Quote from: kushti on January 14, 2015, 03:53:27 PM

To summarize the discussion, known claimed attacks on proof-of-stake distributed consensus algorithm(and concrete implementations) at the moment:

1. Short-range attack - attacker can offer better chain started few blocks behind current canonical chain. The attack is possible at the moment, the only likely outcome though is just gathered fees increase for an attacker. In our simulations this kind of attack is possible mostly when a long delay occurs due to low target. By the way, the attack has positive aspect for network, as it shorten delays average between blocks. So attacker gets extra fees for a good job done Grin

I just performed this type of attack in APEXcoin. Please see here: https://bitcointalk.org/index.php?topic=897493.0
It was a short-range attack, but the consequences are not just more fees: I successfully double-spent.

You may want to expand this "Short-range attack" category, since there can be many different ways to achieve this.
I did it by splitting the coins and waiting for age to accumulate, and as I mention in the linked thread, I think it may be possible to do something similar in nxt.

Just like with POW, 51% guarrantees success but if you have 10% of the hashrate you will eventually have the chance to double spend. Same thing here: small stake + patience = double-spend. Only worse because in most POS coins the % of actively staked coins is low.