TLDR: a change to BIP158 would allow decision on which filter chain is correct 
at lower bandwith use

Assume there is a BIP157 client that learned a filter header chain earlier and 
is now offered an alternate reality by a newly connected BIP157 server.

The client notices the alternate reality by routinely asking for filter chain 
checkpoints after connecting to a new BIP157 server. A divergence at a 
checkpoint means that the server disagrees the client's history at or before 
the first diverging checkpoint. The client would then request the filter 
headers between the last matching and first divergent checkpoint, and quickly 
figure which block’s filter is the first that does not match previous 
assumption, and request that filter from the server.

The client downloads the corresponding block, checks that its header fits the 
PoW secured best header chain, re-calculates merkle root of its transaction 
list to know that it is complete and queries the filter to see if every output 
script of every transaction is contained in there, if not the server is lying, 
the case is closed, the server disconnected.

Having all output scripts in the filter does not however guarantee that the 
filter is correct since it might omit input scripts. Inputs scripts are not 
part of the downloaded block, but are in some blocks before that. Checking 
those are out of reach for lightweight client with tools given by the current 
BIP.

A remedy here would be an other filter chain on created and spent outpoints as 
is implemented currently by Murmel. The outpoint filter chain must offer a 
match for every spent output of the block with the divergent filter, otherwise 
the interrogated server is lying since a PoW secured block can not spend coins 
out of nowhere. Doing this check would already force the client to download the 
outpoint filter history up-to the point of divergence. Then the client would 
have to download and PoW check every block that shows a match in outpoints 
until it figures that one of the spent outputs has a script that was not in the 
server’s filter, in which case the server is lying. If everything checks out 
then the previous assumption on filter history was incorrect and should be 
replaced by the history offered by the interrogated server. 

As you see the interrogation works with this added filter but is highly 
ineffective. A really light client should not be forced to download lots of 
blocks just to uncover a lying filter server. This would actually be an easy 
DoS on light BIP157 clients.

A better solution is a change to BIP158 such that the only filter contains 
created scripts and spent outpoints. It appears to me that this would serve 
well both wallets and interrogation of filter servers well:

Wallets would recognize payments to their addresses by the filter as output 
scripts are included, spends from the wallet would be recognized as a wallet 
already knows outpoints of its previously received coins, so it can query the 
filters for them.

Interrogation of a filter server also simplifies, since the filter of the block 
can be checked entirely against the contents of the same block. The decision on 
filter correctness does not require more bandwith then download of a block at 
the mismatching checkpoint. The client could only be forced at max. to download 
1/1000 th of the blockchain in addition to the filter header history.

Therefore I suggest to change BIP158 to have a base filter, defined as:

A basic filter MUST contain exactly the following items for each transaction in 
a block:
        • Spent outpoints
        • The scriptPubKey of each output, aside from all OP_RETURN output 
scripts.

Tamas Blummer
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