Submit only t+1 valid signatures supporting DKG result in phase 14

[pdyraga]

When submitting DKG result in phase 14, it is enough to submit t + 1 supporting signatures, assuming all those signatures were validated in the previous phase and they are all correct. This would allow us to reduce the cost of an on-chain validation.

t stands for threshold <=> minHonest/maxMalicious

[lukasz-zimnoch]

There are two possible solutions here:

1. Off-chain: select only t signatures in phase 14 before submitting DKG result to the contract
2. On-chain: select only t signatures after submitting DKG result to the contract (verifySignatures in KeepRandomBeaconOperator.sol)

I've done some tests in order to check the expected estimated gas cost reduction of both solutions. Average estimated gas costs of submitting DKG result are taken from 5 samples. I've assumed a gas price of 22 Gwei (according to ethgasstation) in order to calculate costs in dollar.

Group size: 5 | Threshold: 3

• Current cost: 490 000 ($2.03)
• Off-chain solution cost: 477 000 ($1.98). Reduces cost by 2.65%
• On-chain solution cost: 485 000 ($2.01). Reduces cost by 1.02%

Group size: 50 | Threshold: 26

• Current cost: 4 650 000 ($19.33)
• Off-chain solution cost: 4 410 000 ($18.34). Reduces cost by 5.16%
• On-chain solution cost: 4 500 000 ($18.71). Reduces cost by 3.23%

[ngrinkevich]

ok some initial findings: looks like the most expensive thing in DKG submission is actually sortition of submitted tickets, even with t signatures we still need to sort all the submitted tickets. I'm investigating whether it's cheaper to spread this cost across all members, i.e. re-sort tickets on every ticket submit + maybe allow submit tickets in batch