Rows 12 and 14 in the 340
Posted: Tue Apr 12, 2016 6:18 amAs you may know, rows 12 and 14 hold the horizontal parts of the pivots (observation by doranchak). There's a chance that something strange is going on with these rows, a bit of a side quest here and it's something I've mentioned before but thought it deserved its own thread.
http://zodiackillerciphers.com/wiki/ind ... tle=Pivots
Explanations of the measurements used:
Flatness:
If the frequency distribution of the symbols of a 340 character cipher would be perfectly flat then each symbol would be repeated 340/63 (fraction) times. Sum the differences of the frequencies versus this "expected" value and then normalize it over the total amount of characters and unique symbols. A flatness of 0 is a perfectly flat distribution of symbols.
Sequential:
My m_2s_cycles measurement, inspired by smokie's system. Higher is more cyclic. (unnormalized)
The measurements and observation:
Flatness / sequential:
408: 108.8 / 2872
340: 144.9 / 2152
340 without "+" symbol: 132.8 / 2139
It can be seen that the 408 is more sequential/cyclic than the 340 (as we know) and that the 408 also has a flatter distribution of frequencies, even after removing the "+" symbol. Because 108.8 is closer to 0 than 144.9 or 132.8.
Now let's check the values of these measurements for the 340 while excluding one column or row at a time. With more perfect sequential/cyclic homophonic substitution the flatness value should go down and the sequential value should go up.
Flatness / sequential:
Column 1: 148.9 / 2014
Column 2: 142.9 / 2095
Column 3: 143.0 / 2055
Column 4: 151.4 / 1969
Column 5: 143.4 / 2048
Column 6: 151.4 / 1886
Column 7: 151.5 / 1925
Column 8: 151.4 / 2113
Column 9: 141.2 / 2045
Column 10: 151.4 / 1997
Column 11: 143.0 / 2003
Column 12: 147.3 / 2021
Column 13: 147.6 / 2115 <---
Column 14: 147.3 / 1896
Column 15: 141.6 / 1940
Column 16: 153.8 / 1963
Column 17: 140.6 / 2078 <---
For the columns the lowest flatness is 140.6 and the highest sequential is 2115. This seems to be okay.
Flatness / sequential:
Row 1 : 148.3 / 2007
Row 2 : 146.2 / 1986
Row 3 : 148.0 / 1959
Row 4 : 139.6 / 2148
Row 5 : 149.6 / 1865
Row 6 : 145.6 / 2099
Row 7 : 144.1 / 2007
Row 8 : 148.4 / 2061
Row 9 : 143.5 / 2022
Row 10 : 143.8 / 2093
Row 11 : 147.2 / 2068
Row 12 : 137.8 / 2151 <---
Row 13 : 147.2 / 2067
Row 14 : 142.2 / 2244 <---
Row 15 : 154.3 / 1955
Row 16 : 139.6 / 2044
Row 17 : 143.8 / 2134
Row 18 : 149.6 / 2142
Row 19 : 148.0 / 2008
Row 20 : 151.4 / 2065
For the rows the lowest flatness is 137.8 and the highest sequential is 2244 (+92 from the normal 340's 2152). The observation here is that these happen to be the rows that hold the horizontal component of the pivots, row 12 and 14. Coincidence or not, I don't know, but it's not impossible that the Zodiac put the pivots in himself. He did something similar in the 408 where he pulled down a 4-gram.
http://zodiackillerciphers.com/wiki/ind ... tle=Pivots
Explanations of the measurements used:
Flatness:
If the frequency distribution of the symbols of a 340 character cipher would be perfectly flat then each symbol would be repeated 340/63 (fraction) times. Sum the differences of the frequencies versus this "expected" value and then normalize it over the total amount of characters and unique symbols. A flatness of 0 is a perfectly flat distribution of symbols.
Sequential:
My m_2s_cycles measurement, inspired by smokie's system. Higher is more cyclic. (unnormalized)
The measurements and observation:
Flatness / sequential:
408: 108.8 / 2872
340: 144.9 / 2152
340 without "+" symbol: 132.8 / 2139
It can be seen that the 408 is more sequential/cyclic than the 340 (as we know) and that the 408 also has a flatter distribution of frequencies, even after removing the "+" symbol. Because 108.8 is closer to 0 than 144.9 or 132.8.
Now let's check the values of these measurements for the 340 while excluding one column or row at a time. With more perfect sequential/cyclic homophonic substitution the flatness value should go down and the sequential value should go up.
Flatness / sequential:
Column 1: 148.9 / 2014
Column 2: 142.9 / 2095
Column 3: 143.0 / 2055
Column 4: 151.4 / 1969
Column 5: 143.4 / 2048
Column 6: 151.4 / 1886
Column 7: 151.5 / 1925
Column 8: 151.4 / 2113
Column 9: 141.2 / 2045
Column 10: 151.4 / 1997
Column 11: 143.0 / 2003
Column 12: 147.3 / 2021
Column 13: 147.6 / 2115 <---
Column 14: 147.3 / 1896
Column 15: 141.6 / 1940
Column 16: 153.8 / 1963
Column 17: 140.6 / 2078 <---
For the columns the lowest flatness is 140.6 and the highest sequential is 2115. This seems to be okay.
Flatness / sequential:
Row 1 : 148.3 / 2007
Row 2 : 146.2 / 1986
Row 3 : 148.0 / 1959
Row 4 : 139.6 / 2148
Row 5 : 149.6 / 1865
Row 6 : 145.6 / 2099
Row 7 : 144.1 / 2007
Row 8 : 148.4 / 2061
Row 9 : 143.5 / 2022
Row 10 : 143.8 / 2093
Row 11 : 147.2 / 2068
Row 12 : 137.8 / 2151 <---
Row 13 : 147.2 / 2067
Row 14 : 142.2 / 2244 <---
Row 15 : 154.3 / 1955
Row 16 : 139.6 / 2044
Row 17 : 143.8 / 2134
Row 18 : 149.6 / 2142
Row 19 : 148.0 / 2008
Row 20 : 151.4 / 2065
For the rows the lowest flatness is 137.8 and the highest sequential is 2244 (+92 from the normal 340's 2152). The observation here is that these happen to be the rows that hold the horizontal component of the pivots, row 12 and 14. Coincidence or not, I don't know, but it's not impossible that the Zodiac put the pivots in himself. He did something similar in the 408 where he pulled down a 4-gram.
