I like your thought process on this Smokie. Are you still working on a coloured spread sheets showing the period 19? I Can’t wait to get back to a real computer to help a little.. Your spreadsheets are amazing..
I’m glad my solver is working for you smokie, if you have any specific problems with it let me know and I’ll help you out.
You tried to arrange what would be the same as 19 scytale columns into 19 rows and the 340 didn’t solve, is that correct? Were your efforts totally fruitless?
I tried millions of period 15/19 line randomizations and the 340 just managed to touch a 21000+ score but your test cipher scored 21700+. I think the 21000 would be close to what is expected from a random string with so many randomizations.
Reasons I consider in no particular order:
1. It’s not transposition.
2. Something is causing a misalignment, in some way.
3. The encoding additionally has a polyalphabetic element, or has another additional difficulty.
4. Something is different at the language level, non-English language, word reversal (glurk’s idea).
I think option 2 here is most likely because we have a good indication of this with the period 29 should have been period 30 observation. But there other observations that are very strange and frankly off the hook. I’ll illustrate one that I think may be important in understanding what is going on with the 340 (or I don’t understand it properly).
In the following image the graph on the top is the normal 340, it are the bigram repeats c*(c-1) calculation. The graph on the bottom is for the 340 in a 18 by 20 grid with a new set of symbols inserted in the 18th column. Look at how period 5 comes into play now. How can this be? I don’t understand it at all, smokie I’m hoping that you could take a look at it. Are we possibly looking at a cipher with 2 different interlaced periods?
And here’s a visualization of period 5 in a 18 by 20 grid. You can see that it resembles period 15, 19 visually. But it is still period 5.
In the following image the graph on the top is the normal 340, it are the bigram repeats c*(c-1) calculation. The graph on the bottom is for the 340 in a 18 by 20 grid with a new set of symbols inserted in the 18th column. Look at how period 5 comes into play now. How can this be? I don’t understand it at all, smokie I’m hoping that you could take a look at it. Are we possibly looking at a cipher with 2 different interlaced periods?
I looked at this before but only for 18×20 + period 5. You provoked my curiosity again, so I wrote a function to explore all possible "column insertion" operations:
insert(col, shift): Inserts a column of spaces (nulls) at column col, making the cipher col symbols wide as a side effect. Shift can be a value from the range [0,col), which moves the column shift positions to the left. I use spaces (nulls) instead of random symbols, because I don’t want to over count bigrams (spaces are not included in any count).
