First of all, let's define what an SPV proof is: it is a succinct
sequence of bits which can be transmitted as part of a non-interactive
protocol that convincingly establishes for a client without access to
the block chain that for some block B, B has an ancestor A at some
specified height and work distance back, and the cost of creating a
false proof is at least as much work as it claims to represent.

The previous email you quote demonstrates how with additional backlink
commitments this can be done in logarithmic space: using an average of
log(N) headers to construct an SPV proof from block A to block B where N
is the height differential. It can be verified without access to the
block chain or other peers. Note that with back links the cost of
creating a fraudulent SPV proof is the same as 51% attacking bitcoin
itself. The protocol you outlined does not have this property.

Other than that, honestly I'm not really sure what you are trying to
accomplish. An interactive proof is does not meet the above requirements
and is not usable for the driving application of two-way pegs. Maybe you
had some other application in mind? I've looked at your SmartSPV
proposal, but fail to see how it doesn't reduce to simply blind trust in
your view of the network from your peers. SPV proofs on the other hand
put an economic cost to fraud.

On 04/26/2014 06:08 PM, Sergio Lerner wrote:
> I read the post in this threads about Compact SPV proofs via block
> header commitments (archived e-mail in
> I was working on the same problem almost at the same time, which is
> something that's becoming very common nowadays..
> The proposal starts with the following claim:
> "In simple payment verification (SPV) proofs it is currently necessary
> that every intervening block header be provided between two blocks in
> order to establish both connectivity and proof of work."
> I think this is false. Let's first assume that at the time of an attack
> we're connected only to the attacker (no honest nodes). An
> non-interactive SPV proof needs to prove that a transaction belongs to
> the best chain because creating a counterfeit proof cost more than the
> amount of money involved in the proof. Suppose that the proof consist at
> least of a block header and a merkle branch to the claimed transaction.
> Do the proof need connectivity with the last checkpoint known by the
> verifier? (here checkpoint is any block known for sure to be in the best
> chain)
> Not much, because connectivity only proves that the proof was not
> pre-computed before the checkpoint. Only if the checkpoint is very near
> (say 10 blocks back) it brings some practical evidence that the attacker
> did not have much time to prepare an attack.
> Do the proof need to know the interleaving proof-of-work?
> Not much. If the distance between blocks is less than 2016 blocks, then
> the difficulty may have change only by a factor of 4. Currently
> difficult adjustments are much lower (I suppose that about 1.1 or so).
> Then one can assume that the proof block target difficulty is almost the
> same as the last known difficulty if the block distance is less than
> 2016. If the distance is more, we just load all the interleaving
> re-target blocks to detect the actual difficulty.
> Do the proof need to have a certain number of  confirmations?
> Yes and no, because this is the only evidence that the prover has either
> spend money in creating the fake block or took a genuine block.
> The cost of creating a fake block can be approximated as the minimum of:
> - The current reward of the block (since currently fees are much lower
> than the reward)
> - The average block fees (when the reward goes to zero)
> - The minimum electricity cost of mining the block.
> As time passes one could assume that the electricity cost of mining will
> approach the other two. 
> But there is the problem of parallel synchronized attacks: if an
> attacker can reuse the same fake SPV proof to attack several victims,
> then the reward for cheating increases proportionally but the cost stays
> the same.
> For instance, if 6 confirmations are required, and each block can hold
> 2000 transactions, the attacker can find 2000 victims and re-use the
> same 6 block chain to "prove" payments to 2000 victims. Also the cost of
> mining 6 blocks can be amortized by mining 7, and attacking in the first
> two 4000 victims, etc...
> Any scheme than relies on non-interactive SPV proofs will fail if
> Bitcoin will scale up-to a point where victims can be easily found and
> synchronized.
> So I think one should assume that at least one peer is honest...
> But if we assume than during the attack least one peer is honest, then
> we could directly ask every peer to give us the blocks of their
> best-chains at the same heights of the presented proof.  No back-links
> are necessary.  If any peer shows a different block, then we should
> carefully detect which of the two nodes is the one attacking us and ban
> it, by downloading the best-chain headers from the last checkpoint to
> the block of the proof.  This would be rare so I don't see when the
> back-links can help.
> The use case should be:
> ==Use cases==
> For SPV client that has just come online asks peers what is the last block 
> height/time. 
> If a peer replies with an old block, then that peer is still downloading the 
> block-chain and it's ignored.
> For the remaining peers, the client starts asking for parents blocks until 
> all parents agree (this is the last common parent). 
> If (U)TxO hash-tree commitments are available, then the wallet is updated 
> using this data from the common parent block. 
> At the same time the client retrieves compact non-interactive 
> proofs-of-inclusion (possibly orphan) for its transactions 
> without having to download every intervening block header.
> Is there something wrong with this?
> Best regards,
> Sergio.
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