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It is not clear to me, why not we can simply store transaction hashes in a block header instead of storing the Merkle root. I understand that storing transactions' hashes will slightly increase size of a block header. However, the transaction verification process will be greatly simplified as one does not have to compute Merkle tree. In that case, one can verify a transaction by simply searching that transaction hash in the header.
Noman Aslam
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Storing the hash of every transaction in the block header could make the block header much larger than it currently is. Right now the whole header is 80 bytes, and the tx merkle root is 32 bytes of that. You can hash any number of transactions into a 32 byte merkle root, so it works very well as a cryptographically secure compression technique.
I can think of a few effects of larger block headers:
There are probably more, feel free to expand on this list.
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I understand that storing transactions' hashes will slightly increase size of a block header.
That's an understatement. According to this answer, the minimum transaction size is 60 bytes. A block full of these would make the txhash part of the block header 560kb instead of 32 bytes it currently is.
Just to clarify, I am talking about hashes of transactions to store in the header instead of whole transaction. In case a block has 2000 transactions (usually is kind of average these days) then the block size will increase to 32*2000 = 64 KB when SHA-256 is used to compute hash. Hence it is no way near 560KB. – Noman Aslam – 2018-05-15T11:01:12.743
if the transaction is 60 bytes long (minimum size) then a block can fit 17476 transactions. Each txid is 32 bytes so 17476 * 32 bytes = 560kb – Mike D – 2018-05-15T11:06:32.207
The last argument does not hold. Just because the block header contains all txids does not make every store all of them. That's similar to how the Merkle tree itself is not stored anywhere, but implied by the transactions. – Pieter Wuille – 2018-05-15T16:20:00.063
@PieterWuille I'm not sure I follow. At the most basic evel: if the max block weight remains the same, and including txids instead of a merkle root makes the header larger, then that leaves less space in the body for transactions, no? I interpreted OPs question as 'why not just a naive implementation that lists all txids in a row' – chytrik – 2018-05-16T07:09:30.287
They could be part of the block header without storing them (in any situation where you're already storing the transactions too). We could do the same right now with just the root (as it too is implied by the transactiins), but for just 32 bytes it's not really worth it. – Pieter Wuille – 2018-05-16T07:29:25.960
I understand, thanks. I edited the answer to be more accurate. – chytrik – 2018-05-16T10:25:23.713