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Sorted version:
ABABABABA: 7.62 ABAABABAB: 6.80 ABABABBBA: 5.57 ABAABABBA: 5.40 ABABBBABA: 5 ABAAAABAA: 4.91 AABAABAAB: 4.91 ABABABABB: 4.81 AABAAAABA: 4.80 ABAABAAAB: 4.32 ABABABAAB: 4.31 ABBABABAB: 4.25 ABAABAABA: 4.23 AABABABAB: 4.18 AABAABABA: 4.08 ABABAAAAB: 4.04 ABAAABABA: 3.93 ABAAAABAB: 3.90 BABABABAA: 3.67 ABAABABAA: 3.67 ABABBAABB: 3.65 ABABABBAB: 3.59 BABABABAB: 3.53 ABBABBBBB: 3.52 ABABAABAB: 3.50 ABABBABBA: 3.40 BBBABBABB: 3.38 BABABABBA: 3.36 ABAAABAAB: 3.33 BABABBBAB: 3.23 ABABABBAA: 3.16 ABBABBBAB: 3.15 ABBAABBBB: 3.08 BAABABBAB: 3.07 ABABBBBBA: 3.07 AABAAABAA: 3.05 ABAAAAABA: 2.94 ABBBABBAB: 2.92 BAABABABA: 2.79 ABABAABAA: 2.75 BABBBABBA: 2.69 ABBABBBBA: 2.68 ABAABBABA: 2.66 ABBBBABAB: 2.64 ABBBBBBBA: 2.63 ABABAAABA: 2.57 AAAABAAAA: 2.57 ABABBABAB: 2.49 BBABBABBB: 2.33 ABABBBBAA: 2.28 AABABAAAB: 2.26 ABBBABABA: 2.10 ABBAABBAA: 2.09 BBBBBABAB: 2.06 ABABBAABA: 2.02 ABAAABABB: 2.02 BAABBABAB: 2.01 BBAABBABA: 1.98 AAABAAAAB: 1.93 BAAAABAAA: 1.92 ABABAABBB: 1.90 AAABAAABA: 1.87 BABAABAAB: 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BBBAAABBB: -1.90 BBBABAAAA: -1.91 BABAABBAA: -1.92 AABBABBBB: -1.92 ABBBAAAAA: -1.93 AAABBABBA: -1.93 BBABBAAAB: -1.94 BBBBAAABB: -1.95 BAAAAABBA: -1.95 ABBABBAAA: -1.95 ABBABAAAA: -1.97 AAABBBBAB: -2 AAAAAABAB: -2.01 BBBAABAAA: -2.02 BBBAABABA: -2.03 AAABBBAAA: -2.12 BBAAABABB: -2.18 AAAAAABBA: -2.18 AAABAAABB: -2.19 BBAABAABB: -2.22 BABBAAABB: -2.23 BBAAABABA: -2.24 BBABAAAAB: -2.31 ABBBAAABA: -2.31 AAAAABBAA: -2.62 AAABBAAAA: -2.63 AAAABBAAA: -2.72 BBBAAABAA: -3 BBAABAAAA: -3
Posted : November 4, 2018 1:09 am
Topic starter
How does it compare to Z408?
Posted : November 4, 2018 1:10 am
What about RLBT ABAA, which with a bunch of them is ABAAABAAABAAABA?
Posted : November 4, 2018 1:57 am
How does it compare to Z408?
UPDATED
AZdecrypt symbol cycle patterns stats for: 408.txt -------------------------------------------------------- 2-symbol cycle 9-gram patterns: Average distance from 0: 1.78 Highest: ABABABABA: 23.13 Lowest: ABBBAABAA: -2.78 AAAAAAAAA: -1.51 BAAAAAAAA: -1.57 ABAAAAAAA: -0.63 BBAAAAAAA: -0.71 AABAAAAAA: 0.75 BABAAAAAA: 0.01 ABBAAAAAA: -1.06 BBBAAAAAA: -0.91 AAABAAAAA: 0.97 BAABAAAAA: 1.73 ABABAAAAA: -0.15 BBABAAAAA: -0.11 AABBAAAAA: -1.48 BABBAAAAA: -0.10 ABBBAAAAA: -1.33 BBBBAAAAA: -0.96 AAAABAAAA: -0.88 BAAABAAAA: 0.28 ABAABAAAA: 2.64 BBAABAAAA: -0.24 AABABAAAA: 0.80 BABABAAAA: 1.12 ABBABAAAA: -0.04 BBBABAAAA: 0.20 AAABBAAAA: -0.62 BAABBAAAA: -1.67 ABABBAAAA: -0.44 BBABBAAAA: -0.67 AABBBAAAA: -1.71 BABBBAAAA: -1.31 ABBBBAAAA: -1.76 BBBBBAAAA: -1.44 AAAAABAAA: -0.60 BAAAABAAA: -0.12 ABAAABAAA: 1.19 BBAAABAAA: -1.16 AABAABAAA: 0.19 BABAABAAA: 6.93 ABBAABAAA: 1.71 BBBAABAAA: -2.39 AAABABAAA: 1.30 BAABABAAA: 0.70 ABABABAAA: 4.79 BBABABAAA: -1.44 AABBABAAA: 0.49 BABBABAAA: 4.80 ABBBABAAA: 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AABBBABAB: -0.40 BABBBABAB: 0.47 ABBBBABAB: -1 BBBBBABAB: -0.71 AAAAABBAB: -1.37 BAAAABBAB: 0.47 ABAAABBAB: -1.46 BBAAABBAB: -1.75 AABAABBAB: -0.68 BABAABBAB: 1.45 ABBAABBAB: 0.49 BBBAABBAB: -1.62 AAABABBAB: -1.21 BAABABBAB: 0.32 ABABABBAB: 11.20 BBABABBAB: 2.68 AABBABBAB: -0.39 BABBABBAB: 3.52 ABBBABBAB: 0.80 BBBBABBAB: -0.77 AAAABBBAB: -2.25 BAAABBBAB: -1.35 ABAABBBAB: 0.65 BBAABBBAB: -1.11 AABABBBAB: 0.44 BABABBBAB: 0.45 ABBABBBAB: 1.40 BBBABBBAB: -1.09 AAABBBBAB: -1.58 BAABBBBAB: -1.73 ABABBBBAB: -2.43 BBABBBBAB: -1.23 AABBBBBAB: -2.17 BABBBBBAB: -0.24 ABBBBBBAB: -1.45 BBBBBBBAB: -1.89 AAAAAAABB: -1.25 BAAAAAABB: -0.80 ABAAAAABB: -0.77 BBAAAAABB: -1.38 AABAAAABB: 0.63 BABAAAABB: 0.40 ABBAAAABB: -1.34 BBBAAAABB: -1.96 AAABAAABB: -0.51 BAABAAABB: 0.46 ABABAAABB: 0.97 BBABAAABB: -0.85 AABBAAABB: -1.48 BABBAAABB: 0.11 ABBBAAABB: -1.71 BBBBAAABB: -1.40 AAAABAABB: 0.02 BAAABAABB: -0.75 ABAABAABB: 1.12 BBAABAABB: -1.87 AABABAABB: 0.82 BABABAABB: 1.91 ABBABAABB: -0.09 BBBABAABB: -1.03 AAABBAABB: -1.58 BAABBAABB: -1.66 ABABBAABB: 0.54 BBABBAABB: -0.27 AABBBAABB: -2.31 BABBBAABB: -0.46 ABBBBAABB: -2.13 BBBBBAABB: -1.43 AAAAABABB: -1.45 BAAAABABB: -0.71 ABAAABABB: 2.06 BBAAABABB: -1.85 AABAABABB: 1.21 BABAABABB: 2.38 ABBAABABB: -1.07 BBBAABABB: -1.20 AAABABABB: -1.07 BAABABABB: 2.18 ABABABABB: 12.85 BBABABABB: 1.53 AABBABABB: -0.70 BABBABABB: 4.91 ABBBABABB: 0.62 BBBBABABB: -1.52 AAAABBABB: -2.22 BAAABBABB: -1.70 ABAABBABB: -1.08 BBAABBABB: -1.30 AABABBABB: -0.73 BABABBABB: 4.84 ABBABBABB: 1.83 BBBABBABB: 0.02 AAABBBABB: -1.87 BAABBBABB: -0.28 ABABBBABB: 0.94 BBABBBABB: 1.21 AABBBBABB: -1.06 BABBBBABB: -1.08 ABBBBBABB: -1.66 BBBBBBABB: -1.95 AAAAAABBB: -1.69 BAAAAABBB: -1.63 ABAAAABBB: -0.80 BBAAAABBB: -1.82 AABAAABBB: -0.27 BABAAABBB: -0.50 ABBAAABBB: -2.21 BBBAAABBB: -1.49 AAABAABBB: 0.49 BAABAABBB: -1.80 ABABAABBB: -0.53 BBABAABBB: -1.74 AABBAABBB: -1 BABBAABBB: -0.76 ABBBAABBB: -1.75 BBBBAABBB: -1.98 AAAABABBB: -1.68 BAAABABBB: -0.31 ABAABABBB: -0.39 BBAABABBB: -1.36 AABABABBB: -1.62 BABABABBB: 2.35 ABBABABBB: 0.01 BBBABABBB: -1.04 AAABBABBB: -2.17 BAABBABBB: -0.61 ABABBABBB: 2.53 BBABBABBB: -0.47 AABBBABBB: -1.15 BABBBABBB: -0.46 ABBBBABBB: -1.34 BBBBBABBB: -1.96 AAAAABBBB: -1.70 BAAAABBBB: -1.38 ABAAABBBB: -0.66 BBAAABBBB: -1.61 AABAABBBB: -1.05 BABAABBBB: -1.91 ABBAABBBB: -2.54 BBBAABBBB: -1.45 AAABABBBB: -1.01 BAABABBBB: -1.20 ABABABBBB: -1.71 BBABABBBB: -1.84 AABBABBBB: -1.34 BABBABBBB: -0.93 ABBBABBBB: -0.05 BBBBABBBB: -1.75 AAAABBBBB: -1.79 BAAABBBBB: -1.05 ABAABBBBB: -0.82 BBAABBBBB: -1.84 AABABBBBB: -0.56 BABABBBBB: -1.45 ABBABBBBB: -1.93 BBBABBBBB: -1.01 AAABBBBBB: -1.32 BAABBBBBB: -0.74 ABABBBBBB: -1.71 BBABBBBBB: -1.14 AABBBBBBB: -0.58 BABBBBBBB: -1.51 ABBBBBBBB: -1.53 BBBBBBBBB: -1.04
Posted : November 4, 2018 1:51 pm
UPDATED
I have not sorted the patterns because I wanted to do something like this:
The red graph is the 340 and the green graph is the 408. These are 2-symbol cycle 6-grams patterns from "AAAAAA" to "BBBBBB" for a total of 64 combinations. Observe that the 340 lines up with the 408. The big green peak is "ABABAB" and the runner up is "BABABA".
