On Mon, 16 Mar 2015 09:29:03 -0700, Sergio Lerner  
<sergioler...@certimix.com> wrote:
> I proposed a (what I think) is better protocol for Proof of Storage that
> I call "Proof of Local storage" here
> https://bitslog.wordpress.com/2014/11/03/proof-of-local-blockchain-storage/

Thanks so much for publishing this. It could be useful in any application  
to try to prove a keyed copy of some data.

If I understand correctly, transforming raw blocks to keyed blocks takes  
512x longer than transforming keyed blocks back to raw. The key is public,  
like the IP, or some other value which perhaps changes less frequently.

The verifier keeps blocks in the keyed format, and can decrypt quickly to  
provide raw data, or use the keyed data for hashing to try to demonstrate  
they have a pre-keyed copy.

> Two protocols can be performed to prove local possession:
> 1. (prover and verifier pay a small cost) The verifier sends a seed to
> derive some n random indexes, and the prover must respond with the hash
> of the decrypted blocks within a certain time bound. Suppose that
> decryption of n blocks take 100 msec (+-100 msec of network jitter).
> Then an attacker must have a computer 50 faster to be able to
> consistently cheat. The last 50 blocks should not be part of the list to
> allow nodes to catch-up and encrypt the blocks in background.

Can you clarify, the prover is hashing random blocks of *decrypted*, as-in  
raw, blockchain data? What does this prove other than, perhaps, fast  
random IO of the blockchain? (which is useful in its own right, e.g. as a  
way to ensure only full-node IO-bound mining if baked into the PoW)

How is the verifier validating the response without possession of the full  

> 2. (prover pay a high cost, verified pays negligible cost). The verifier
> chooses a seed n, and then pre-computes the encrypted blocks derived
> from the seed using the prover's IP. Then the verifier sends the  seed,
> and the prover must respond with the hash of the encrypted blocks within
> a certain time bound. The proved does not require to do any PH
> decryption, just take the encrypted blocks for indexes derived from the
> seed, hash them and send the hash back to the verifier. The verifier
> validates the time bound and the hash.

The challenger requests a hash-sum of a random sequence of indices of the  
keyed data, based on a challenge seed. So in a few bytes round-trip we can  
see how fast the computation is completed. If the data is already keyed,  
the hash of 1,000 random 1024-bit blocks should come back much faster than  
if the data needs to be keyed on-the-fly.

To verify the response, the challenger would have to use the peer's  
identity key and perform the slower transforms on those same 1,000 blocks  
and see that the result matches, so cost to challenger is higher than  
prover, assuming they actually do the computation.

Which brings up a good tweak, a full-node challenger could have to do the  
computation first, then also include something like HMAC(identityKey,  
expectedResult). The prover could then know if the challenger was honest  
before returning a result, and blacklist them if not.

> Both protocols can me made available by the client, under different
> states. For instance, new nodes are only allowed to request protocol 2
> (and so they get an initial assurance their are connecting to
> full-nodes). After a first-time mutual authentication, they are allowed
> to periodically perform protocol 1. Also new nodes may be allowed to
> perform protocol 1 with a small index set, and increase the index set
> over time, to get higher confidence.

I guess a new-node could see if different servers all returned the same  
challenge response, but they would have no way to know if the challenge  
response was technically correct, or sybil.

I also wonder about the effect of spinning disk versus SSD. Seek time for  
1,000 random reads is either nearly zero or dominating depending on the  
two modes. I wonder if a sequential read from a random index is a possible  
trade-off,; it doesn't prove possession of the whole chain nearly as well,  
but at least iowait converges significantly. Then again, that presupposes  
a specific ordering on disk which might not exist. In X years it will all  
be solid-state, so eventually it's moot.

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