I am fairly new to the bitcoin and blockchain technology and have recently started reading about it. So my understanding and the question bellow may not be very accurate.
As I have understood so far, proof of work is the basic building block for a bitcoin block chain and because of it, an attacker will have to produce more than 50% of the total compute power (i.e control more than 50% of the nodes) in order to manipulate the block chain by being able to produce longest block chain consistently.
Now bitcoin guys were bit lucky as they were the first and nobody paid attention in there early days. Once bitcoin gathered momentum, number of honest nodes become predominant and system became inherently secure.
But now, how someone can start a new public blockchain (for completely different application) safely ? Because, if a new blockchain is floated with few mining nodes, any attacker can come with more compute nodes and hijack the blockchain as there are small number of honest nodes.