Milestone to crack RSA.

By SarK0Y
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SarK0Y

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Story of tails, windows and how it impacts integer factorization..
In other words, MILESTONE has been done :D



From the very start of my journey to discover the innards of stubborn IF, the prime goal was to have
developed binary-search-tree algos. At some point, it seemed utterly impossible. But here we go..


Actually, algo consists of three stages..
 

  • it picks initial (probable) Z’s (pZ_L and pZ_R) up (Z = P + Q, N = P*Q). So, now algo needs to guess which one is closest to original Z.
  • for pZ_L, it generates N_L which is closest to N from left/right and the same way for N_R of pZ_R.
  • for N_R/L, it collects statistics of bit windows against N (their positions, widths..)..

 

Window(N, EntryPoint, Width) == NOT Window(N_L, EntryPoint, Width).



For instance, let Window(N, EntryPoint, Width) == “010”, then Window(N_L, EntryPoint, Width) == “101”. And now it’s possible to choose probable Z according to collected statistics for given iteration.


For tests, RSA-150 (https://en.wikipedia.org/wiki/RSA_numbers#RSA-150) has been taken, criterion to go left/right is widths of greatest windows. Output…


test mode gets activated
Wrong turn @ 1
Wrong turn @ 2
Wrong turn @ 3
Wrong turn @ 4
Wrong turn @ 5
Wrong turn @ 6
Wrong turn @ 7
Wrong turn @ 8
Wrong turn @ 9
Wrong turn @ 10
Wrong turn @ 11
Wrong turn @ 12
Wrong turn @ 13
Wrong turn @ 14
Wrong turn @ 15
Wrong turn @ 16
Wrong turn @ 17
Wrong turn @ 18
Wrong turn @ 19
Wrong turn @ 20
Wrong turn @ 21
Wrong turn @ 22
Wrong turn @ 23
Wrong turn @ 24
Wrong turn @ 25
Wrong turn @ 26
Wrong turn @ 27
Wrong turn @ 28
Wrong turn @ 29
Wrong turn @ 30
Wrong turn @ 31
Wrong turn @ 32
Wrong turn @ 33
Wrong turn @ 34
Wrong turn @ 35
Wrong turn @ 36
Wrong turn @ 37
Wrong turn @ 38
Wrong turn @ 39
Wrong turn @ 40
Wrong turns == 40
nice turns == 208
Total iterations == 248


In short, algo doesn’t do gaps (good and bad turns ain’t shuffled/mixed) even with such rather primitive criterion.
Archive: https://sourceforge.net/projects/fastprimecruncher/
Password for archive: ᬓꨒꛏ78🁶

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