New test analysis


BifidCM
Bifid
PlayfrFrac
Morse
Baze2sq4sq
Mean0.660.8740.7240.8250.9500.6370.748
Max1.0041.2631.1001.2051.2151.1741.148
Min0.3030.5490.3310.4830.7190.2910.39
Mode0.6850.9280.8590.7790.8800.730.758

Above are the results of running my new test on a series of plaintexts (pt) from Gutenberg.org enciphered with the cipher types shown. The number of pts was over 3000 in every case. The test clearly has some value in distinguishing cipher types based on the ct. However, as I analyzed the results, I see they are very similar to the Normor test and for a very simple reason. Both tests tend to measure the extent to which a cipher type enciphers pt with letters that have the same or similar frequency as the pt.

The Two-Square is a good example to understand this. Whenever both pt letters are on the same row, the resulting ct digraph is a reversal of those same two letters. Similarly, if one or both the left and right squares use vertical keywords, the resulting digraph is likely to contain a letter from the same keyword used for that vertical (column) key. For this reason, the Two-square ct tends to be closer to normal pt frequencies. When you consider how the other ciphers are constructed, it is not difficult to see that the numbers reflect this same phenomenon.

I believe this new test is simply another way of measuring the same thing the Normor test does. The real question is whether it does so more accurately and reliably, i.e. with finer, sharper separation between types. The data cts used here were enciphered with a random choice of keyword and route, but when I first invented the Normor test, I checked it on different polybius square routes. The results were strikingly different depending on the route chosen. Again, if you consider how some routes tend to cause the ct letter to be the same letter as the pt, or from the same keyword, and others don’t, especially where two different keysquares are used, this becomes understandable.

6 thoughts on “New test analysis”

  1. The difference in means between bifid and CM bifid is about the same as the difference in means between two-square and four-square. Maybe this stat would be good at distinguishing between bifid and cm bifid. My own ID tests don’t do too good a job in telling bifid and cm bifid apart.

    1. Yes, I have already programmed this test into the Bifid and CM Bifid test protocols in my Analyzer. It distinguishes very well, although not perfectly. Where I have trouble is between Bifid and Phillips. Both get a big boost if the length of the ct is an odd number since the digraphic ones must be an even number, assuming no trickery. Where it’s an even number, all the polybius types cluster near the top, but my program usually gets it right. I haven’t tested this new test on a set of Phillips or Tri-square ciphers yet.

  2. I trained a neural net on about 12000 ciphers (about 230 of almost every ACA type). The only input information was the even and odd frequencies of the cipher symbols (37 even and 37 odd frequencies of letters, digits, and the # symbol). It got the correct type for about half of the ciphers that I kept out of the training set (2599 out of about 5000). It did petty well on plaintext (just 1 wrong), 6×6 Bifid, 6×6 Playfair, homophonic, checkerboard, digrafid, portax, morbit, and bazeries. It was terrible on transposition ciphers.

    1. I don’t understand what you mean by even and odd frequencies. Do you mean frequency in the odd numbered positions, i.e. the 1st, 3rd, etc. letter of ct vs. the 2nd, 4th, etc.? “37 even and 37 odd” means all the cts were 74 letters long?

      1. By even and odd frequencies I was referring to frequencies at even and odd positions within the ciphertext. The even positions are 0,2,4,etc. The odd positions are 1,3,5,… etc. I thought separating the frequencies into two parts might help with digraphic ciphers like playfair, two-square, four-square, etc. As for 37, 37 is the number of possible symbols in an ACA ciphertext: 26 letters, 10 digits, and the # symbol that appears in trifids and digrafids.

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