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jdege
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First, are you Anchises? Hello, I am Peristalsis.

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First let me make a few comments on your brute force cryptarithm programs, which I hope you will find helpful. In essence the times you quote are very slow. For a base-10 cryptarithm my brute program goes through all perms in 2 seconds, and for a base-12 cryptarithm in four and a half minutes (on my old 2.3GHz PC). I suspect that either you are not using the fastest algorithm for generating perms, or your method of handling numbers is not optimum (or your computer is very old! which I doubt).


I'm running on a 1.2GHz AMD Sempron. I'm a computer programmer - I have no interest at all in chasing the latest computer hardware.

And as for my cryptarithm program, it was something I threw together in a hurry because I have absolutely no interest in cryptarithms. I'm sure that there are faster ways of doing things.

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If you would like to see any of my programs (written in C++) I’d be happy to send them to you.

I would be interested.

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Turning now to ADFGVX, I am afraid I am not finding your inputs helpful to develop or improve my algorithm.

And I'm afraid you're not going to find much help from anyone in this forum. There are only three or four of us who seem to have written hill-climbers, and perhaps only one of us who's ever tried to apply them to ADFGVX, and he seems to have had far less success than you have had.

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It’s been self-evident since the beginning of this thread that ANY algorithm based on brute force will take too long to solve ADFGVX with a transposition key of 15 to 20. Even brute forcing a base-20 cryptarithm (a trivial task compared with solving ADFGVX) would take thousands of years!

Actually, I was thinking of Jim Gillogly's publication of his ciphertext only solution for Enigma. His solver would work reliably on most messages over, IIRC, 420 characters. And since he'd found several messages of over 420 characters within the archives of historical Enigma messages, he concluded that it would have worked at least part of the time on the original traffic. Someone else pointed out that those longer messages were in fact concatenations of multi-part messages, and that no individual part ever exceeded 200 characters, at which length Gillogly's attack never worked at all.

You've developed an attack that works on a sophisticated WWI cipher, had they used keys that were half the length of the keys they actually used. I don't mean that to belittle your work, just as I don't mean to belittle Gillogly's work. I'm just fascinated that these guys - who could never have foreseen the types of attacks you've developed, nevertheless had enough foresight to choose message and key lengths that would have forestalled them.

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Your comment 'find a heuristic search that does work' is of no more help than ‘find a way of making gold out of lead’!

What was it Reagan used to say? "They say there aren't any simple answers. They're wrong. There are simple answers, there just aren't any easy answers."

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When you have the time to devote to this topic, and can suggest something of practical use, I assure you I shall be all ears.

If I were to address this problem, I'd be doing exactly what you have been doing.

1st. make sure that the attack on the substitution phase worked.

2nd, make sure that the scoring routine worked - by testing with exhaustive search of small transposition keys

3rd, try to work out where it is, or why it is, that a heuristic search of the transposition key space goes wrong.

In that, I can think of two possibilities. 1, the scoring routine doesn't give the highest score to the right anwser. Or 2, the adjacency search doesn't include keys that really should be considered neighbors. (I'm thinking of the way that Playfair breakers often work better when you include flipped key squares, instead of just swapped letters, as neighboring keys).

I'd think you'd be already be certain that your scoring routine was successfully assigning the highest score to the proper transposition. When you were trying to hill-climb the transpositions, what were you considering as neighboring keys?

When cryptography is outlawed, bayl bhgynjf jvyy unir cevinpl.
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