According to posts of @gmaxwell, there are techniques which will probably allow full nodes in the future to verify transactions and blocks without having to store the full blockchain.
Originally, the topic came up due to the discussion about illegal material stored in the local database of full nodes (copyright infringement, illegal pornography, classified information etc.). However, such a technique would also allow to reduce the amount of data which has to be shared between full nodes, which could lead to a significant scalability improvement.
I quote some of the relevant sections:
It's possible using cryptography to construct proof for statements like "0xDEADBEEF is the hash of the tip of a blockchain starting at the genesis block where all rules pass, with total difficulty Y", where the proof is much smaller than the blockchain (in some cases only a few hundred bytes).
Such systems are already in production use for small programs today. Scaling them up to work over the whole bitcoin blockchain is a (considerable) engineering exercise, but I think it's inevitable-- well inevitable that the proof systems are developed to that extent. If Bitcoin will deploy them or not will depend on if anyone is still willing to work on it.
i'm skeptical that such a system could work for bitcoin unless they changed up the structure of bitcoin blocks to include some type of utxo set commitment inside each block. but i guess if you did that, maybe it could work.
because the way it is right now, an individual block doesn't really tell you anything about what the existing utxo set is or any of its properties. that would need to change somehow.
Nah. That could be side information computed as part the proving process, it doesn't need to be part of the block commitment.
E.g. prove "block hash x with resulting utxo state hash xu is a valid successor to block y with utxo state hash yu".
And each block commits to every prior utxo set state by committing to the history of all blocks before it. So, for example its possible to construct a proof that says "output 0xDEADBEEF:01 is a member of the utxo set at height 1000 of this chain with height 1001 hash Y" its just that the prover must process the whole chain up to height 1000 while constructing the proof. The prover might be more efficient with an optimized commitment structure but it isn't necessary. You can produce a proof for the output of ANY program. If a program can validate it, a proof can be provided.
I'd like to discuss this topic here as it was OT in the BRC-20/Ordinals thread and thus the discussion there didn't last long nor reached the depth I'd have desired. Above all, it would be cool to see some examples and ELI5-style explanations (if this is possible).
In the BRC-20 thread I cited some research I found on related topics, but I think gmaxwell's solution refers to another one. I'll list them here anyway:
- The mini-blockchain scheme [1][2] allows a collective pruning of everything but the latest blocks, but it has flaws which increase the danger of an 51% attack.
- "Rollerchain" [3] seems to improve on mini-blockchain. I've not found a "rebuttal" of its claims, but it doesn't seem to have been applied in a major altcoin.
- There are some techniques to at least make the data required for verification a bit smaller (approx. by half or more), maybe in a similar vein this could ignore Taproot/OP_RETURN data? [4]
- One I stumbled upon recently is the Mina Protocol, a centralized altcoin but the tech may be related to what gmaxwell wrote - it aims to reduce the storage requirement for all nodes. Have not researched it thoroughly, so it may be dubious. [5]
[1]
https://www.semanticscholar.org/paper/The-Mini-Blockchain-Scheme-Bruce/2b52355f76fca0ac23c5730f4e1a6a7e653f0237[2]
http://cryptonite.info/wiki/index.php?title=Weaknesses_and_attack_vectors[3]
https://www.semanticscholar.org/paper/A-Prunable-Blockchain-Consensus-Protocol-Based-on-Chepurnoy-Larangeira/48f1b027c7ec96fa8a4ca4f53e2be6b95643e3f4[4]
https://www.semanticscholar.org/paper/How-to-Securely-Prune-Bitcoin%E2%80%99s-Blockchain-Matzutt-Kalde/d855ac1c3fe47a5b47d808bf763ba95b993ce8da[5]
https://minaprotocol.com/lightweight-blockchain 
