I'm studying how Proof-of-Stake systems work. This answer on "How does proof-of-stake “mining” work?" explains specifically the Nextcoin implementation of PoS. The idea is that the next "miner" is chosen randomly from a pool of online users. However, my main concern with this system is: how do you stop someone from simply building a longer chain (from scratch) of made up transactions towards thousand of addresses that were randomly created by the malicious user? If it were higher than the current "valid" chain, wouldn't the fake one replace the valid one?

I'm studying how Proof-of-Stake systems work. This answer on "How does proof-of-stake “mining” work?" explains specifically the Nextcoin implementation of PoS. The idea is that the next "miner" is chosen randomly from a pool of online users. However, my main concern with this system is: how do you stop someone from simply building a longer chain (from scratch) of made up transactions towards thousand of addresses that were randomly created by the malicious user? If it were higher than the current "valid" chain, wouldn't the fake one replace the valid one?