The path to general computation on Bitcoin (with OP_CAT)

[victorkstarkware]

@moonsettler

Heard this mentioned before, what exactly can you do with 4 bytes? Is this related to the M31 field? But how do these 4 byte elements relate to something like a distribution of funds? I keep getting stuck on that one would need to construct a CTV hash or a hash of a signature on stack somewhere along the line. (ofc this is trivial with CAT)

Andrew Poelstra coined the terms “Small Script” and “Big Script” for this. With Small Script (4 byte elements), you can do arithmetic and comparisons such as OP_GREATERTHAN, meaning you can have arbitrary logic. In contrast, in Big Script, you can’t make any comparisons beyond OP_EQUAL, but you have native access to hashing and signature opcodes. so CAT gives you a way to bridge the gap between these two domains.

We wrote a fairly detailed documentation of Big Script vs Small Script in section 2.2.3 here: https://eprint.iacr.org/2024/1802.pdf

@moonsettler

If I understand correctly, CAT is actually used for SPLIT, to cut an arithmetically useful sized chunk off of a cryptographic hash?

You need both combining and splitting. Splitting is used to perform arbitrary logic (as mentioned above), and combining is used for native hash/signature operations. You can achieve both with either CAT or SUBSTR.