[Bitcoin-development] About Compact SPV proofs via block header commitments

[Sergio Lerner]

On 27/04/2014 02:05 p.m., Mark Friedenbach wrote:
>
> On 04/27/2014 05:36 AM, Sergio Lerner wrote:
>>> Without invoking moon math or assumptions of honest peers and
>>> jamming-free networks, the only way to know a chain is valid is to 
>>> witness the each and every block. SPV nodes on the other hand,
>>> simply trust that the most-work chain is a valid chain, based on
>>> economic arguments about the opportunity cost of mining invalid
>>> blocks.
>> I argue that you cannot talk about "the most-work chain" without 
>> actually making an assumption about honest peers.
> I should have said "without invoking moon math or interactive protocols
> requiring honest peers over jamming-free networks." The interactive
> protocol was more the point than the honest peers and jamming-free
> network. Yes, without an honest peer and an un-jammed network, you might
> never learn about the most-work chain in the first place. But having the
> security of the proof not depend on query access to an honest full node
> is absolutely necessary for some applications and certainly desirable in
> others.
The problem is not having or not access to a honest full node. The SPV
client MUST have access to a honest full node sometime.
The problem is WHEN. One can make the security assumption that during an
attack (someone gives you a fake block) you also loose the possibility
to reach any honest node. Then SPV proofs come into play.

Here are the security assumptions I added to my post about SmartSPV to
clarify this:

*Security Assumptions
*

First let’s review the main security assumption of headers-only SPV:

  * The attacker does not control all your communications with the
    payment network.

This means that there is at least a single connected peer that behaves
honestly. This assumption is quite strong and may not hold during short
periods of time, such as during application power-on (when only a few
peers have been connected), or when moving to a place where the ISP is
untrusted. For SmartSPV we’ll require weaker security assumptions:

  * The attacker cannot control all your communications with the payment
    network for more than a fixed period of time (e.g. 2016 blocks for
    Bitcoin or approximately 15 days)
  * The attacker is rational: it won’t spend an huge amount of money to
    steal a much smaller amount.

This assumptions imply that the attacker may control all your Internet
connections while he sends you a malicious block branch containing a
fake payment to you.


>
>> First this is a method that uses NPPs, not SPV proofs. Since the
>> method chooses all peers that are synchronized (have the latest
>> current block) then going back means only skipping a potential short
>> fork (which I suppose has never been more than 3 blocks during normal
>> network conditions). You're looking for a common ancestor, not the
>> checkpoint. So the linear scan is actually O(1). The exact value can
>> be approximated by the sum of the convergent infinite geometrical
>> sequence of forking probabilities, which it's about 1.03 without
>> considering selfish-mining, and probably less than 2.03 considering
>> it.
> Unless you're connected to attacker nodes which are wildly divergent
> from each other. It's relatively easy to create a massive fake history
> of difficulty-1 blocks.
Since in my use case (SmartSPV) I proposed you start from the most
recent block and go backwards, the attacker must compete in PoW with the
real current difficulty informed.
Suppose the SPV client looks for 6-block chains backwards starting from
the last current block. Suppose you know or estimate the current network
difficulty. Suppose a malicious peer creates a fake 6-block chain Cm and
the honest peer gives you the 6-block chain Ch. If Ch has not the
expected work it's discarded. If both has the expected work, then you
better not true any of them and walk their parents until you find a
common parent. That's the block you should trust. If you don't have an
honest node connected, then the only decide to trust or not Cm is by
it's accumulated work (and you have already a bound for it)


> If you assume honest peers things get very easy. But that's not a safe
> assumption to be making. With back-link block-history commitments, on
> the other hand, an interactive protocol allows you to do a binary search
> to find common ancestors, and have trust that the intermediate links
> actually exist.
So you agree that:  you need a periodic connection to a honest node, but
during an attack you may loose that connection. This is the assumption
we should be working on, and my use case (described in
http://bitslog.wordpress.com/2014/04/25/smartspv-a-better-simplified-payment-verification-for-smartphones/)
assumes that.

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