In theory, modular traversal is bijective and randomizedI think I’ve approached all of this the keyspace)wrong way.
I’m offering a 0.1 BTC bounty for the formal proof of any traversal method that provides a statistical edge over a linear scan for puzzle 69. By statistical edge I mean that this new traversal method running on a statistically significant number of executions requires significantly fewer checks (let’s put the threshold at 5%) to find the key.
Conditions :
- Has to be written using math semantics. Not “where does John lives” metaphors.
- Has to be empirically validated using a python / nodeJS script.
- First one posting it to this thread will be recipient of the bounty.
In theory, modular traversal is bijective and randomized. So, generally speaking, if the target keys are randomly distributed across the keyspace, modular traversal can be as efficient as linear traversal. But, for clustered targets like in the 2^69 puzzle, modular traversal is not efficient because the targets were clustered near the starting point (within a small range of the keyspace). So we need a "new" linear traversal.
just my 2cents.