Slasher still has mining and is thus a hybrid-mining system that if operating on the bitcoin network would result in $100 million in mining expenses for the DAC each year.
But here we see the difference between proof of work and proof of stake: in proof of work, a miner can only mine on one fork at a time, so the legitimate network will support the legitimate blockchain and not an attacker’s blockchain. In proof of stake, however, as soon as a fork happens miners will have money in both forks at the same time, and so miners will be able to mine on both forks.
This process is solved by Transactions as Proof of Stake because the Coin Days Destroyed by a transaction can only be used on a single chain and cannot be used to confirm all chains.
Suppose the total money supply is M. At block K, an address A with balance B gains a “signing privilege” if sha256(K.hash + A) < 2^256 * 64 * B / M. Essentially, an address has a chance of gaining a signing privilege proportional to the amount of money that it has, and on average 64 signing privileges will be assigned each block.
There exists a 1/65 chance that random addresses will not be available or online to sign a block.
Only a small percentage of users will attempt to MINE under this hybrid system which means that the majority of the hashing power is actually allocated to a minority of the share holders.
At block K+2000, miners with signing privileges from block K have the opportunity to sign the block. The number of signatures is what determines the total length of one blockchain versus another. A signature awards the signer a reward that is substantially larger than the proof of work reward, and this reward will unlock by block K+3000.
More inflation and expenses for securing the network.
Other Comments: This paper shamefully ignores Momentum as a memory hard POW.