> 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.
Yes. I was thinking that the IP could be part of a first layer of
encryption done to the blockchain data prior to the asymetric operation.
That way the asymmetric operation can be the same for all users (no
different primers for different IPs, and then the verifiers does not
have to verify that a particular p is actually a pseudo-prime suitable
for P.H. ) and the public exponent can be just 3.

>> 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 blockchain?

You're right, It is incorrect. Not the decrypted blocks must be sent,
but the encrypted blocks. There correct protocol is this:

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 the
encrypted blocks within a certain time bound. The verifier decrypts
those blocks to check if they are part of the block-chain.

But then there is this improvement which allows the verifier do detect
non full-nodes with much less computation:

3. (prover pays a small cost, verifier smaller cost) The verifier asks
the prover to send a Merkle tree root of hashes of encrypted blocks with
N indexes selected by a psudo-random function seeded by a challenge
value, where each encrypted-block is previously prefixed with the seed
before being hashed (e.g. N=100). The verifier receives the Markle Root
and performs a statistical test on the received information. From the N
hashes blocks, it chooses M < N (e.g. M = 20), and asks the proved for
the blocks at these indexes. The prover sends the blocks, the verifier
validates the blocks by decrypting them and also verifies that the
Merkle tree was well constructed for those block nodes. This proves with
high probability that the Merkle tree was built on-the-fly and
specifically for this challenge-response protocol.

> 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.
Good idea.

Also we don't need that every node implements the protocol, but only
nodes that want to prove full-node-ness, such as the ones which want to
receive bitnodes subsidy.

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