Utilize Simplified Payment Verification (SPV) to operate without validating the full blockchain
They only download the block headers (no transactions)
Lightweight clients verify transactions by referencing there depth in the blockchain
If a block that contains a transaction has multiple blocks on top of it can an verify by proxy that the transaction is valid
They verify the PoW of each block not the transactions present in them
The lightweight clients use a Merkle path proof to verify that a transaction does exist in a block
Cannot check if a transaction is being double-spend as does not have the full view of the blockchain
Just by looking at the block header a lightweight client cannot tell which UTXOs belong to its wallet
Bitcoin wallets utilizes Bloom Filters to allow them to request a subset of transactions without reveling directly which transactions they are interested in
Lightweight clients are offer less privacy then full nodes
Bloom Filter
Bloom Filter is an probabilistic search filter
It provides a way to provide a search pattern without compromising privacy
Used by lightweight clients to request information from peers
Using bloom filters lightweight clients can decide to either to make a search the favors accuracy or one that favors privacy
The bloom filter can with probabilistically say if a patten was included and can with certainty say if a pattern was not included
The filterload message is used by lightweight clients to request a filtered list of transactions from an full node
The peer node can use the transaction ids, data in script outputs, script inputs and signatures against the filter
The peer node will send the block headers of the blocks that contain transactions that match the filter. The Merkle path to the transaction is also shared
Peer will also send a message that contains the transactions that match the filter
Using the information that is sent by the peer the lightweight node updates its UTXO balance
The bloom filter is also modified to search in the future for UTXOs that were found
It was later realized that is method is not very private and using certain filters that peer nodes could be forced to perform a lot of work
Compact Block Filters
Instead of the lightweight clients creating the filter the full nodes create the filters
The compact block filter is a filter that is created by hashing the addresses that are present in a block
Filters are created for each blockchain that is confirmed into the blockchain
This filter is sent to the lightweight client which can check if it contains any of its addresses
If the filter contains its address it can download the required block from the node
From the node the lightweight client can then use the transactions that it requires
Golomb-Rice Coded Sets (GCS)
GCS is an optimization that is used for sharing the filters
We arrange the list of numbers that need to be shared in ascending order
The 1st number is transmitted as is, the remainder of the numbers is transmitted as a difference from the previous term
This allows to transmit the same information while using less bandwidth
GCS filters have 100% true positive rate
Data in Compact Block Filter
Lightweight client needs to identify the outputs that are sent to it and it also needs to identify outputs that have been spend by it
The GCS filter that is sent to the lightweight clients contain information about all the output scripts and additionally contains information output outputs scripts that are referenced by the outpoint of an input (spent output)
Lossy encoding using SigHash is used to convert the output script into a 64-bit commitment hash
Using Compact Block Filter
The 64-bit commitment hash is calculated for all the outputs in a transaction
The duplicate values are removed and the values are arranged in ascending order
Then using GCS they are represented as difference (Delta) values
This filter is shared with the lightweight nodes
Lightweight client can then create commitment hash the outputs it is monitoring Then check if the compact block filter contains transactions that matches its commitment hash