Binohash: Transaction Introspection Without Softforks

In a recent series of empirical tests focused on the (n,t) subset grinding mechanism (section 4.5) using Bitcoin Core's regtest environment, significant findings were revealed concerning the efficiency and success rates of various configurations. The research meticulously examined the FindAndDelete function and legacy sighash algorithm, leveraging the python-bitcoinlib for validation purposes. Through a structured approach, the experiments encompassed fifty trials across different groups, each differentiated by specific parameters including bits and space (C).

The outcomes from these trials varied notably across the configurations tested. For instance, the configuration tagged as B, with parameters (10,5), 10 bits, and a space value of 252, yielded a success rate of 26% with an average of 223 attempts required for all trials. Contrastingly, the D setup (12,6), maintaining 10 bits but expanding the space to 924, improved the success rate substantially to 44%, albeit requiring a higher average attempt count of 688. Remarkably, the E configuration (14,7) at 10 bits and a space of 3432 demonstrated a near-perfect success rate of 98%, with an average of 921 attempts. However, altering this successful E setup by increasing the bits to 14 while keeping the same space resulted in a drastic reduction in success rate to 14%, with the average attempts skyrocketing to 3253. A further adjustment to group G, which involved both increasing the bits to 14 and expanding the space significantly to 12870, managed to recover the success rate to 56%, although the average attempts required surged to 8731.

A critical observation from these experiments was the verification that all groups achieved a 100% success rate upon reaching a successful outcome, underscoring the reliability of the tested methods once they converge on a solution. The data collected strongly supports the E≈W2 tradeoff empirically. This principle suggests that at a consistent bit level of 10, achieving a space of approximately 3432 yields a success rate nearing 98%. However, increasing the bits to 14, even within the same spatial parameters, drastically diminishes success to about 14%. It was noted that an increase in space by approximately 3.75 times (as seen in group G) ameliorates the success rate to around 56%, illustrating a nuanced balance between bit complexity and spatial allocation.

For those interested in delving deeper into the specifics of the methodology, configurations, and raw logs of these experiments, the complete set of materials and code has been made available on GitHub at github.com/aaron-recompile/binohash-experiments. This repository provides an invaluable resource for researchers and practitioners alike aiming to explore the intricacies of the (n,t) subset grinding mechanism and its implications for cryptographic applications.