Quote from: markm on May 29, 2015, 11:28:38 AM

Pure proof of stake is not secure, because somewhere in the workings of it there has to be some kind of random or pseudorandom number generator used to decide which staking client wins the/a stake on any particular block.

Someone with more computer power can explore multiple possible futures, generating billions trillions quadrilions etc such random or pseudorandom numbers, massively increasing their chance of having their stake, of whatever size, "get lucky".

This is pretty much a pure nature of the problem kind of problem, not only has it not been solved it probably is not solvable.

Research >>> https://bitcointalk.org/index.php?topic=897488.0

And so far, so good... Nxt's pure POS implementation has been found to be secure against all formally described (i.e. testable) attacks so far. You can also repeat Kushti's finding's using the models he has made available, if you so choose.

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

2. Long-range attack - attacker can start fork hundreds or thousands blocks behind current chain. From our investigations the attack isn't possible.

3. Nothing-at-stake attack - not possible at the moment! Will be possible when a lot of forgers will use multiple-branch forging to increase profits. Then attacker can contribute to all the chains(some of them e.g. containing a transaction) then start to contribute to one chain only behind the best(containing no transaction) making it winner. Previous statements on N@S attack made with assumption it costs nothing to contribute to an each fork possible and that makes N@S attack a disaster. In fact, it's not possible at all to contribute to each fork possible, as number of forks growing exponentially with time. So the only strategy for a multibranch forger is to contribute to N best forks. In such scenario attack is possible only within short-range e.g. with 25 confirmations needed 10% attacker can't make an attack. And attack is pretty random in nature, it's impossible to predict whether 2 forks will be within N best forks(from exponentially growing set) for k confirmations. So from our point of view the importance of the attack is pretty overblown.

4. History attack - attacker can buy whale's private key for $5 and build alternative story. Solved with some checkpoints now, located behind max rollback possible, so the solution is not so scary in terms of centralization etc.

If you know any other kind of attack, please add. Please note IPO properties of a concrete coins etc isn't related to proof-of-stake distributed consensus problems.

And Consensus Research is going to work on better proof-of-stake prototyping & implementation !

This is a summary form January, you'll see in the thread more work has been done and a test environment has been developed (Scorex*) to test improvements to the Nxt POS algo as we speak, based on the groups research.

*https://bitcointalk.org/index.php?topic=1060567.0

Where are you getting your information from?