Here are some examples based on yours:
insert(18, 0): [HER>pl^VPk|1LTG2d ] [Np+B(#O%DWY.<*Kf) ] [By:cM+UZGW()L#zHJ ] [Spp7^l8*V3pO++RK2 ] [_9M+ztjd|5FP+&4k/ ] [p8R^FlO-*dCkF>2D( ] [#5+Kq%;2UcXGV.zL| ] [(G2Jfj#O+_NYz+@L9 ] [d<M+b+ZR2FBcyA64K ] [-zlUV+^J+Op7<FBy- ] [U+R/5tE|DYBpbTMKO ] [2<clRJ|*5T4M.+&BF ] [z69Sy#+N|5FBc(;8R ] [lGFN^f524b.cV4t++ ] [yBX1*:49CE>VUZ5-+ ] [|c.3zBK(Op^.fMqG2 ] [RcT+L16C<+FlWB|)L ] [++)WCzWcPOSHT/()p ] [|FkdW<7tB_YOB*-Cc ] [>MDHNpkSzZO8A|K;+ ] insert(18, 1): [HER>pl^VPk|1LTG2 d] [Np+B(#O%DWY.<*Kf )] [By:cM+UZGW()L#zH J] [Spp7^l8*V3pO++RK 2] [_9M+ztjd|5FP+&4k /] [p8R^FlO-*dCkF>2D (] [#5+Kq%;2UcXGV.zL |] [(G2Jfj#O+_NYz+@L 9] [d<M+b+ZR2FBcyA64 K] [-zlUV+^J+Op7<FBy -] [U+R/5tE|DYBpbTMK O] [2<clRJ|*5T4M.+&B F] [z69Sy#+N|5FBc(;8 R] [lGFN^f524b.cV4t+ +] [yBX1*:49CE>VUZ5- +] [|c.3zBK(Op^.fMqG 2] [RcT+L16C<+FlWB|) L] [++)WCzWcPOSHT/() p] [|FkdW<7tB_YOB*-C c] [>MDHNpkSzZO8A|K; +] insert(18, 2): [HER>pl^VPk|1LTG 2d] [Np+B(#O%DWY.<*K f)] [By:cM+UZGW()L#z HJ] [Spp7^l8*V3pO++R K2] [_9M+ztjd|5FP+&4 k/] [p8R^FlO-*dCkF>2 D(] [#5+Kq%;2UcXGV.z L|] [(G2Jfj#O+_NYz+@ L9] [d<M+b+ZR2FBcyA6 4K] [-zlUV+^J+Op7<FB y-] [U+R/5tE|DYBpbTM KO] [2<clRJ|*5T4M.+& BF] [z69Sy#+N|5FBc(; 8R] [lGFN^f524b.cV4t ++] [yBX1*:49CE>VUZ5 -+] [|c.3zBK(Op^.fMq G2] [RcT+L16C<+FlWB| )L] [++)WCzWcPOSHT/( )p] [|FkdW<7tB_YOB*- Cc] [>MDHNpkSzZO8A|K ;+] insert(18, 3): [HER>pl^VPk|1LT G2d] [Np+B(#O%DWY.<* Kf)] [By:cM+UZGW()L# zHJ] [Spp7^l8*V3pO++ RK2] [_9M+ztjd|5FP+& 4k/] [p8R^FlO-*dCkF> 2D(] [#5+Kq%;2UcXGV. zL|] [(G2Jfj#O+_NYz+ @L9] [d<M+b+ZR2FBcyA 64K] [-zlUV+^J+Op7<F By-] [U+R/5tE|DYBpbT MKO] [2<clRJ|*5T4M.+ &BF] [z69Sy#+N|5FBc( ;8R] [lGFN^f524b.cV4 t++] [yBX1*:49CE>VUZ 5-+] [|c.3zBK(Op^.fM qG2] [RcT+L16C<+FlWB |)L] [++)WCzWcPOSHT/ ()p] [|FkdW<7tB_YOB* -Cc] [>MDHNpkSzZO8A| K;+] insert(18, 4): [HER>pl^VPk|1L TG2d] [Np+B(#O%DWY.< *Kf)] [By:cM+UZGW()L #zHJ] [Spp7^l8*V3pO+ +RK2] [_9M+ztjd|5FP+ &4k/] [p8R^FlO-*dCkF >2D(] [#5+Kq%;2UcXGV .zL|] [(G2Jfj#O+_NYz +@L9] [d<M+b+ZR2FBcy A64K] [-zlUV+^J+Op7< FBy-] [U+R/5tE|DYBpb TMKO] [2<clRJ|*5T4M. +&BF] [z69Sy#+N|5FBc (;8R] [lGFN^f524b.cV 4t++] [yBX1*:49CE>VU Z5-+] [|c.3zBK(Op^.f MqG2] [RcT+L16C<+FlW B|)L] [++)WCzWcPOSHT /()p] [|FkdW<7tB_YOB *-Cc] [>MDHNpkSzZO8A |K;+]
Specifying different values for "col" will adjust the width accordingly. Example:
insert(11, 0): [HER>pl^VPk ] [|1LTG2dNp+ ] [B(#O%DWY.< ] [*Kf)By:cM+ ] [UZGW()L#zH ] [JSpp7^l8*V ] [3pO++RK2_9 ] [M+ztjd|5FP ] [+&4k/p8R^F ] [lO-*dCkF>2 ] [D(#5+Kq%;2 ] [UcXGV.zL|( ] [G2Jfj#O+_N ] [Yz+@L9d<M+ ] [b+ZR2FBcyA ] [64K-zlUV+^ ] [J+Op7<FBy- ] [U+R/5tE|DY ] [BpbTMKO2<c ] [lRJ|*5T4M. ] [+&BFz69Sy# ] [+N|5FBc(;8 ] [RlGFN^f524 ] [b.cV4t++yB ] [X1*:49CE>V ] [UZ5-+|c.3z ] [BK(Op^.fMq ] [G2RcT+L16C ] [<+FlWB|)L+ ] [+)WCzWcPOS ] [HT/()p|Fkd ] [W<7tB_YOB* ] [-Cc>MDHNpk ] [SzZO8A|K;+ ] insert(11, 