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Most proof of work cryptocurrencies, including Bitcoin, have most of their hashrate controlled by the biggest mining pools which significantly decreases decentralization. Would it be theoretically possible to create a proof of work algorithm that distributes the block reward to miners relative to how many shares they have submitted? Basically make it so that the algorithm itself is a decentralized mining pool.

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biggest mining pools which significantly decreases decentralization

Not at all. Pools contribute to decentralization. Without pools, small miners would never be able to mine feasibly, because they would never find a block. No matter how much time they spent mining, no block = no reward. Pools allow them a fair share of block rewards proportional to their work.

Would it be theoretically possible to create a proof of work algorithm that distributes the block reward to miners relative to how many shares they have submitted

It's called P2Pool

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Stratum v2 (a protocol for pooled mining) will improve few things:

  1. Miner will broadcast block instead of mining pool
  2. Signalling bits
  3. Choose own transaction set (if refused by pool, miner will know the reason)

https://danielabrozzoni.github.io/posts/20210221-btc-munich.html

For decentralized payouts, maybe we can use discreet log contracts however this depends on mining pool and difficult to change the protocol so that everyone follows it:

  1. Miner that broadcasted the mined block (Peer 1), Mining pool (Peer 2)
  2. Payout address used in coinbase transaction is 2 of 2 multisig funding address for this DLC
  3. Multiple miners with some oracles provide information about value of the shares miners submitted
  4. This contract is settled based on M of N oracles and specifications used for multiple oracles

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