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Ouroboros is a proof of stake type blockchain consensus mechanism. Here is the paper describing it https://eprint.iacr.org/2016/889.pdf
I have written a general paper about why PoS is not possible https://github.com/zack-bitcoin/amoveo/blob/master/docs/other_blockchains/proof_of_stake.md
The goal of this paper is to analyze ouroboros to see if they have managed to prove me wrong. I will try to show that Ouroboros can not be secure.
Others have written about the myth that PoS is cheaper than PoW, so I will just link to their work on the subject http://www.truthcoin.info/blog/pow-cheapest/
A mathematical strategy
Ouroboros is designed with the goal of being able to prove that it is secure, instead of the ad-hoc trial and error methods that most people are using to design blockchains. This is a refreshing perspective that I agree with.
That is why I came up with this system for quantifying what exactly we mean by "secure". https://github.com/zack-bitcoin/amoveo/blob/master/docs/basics/trust_theory.md
This way it is possible to compute if one blockchain mechanism is more or less secure than another.
The proofs from the Ouroboros paper are probably all correct, I will not be attempting to disprove any of them.