Posted : November 4, 2018 2:24 pm
UPDATED
Here is the 340 versus a palindromic cycles cipher of mine. Also much similarity between the two.
Posted : November 4, 2018 2:32 pm
UPDATED
340 versus a cipher with about 25% cycle randomization.
Posted : November 4, 2018 2:35 pm
Topic starter
Very interesting comparisons! I wonder if you can quantify the similarity. For example, calculate the Euclidian distance between the two vectors of cycle values (are they sigmas?) Or maybe calculate a correlation coefficient. Then compare with a wide variety of cyclic and non-cyclic ciphers.
Posted : November 4, 2018 2:43 pm
Topic starter
I’m also curious if the correlation gets stronger or weaker if you look at permutations of 3 symbols instead of 2.
Posted : November 4, 2018 2:48 pm
What about RLBT ABAA, which with a bunch of them is ABAAABAAABAAABA?
UPDATED
Patt: LRTB RLBT ------------------ AAAA: -2.49 -1.11 BAAA: 0.34 -1.18 ABAA: 3.77 1.98 BBAA: -1.40 -2.11 AABA: 1.97 2.55 BABA: 4.48 5.05 ABBA: -0.40 0.82 BBBA: -0.89 -0.64 AAAB: -2.78 -0.91 BAAB: 3.57 1.79 ABAB: 4.85 4.47 BBAB: 0.53 2.49 AABB: -4.45 -4.13 BABB: 0.80 0.42 ABBB: -1.85 -2.55 BBBB: -0.51 -1.74
Posted : November 4, 2018 2:51 pm
Very interesting comparisons! I wonder if you can quantify the similarity. For example, calculate the Euclidian distance between the two vectors of cycle values (are they sigmas?) Or maybe calculate a correlation coefficient. Then compare with a wide variety of cyclic and non-cyclic ciphers.
I tried the quantify the similarity in a variety of ways in the last couple of pages of: viewtopic.php?f=81&t=3616 I since removed this code and functionality from AZdecrypt because something seemed off. Using the Euclidian distance is a good idea! I understand this is just the distance between 2 points in 2 dimensions?
Posted : November 4, 2018 3:08 pm
Topic starter
Using the Euclidian distance is a good idea! I understand this is just the distance between 2 points in 2 dimensions?
Yes but it can be extended to arbitrary dimensions.
1 dimension: Distance = x1-x2
2 dimensions: Distance = sqrt( (x1-x2)^2 + (y1-y2)^2 )
3 dimensions: Distance = sqrt( (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)
4 dimensions: Distance = sqrt( (w1-w2)^2 + (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)
And so on. In your case you’d be calculating it for 64 dimensions.
Posted : November 4, 2018 3:16 pm
Topic starter
Another way to measure similarity of two vectors is https://en.wikipedia.org/wiki/Cosine_similarity . Interestingly, that measurement was used to help crack the Copiale cipher. In that case vectors were made of symbol contact frequencies (i.e., numbers of times symbols followed or preceded other symbols). Cosine similarity was used to find similar vectors, indicating symbols that seem to behave like other symbols and are therefore homophones.
Posted : November 4, 2018 3:21 pm
I’m also curious if the correlation gets stronger or weaker if you look at permutations of 3 symbols instead of 2.
UPDATED
First we will have to decide on how to correlate. I am using sigmas. With more symbols or longer n-grams the combinations increase and the correlation will grow increasingly detailed and more differences/similarities will become more apparent.
3-symbol cycle 5-gram patterns, 340 versus 408:
Posted : November 4, 2018 3:23 pm
Another way to measure similarity of two vectors is https://en.wikipedia.org/wiki/Cosine_similarity . Interestingly, that measurement was used to help crack the Copiale cipher. In that case vectors were made of symbol contact frequencies (i.e., numbers of times symbols followed or preceded other symbols). Cosine similarity was used to find similar vectors, indicating symbols that seem to behave like other symbols and are therefore homophones.
You used it as well to score the cycles in the 408. And to differentiate the correct symbols for the 7-symbol cycle in the 408.
How about using the chi-square?
Posted : November 4, 2018 3:27 pm
