Re: Proof-of-stake is more decentralized, efficient and secure than PoW- white paper
Exactly. The percentage of mining from other people would drop to zero in a false chain that the attacker generates on his own through grinding. It would have to, by definition, since the attacker must create the entire chain. However, since no one really knows who owns what coins, the network would not be able to tell the difference except that perhaps there is a longer time than usual between blocks.
Ok I think the reason why we had a hard time understanding each other is because you're talking about an entirely different implementation of PoS than that derived from Peercoin.
I guess it's closer to NXT's protocol although I'm not particularly familiar with it.
Explaining in details how NeuCoin's (and Peercoin's) implementation works would be too long to do here but you can take a look at the white paper (sections 3.1 to 3.2 starting page 13) if you want more details.
However, it's not possible to grind through stakes the way you described. Basically, the kernel (which is the equivalent of the stake modifier in Peercoin) is designed in way that prevents you from grinding in a efficient manner. This is explained in details in sections 3.3.3 of the white paper.
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One idea I've seen to prevent these kinds of PoS attacks is Vitalik Buterin's suggestion of using security deposits, but even that doesn't solve the problem
I thought Vitalik's suggestion of using security deposits were linked to the problem of users mining on multiple branches in case of a network fork, not of attackers trying to rewrite history. I should go take another look at his post
If you find some time to read the technical part of the white paper I'd love to get your feedback on the attacks and whether you think there are more efficient attack vectors.