Efficient Multi-Input Transaction Grinding for OP_CAT-based Bitcoin Covenants

In the realm of stack-based programming, a specific technique can be employed to ascertain the equality of two values with a particular relation, specifically that y is equal to x+1. This verification process involves a sequence of operations that manipulate the stack to compare the given values effectively. Initially, both values under consideration are duplicated on the stack. Following this duplication, a byte represented by 0x01 is appended to each value's suffix. This step is crucial as it prevents either value from being interpreted as negative or non-minimal, which includes representations such as 0x00, 0x80, or any multibyte string terminating in 0x00 or 0x0080.

Subsequently, one of the values is incremented by 1. The process leverages the stack's alternative storage to temporarily hold one of the modified values, thereby facilitating a direct comparison. The comparison aims to verify the equality of the original and incremented values, essentially confirming if y=x+1.

The methodology described is versatile, accommodating suffixes of varying lengths, including one, two, or three bytes. However, it's noteworthy that this approach encounters limitations under specific conditions, such as when the smaller hash concludes with FFFFFF. The likelihood of encountering such a scenario is relatively rare, approximately one in 16 million, which contrasts significantly with more common odds such as 1-in-2 or 255-in-256. This distinction underscores the method's efficiency and reliability in most situations, barring exceedingly uncommon exceptions.