Is it possible to implement such a hash function, and if so, what are your thoughts on this?

Question

Cryptography

The question is probably for people who are well versed in cryptography.
It refers to the fact that the balance of decentralization using proof of work in various blockchains is broken by those who have more iron and can recalculate more hashes per unit of time.
For example, here is the news recently caught on the topic of this problem.
Roughly speaking, a hashing algorithm appears that does not work well on FPGAs, ASICs and GPUs, but over time it is optimized, and hardware developers are not asleep, adjusting it in such a way as to wipe the nose of everyone else who uses the CPU or just weak computing devices.
So here it isis it possible to create such a hash function, in the calculation of which several specially formed participants will participate in the iterative scheme , so that they cannot agree with each other in advance, and at the same time they would all need to perform part of the iterations calculating the common hash + sign the calculated data with your private key, wrap it all up in a common hash, and so that the validity of such a hash can be checked knowing the public keys of the group that jointly calculated this hash?
Thus, the hashrate will greatly depend on the slowest member of the group and the speed of data exchange between them. And accordingly, the reward for the selected valid hash for the block will be distributed not to the pool members, but to those who were formed by a special algorithm into a group to calculate this hash.
Well, then there will be no point in maintaining powerful farms, because. they will simply be idle due to the slowest miners, and then everyone with their smartphone can become an equal miner of such a blockchain network. And such decentralization, it seems to me, should turn out to be more balanced.

Answer 1

Nobody wants to develop such a network, IMHO, or they will disassemble the algorithm for selecting participants in a group and collect only fast ones in one group, and artificial balancing was crying. You can create a function, but you can't apply it normally.

Answer 2

You can look towards the Merkle Tree / signature .

Answer 3

Found interesting developments in this direction: https://github.com/dedis/cothority/wiki