the resulting NU allocated to a participant is above the maximum allowed NU needed to operate a network node, then such a participant has their escrow partially refunded until the corresponding amount of NU is within the allowed limits for node operation.

Finally, if WorkLock participants use that stake-locked NU to run a node and provide threshold cryptography services on the live network for a minimum of six months, the NU will subsequently unlock and their temporarily escrowed ETH will be returned in full. Participants that fail to successfully run a NuCypher network node for six months of the live network will not receive stake-rewarded NU and their ETH will remain escrowed in the WorkLock contract.

## Hypothetical Escrow Scenarios¶

Note

To reduce complexity, calculations are performed in a step-wise manner which may lead to minor rounding differences in the determined values.

For each scenario, assume the following hypothetical WorkLock properties:

1. WorkLock holds 280,000,000 NU and the minimum escrow is 15 ETH.

2. The minimum amount of NU required to stake is 15,000 NU and the maximum stake size is 4,000,000 NU.

3. The total number of participants is 1000 (including you) with a total of 50,000 ETH escrowed (including your escrow).

4. For our purposes, a whale escrow is an escrow that causes the calculated stake size to be larger than the maximum stake size (4,000,000 NU).

### Scenario 1: Resulting stake size does not exceed maximum stake size (no whale escrows)¶

You submit an escrow of 22 ETH i.e. 15 ETH minimum + 7 bonus ETH.

How many NU would be allocated to your network node?

• Each of the 1000 participants (including you) would be allocated at least the minimum NU to stake = 15,000 NU

• Remaining NU in WorkLock after minimum allocation is

$280,000,000 NU - (15,000 NU \times 1000 \,participants) = 265,000,000 NU$
• Bonus ETH supply (i.e. total ETH not including minimum escrows) is

$50,000 ETH - (15 ETH \times 1000 \,participants) = 35,000 ETH$
• Your bonus portion of the bonus ETH supply is

$\frac{7 ETH}{35,000 ETH} = 0.02\%$
• Your allocation of the remaining NU is

$0.02\% \times 265,000,000 NU= 53,000 NU$

Total NU received = 15,000 NU + 53,000 NU = 68,000 NU

### Scenario 2: Resulting stake size exceeds maximum stake size (1 whale escrow)¶

You submit an escrow of 715 ETH i.e. 15 ETH minimum + 700 bonus ETH.

How many NU would be allocated to your network node?

• Each of the 1000 participants (including you) would be allocated at least the minimum NU to stake = 15,000 NU

• Remaining NU in WorkLock after minimum allocation is

$280,000,000 NU - (15,000 NU \times 1000 \,participants) = 265,000,000 NU$
• Bonus ETH supply (i.e. total ETH not including minimum escrows) is

$50,000 ETH - (15 ETH \times 1000 \,participants) = 35,000 ETH$
• Your bonus allocation of the bonus ETH supply is

$\frac{700 ETH}{35,000 ETH} = 2\%$
• Your allocation of the remaining NU is

$2\% \times 265,000,000 NU= 5,300,000 NU$

However, the total amount of NU to be allocated is 15,000 NU + 5,300,000 NU = 5,315,000 NU which is greater than the maximum stake amount (4,000,000 NU). Therefore, the amount of NU allocated to you needs to be reduced, and some of your bonus ETH refunded.

• Typically the calculation for the NU allocated from the bonus portion is

$\frac{\text{your bonus ETH}}{\text{bonus ETH supply}} \times \text{remaining NU bonus supply}$
• The additional complication here is that refunding bonus ETH reduces your bonus ETH AND the bonus ETH supply since the bonus ETH supply includes the bonus ETH portion of your escrow.

• A more complicated equation arises for the bonus part of the calculation, where x is the refunded ETH:

$\text{stake size} = \frac{\text{(your bonus ETH - x)}}{\text{(bonus ETH supply - x)}} \times \text{remaining NU}$
• Since you will be allocated a 15,000 NU minimum, and the maximum stake size is 4,000,000 NU, the most you can be allocated from the remaining NU is

$4,000,000 NU - 15,000 NU = 3,985,000 NU$
• Therefore using values in the equation above yields

$3,985,000 NU = \frac{700 ETH - x ETH}{35,000 ETH - x ETH} \times 265,000,000 NU$
• Reorganizing the equation

$\begin{split}x &= \frac{700 ETH \times 265,000,000 NU - 35,000 ETH \times 3,985,000 NU}{265,000,000 NU - 3,985,000 NU} \\ &\approx 176.33 ETH\end{split}$
• Therefore, your final bonus escrow is

$700 ETH - 176.33 ETH \approx 523.67 ETH$
• Your portion of the bonus ETH supply is

$\frac{523.67}{(35,000 ETH - 176.33 ETH)} \approx 1.504\%$
• Your allocation of the remaining NU is

$1.504\% \times 265,000,000 NU \approx 3,985,006.46 NU$

Total NU allocated ~ 15,000 NU + 3,985,006.46 NU (rounding) ~ 4,000,000 NU, and refunded ETH ~ 176.33 ETH

### Scenario 3: Resulting stake size exceeds maximum stake size (2 whale escrows)¶

Someone else submitted an escrow of 715 ETH (15 ETH + 700 bonus ETH); we’ll call them whale_1.

