I want to propose a new way of building blockchain without relying on CPU power. It should be as secure as POW. The consensus of the Bitcoin blockchain is the chain that consumed the most CPU power. In POR, the consensus is the chain that represents the most miners. The representation ratio can be quantitively calculated like the difficult factor in POW. Here is how it works.
Instead of one miner mining a block each time, a fixed number (N) of miners are selected to sign each new block using his private key. The miners are selected based on his distance to the previous block hash
Distance = hash ( prev block hash + miners public key ) / ( number of miners Bitcoins )
The first N miners with the shortest distances are selected. The smaller the sum(N distances) the greater the number of miners (total miners coins, to be precise) it can represent - the more miners participate the smaller the sum of the N smallest distances. At the end of every 10 min the block with the smallest sum is the winner. In case of a fork, the chain that has the smallest sum(block distances) is the consensus, since it represents the most miners.
If N (around 100) is selected correctly the POR blockchain is very secure. Like POW it requires more than 50% of the miners (coins) to attack.
For more detail please see
http://txngrid.com/txngrid.pdf