Warning I as AnonyMint proposed this in mid-2013 and referred to it as Proof-of-Storage. I also discovered it was fundementally flawed. If you continue, you will be wasting your time. Eventually I will come back and explain to you and Andrew Miller PhD why this is flawed.
Details are definitely needed here. I know about Proofs-of-Space and Proofs of Space-Time(
http://eprint.iacr.org/2016/035.pdf ), Miller's Proof-of-Retrievability(Permacoin), and White's Proof-of-Storage in Qeditas. What's Anonymint's proposal about?
We found some possible drawbacks and attack vectors in Permacoin, but no fundamental flaws.
Acknowledgement: we would like to thank IOHK (new project of Charles Hoskinson et al,
http://iohk.io/) for sponsorship, Andrew Miller for answering questions on Permacoin.
Is it that Andrew Miller who claimed that PoS is impossible because there is nothing at stake?
No, the claim was from Andrew Poelstra.