This method significantly streamlines the signature computation process by employing a specialized technique for selecting signing and ephemeral keys. A critical challenge in the conventional system stems from the inability of Bitcoin Script's OP_ADD operation to directly increment a 256-bit integer, which represents the SHA256 hash of transaction data. To overcome this, a workaround involves dividing the hash into two segments: the least significant byte and the remainder. The process involves concatenating these parts after incrementally adjusting the least significant byte until the hash's final digit is one, mimicking a proof-of-work system but with minimal difficulty.

However, this method encounters efficiency issues when dealing with transactions that have multiple inputs. The time required for "transaction grinding" can become prohibitively long as the number of inputs increases, compounded by the limited range of fields like nLocktime that can be adjusted. To address these limitations, a new solution proposes extending the range of acceptable values for the least significant byte beyond its original constraints. This adjustment allows for a more extensive range of potential modifications, drastically reducing the number of attempts needed to achieve a successful hash modification, even in scenarios with numerous inputs.

Further optimization is possible by expanding the range of the least significant byte even more, excluding only the extreme values to prevent underflows and overflows. This method adopts a signed magnitude representation for integers within Bitcoin Script, facilitating the incrementation of negative integers. The proposed changes are demonstrated through sCrypt code examples, showcasing the process's efficacy in reducing the computational demands of transaction grinding. These advancements are documented in detail in the provided Github commit, offering a comprehensive overview of the technical implementations and their implications for Bitcoin covenants.