The path to general computation on Bitcoin (with OP_CAT)

In the realm of programming, particularly when dealing with cryptographic protocols and script complexities, understanding the functionality and limitations of different scripting sizes is crucial. The differentiation between "Small Script" and "Big Script," terms coined by Andrew Poelstra, plays a significant role in this context. Small Script, identified by its use of 4-byte elements, allows for arithmetic operations and comparisons, such as OP_GREATERTHAN. This enables the implementation of arbitrary logic within these constraints. In contrast, Big Script does not permit any comparisons other than OP_EQUAL. However, it provides direct access to more complex operations like hashing and signature verification.

The concept of CAT, as discussed, serves as a bridge between Small Script and Big Script, offering a solution to the limitations faced by each. Specifically, CAT is instrumental in the process of SPLIT, which refers to separating an arithmetically useful sized chunk from a cryptographic hash. This technique is essential for executing arbitrary logic through splitting, and for performing native hash and signature operations through combining. Both CAT and SUBSTR functions are mentioned as viable methods for achieving the necessary splitting and combining required for these processes.

For those seeking a deeper understanding of these concepts, a detailed documentation comparing Big Script versus Small Script is available in section 2.2.3 of a document found at https://eprint.iacr.org/2024/1802.pdf. This resource elaborates further on how these scripting domains interact and complement each other within the broader scope of cryptographic and programming tasks.