the length is probably not that much shorter than the one he came up with
What's your intuition for what "not that much shorter" means here? I'm not seeing the math clearly, but it seems like solving for 1/2 vs solving for 1/(2^many) would make a big difference when many is large double digits. I'm not sure how big "big" is, but I'd guess it would be large enough to dwarf the chosen two decimal places and 2-bit difference over a 5 year projection.
Another factor that would move things in the same direction (of a shorter string being the correct answer) is that if we are presuming random bits, I think we can multiply the total number bits transmitted by the length of the bit string. This would be to account for the fact that the match doesn't have to start on any particular boundary, rather the target can be "swept through" the entire corpus bit-by-bit.
What's your intuition for what "not that much shorter" means here? I'm not seeing the math clearly, but it seems like solving for 1/2 vs solving for 1/(2^many) would make a big difference when many is large double digits. I'm not sure how big "big" is, but I'd guess it would be large enough to dwarf the chosen two decimal places and 2-bit difference over a 5 year projection.
Another factor that would move things in the same direction (of a shorter string being the correct answer) is that if we are presuming random bits, I think we can multiply the total number bits transmitted by the length of the bit string. This would be to account for the fact that the match doesn't have to start on any particular boundary, rather the target can be "swept through" the entire corpus bit-by-bit.