You submit an escrow of 785 ETH i.e. 15 ETH minimum + 770 bonus ETH; you are whale_2.

How many NU would be allocated to your network node?

• Each of the 1000 participants (including you) would receive at least the minimum NU to stake = 15,000 NU

• Remaining NU in WorkLock after minimum allocation is

$280,000,000 NU - (15,000 NU \times 1000 \,participants) = 265,000,000 NU$
• Bonus ETH supply (i.e. total ETH not including minimum escrows) is

$50,000 ETH - (15 ETH \times 1000 \,participants) = 35,000 ETH$
• Your portion of the bonus ETH supply is

$\frac{770 ETH}{35,000 ETH} = 2.2\%$
• Your allocation of the remaining NU is

$2.2\% \times 265,000,000 NU= 5,830,000 NU$

However, the total amount of NU to be allocated to receive is 15,000 NU + 5,830,000 NU = 5,845,000 NU which is greater than the maximum stake amount (4,000,000 NU).

• From the previous scenario, the equation for the bonus part of the calculation is as follows, where x is the refunded ETH

$\text{stake size} = \frac{\text{(your bonus ETH - x)}}{\text{(bonus ETH supply - x)}} \times \text{remaining NU}$
• Additionally, there is more than one whale escrow, which would also cause the bonus ETH supply to reduce as well

• Instead the following whale resolution algorithm is employed:

1. Select the smallest whale bonus ETH escrow; in this case 700 ETH from whale_1 < 770 ETH from whale_2

2. Equalize the bonus ETH whale escrows for all other whales (in this case, just whale_2 i.e. just you) to be the smallest whale bonus escrow i.e. 700 ETH in this case

3. Since your bonus ETH escrow is > 700 ETH, you will be refunded

$770 ETH - 700 ETH = 70 ETH$
4. This reduces the resulting bonus ETH supply which will now be

$35,000 ETH - 70 ETH = 34,930 ETH$
5. We now need to calculate the bonus ETH refunds based on the updated bonus ETH supply, and the maximum stake size.

6. Remember that everyone is allocated a 15,000 NU minimum, and the maximum stake size is 4,000,000 NU, so the most that can be allocated to you from the remaining NU is

$4,000,000 NU - 15,000 NU = 3,985,000 NU$
7. Since we have multiple participants, our equation is the following , where n is the number of whale escrows

$x = \frac{\text{(min whale escrow} \times \text{NU supply - eth_supply} \times \text{max stake)}}{\text{(NU supply - n} \times \text{max stake)}}$
8. Plugging in values

$\begin{split}x &= \frac{(700 ETH \times 265,000,000 NU - 34,930 ETH \times 3,985,000 NU)}{(265,000,000 NU - 2 \times 3,985,000 NU)} \\ &\approx 180.15 ETH\end{split}$
• hence each whale gets refunded ~ 180.15 ETH

9. Therefore,

• whale_1 is refunded ~ 180.15 ETH

• whale_2 (i.e. you) is refunded ~ 180.15 ETH + 70 ETH (from Step 3) = 250.15 ETH

10. Based on the refunds

• The bonus escrows for the whales will now be equalized:

• whale_1 bonus = 700 ETH - 180.15 ETH = 519.85 ETH

• whale_2 bonus = 770 ETH - 250.15 ETH = 519.85 ETH

• The updated bonus ETH supply will be

$35,000 ETH - (180.15 ETH + 250.15 ETH) = 34,569.70 ETH$
11. Each whale’s portion of the bonus ETH supply is therefore

$\frac{519.85 ETH}{34,569.70 ETH} \approx 1.504\%$
12. And each whale’s allocation of the remaining NU is

$1.504\% \times 265,000,000 NU = 3,985,600 NU$

Total NU allocated ~ 15,000 NU + 3,985,600 NU (rounding) ~ 4,000,000 NU, and refunded ETH ~ 176.33 ETH

Note

In Scenarios 2 and 3, you will notice that the bonus ETH supply was reduced. This produces a very subtle situation - for previous non-whale participants (escrows in the original bonus ETH supply that did not produce a stake larger than the maximum stake) their escrows remained unchanged, but the bonus ETH supply was reduced. This means that some participants that were not originally whales, may become whales once the bonus ETH supply is reduced since their proportion of the bonus pool increased. Therefore, the whale resolution algorithm described in Scenario 3 may be repeated for multiple rounds until there are no longer any whales. To keep the explanation simple, both Scenarios 2 and 3 ignore such a situation since the calculations become even more complex.