1): [HER>pl^VP k] [|1LTG2dNp +] [B(#O%DWY. <] [*Kf)By:cM +] [UZGW()L#z H] [JSpp7^l8* V] [3pO++RK2_ 9] [M+ztjd|5F P] [+&4k/p8R^ F] [lO-*dCkF> 2] [D(#5+Kq%; 2] [UcXGV.zL| (] [G2Jfj#O+_ N] [Yz+@L9d<M +] [b+ZR2FBcy A] [64K-zlUV+ ^] [J+Op7<FBy -] [U+R/5tE|D Y] [BpbTMKO2< c] [lRJ|*5T4M .] [+&BFz69Sy #] [+N|5FBc(; 8] [RlGFN^f52 4] [b.cV4t++y B] [X1*:49CE> V] [UZ5-+|c.3 z] [BK(Op^.fM q] [G2RcT+L16 C] [<+FlWB|)L +] [+)WCzWcPO S] [HT/()p|Fk d] [W<7tB_YOB *] [-Cc>MDHNp k] [SzZO8A|K; +] [HER>pl^V Pk] [|1LTG2dN p+] [B(#O%DWY .<] [*Kf)By:c M+] [UZGW()L# zH] [JSpp7^l8 *V] [3pO++RK2 _9] [M+ztjd|5 FP] [+&4k/p8R ^F] [lO-*dCkF >2] [D(#5+Kq% ;2] [UcXGV.zL |(] [G2Jfj#O+ _N] [Yz+@L9d< M+] [b+ZR2FBc yA] [64K-zlUV +^] [J+Op7<FB y-] [U+R/5tE| DY] [BpbTMKO2 <c] [lRJ|*5T4 M.] [+&BFz69S y#] [+N|5FBc( ;8] [RlGFN^f5 24] [b.cV4t++ yB] [X1*:49CE >V] [UZ5-+|c. 3z] [BK(Op^.f Mq] [G2RcT+L1 6C] [<+FlWB|) L+] [+)WCzWcP OS] [HT/()p|F kd] [W<7tB_YO B*] [-Cc>MDHN pk] [SzZO8A|K ;+] insert(11, 2): [HER>pl^ VPk] [|1LTG2d Np+] [B(#O%DW Y.<] [*Kf)By: cM+] [UZGW()L #zH] [JSpp7^l 8*V] [3pO++RK 2_9] [M+ztjd| 5FP] [+&4k/p8 R^F] [lO-*dCk F>2] [D(#5+Kq %;2] [UcXGV.z L|(] [G2Jfj#O +_N] [Yz+@L9d <M+] [b+ZR2FB cyA] [64K-zlU V+^] [J+Op7<F By-] [U+R/5tE |DY] [BpbTMKO 2<c] [lRJ|*5T 4M.] [+&BFz69 Sy#] [+N|5FBc (;8] [RlGFN^f 524] [b.cV4t+ +yB] [X1*:49C E>V] [UZ5-+|c .3z] [BK(Op^. fMq] [G2RcT+L 16C] [<+FlWB| )L+] [+)WCzWc POS] [HT/()p| Fkd] [W<7tB_Y OB*] [-Cc>MDH Npk] [SzZO8A| K;+]
So, I think your example corresponds to insert(18, 0), which in my setup produces 35 bigrams at period 5 (I think you get more in your setup because some new random symbols are accidentally included in the counts). But many combinations of col and shift produce as many or more bigrams at a variety of periods. Here are all that have at least 30 bigrams (I tested col in the range [1,30], along with all possible valid values for shift):
bigrams col shift period 39 26 6 20 39 22 7 20 39 22 3 20 39 21 18 20 39 16 8 20 38 23 22 20 38 23 0 20 38 21 7 20 38 21 5 20 38 21 19 20 38 21 17 20 38 21 15 20 38 21 13 20 38 21 1 20 38 21 0 20 37 26 7 20 37 23 1 20 37 22 8 20 37 21 9 20 37 21 8 20 37 21 6 20 37 21 20 20 37 21 14 20 37 21 12 20 37 21 11 20 37 20 9 20 37 20 8 20 37 20 7 20 37 20 6 20 37 20 5 20 37 20 4 20 37 20 3 20 37 20 2 20 37 20 19 20 37 20 18 20 37 20 17 20 37 20 16 20 37 20 15 20 37 20 14 20 37 20 13 20 37 20 12 20 37 20 11 20 37 20 10 20 37 20 1 20 37 20 0 20 37 2 1 38 37 2 0 38 37 18 12 20 37 17 10 20 37 1 0 38 36 27 12 5 36 27 11 20 36 23 13 20 36 22 9 20 36 22 2 20 36 22 10 20 36 21 4 20 36 21 2 20 36 21 16 20 36 19 4 20 35 27 11 5 35 26 5 20 35 26 4 20 35 22 6 20 35 22 4 20 35 22 20 20 35 22 19 20 35 22 13 20 35 22 11 20 35 21 10 20 35 19 6 20 35 19 3 20 35 18 14 20 35 18 11 20 ===> 35 18 0 5 <=== 35 17 11 20 35 15 1 20 35 14 11 5 35 11 5 21 34 28 5 40 34 27 5 20 34 27 13 20 34 26 5 5 34 25 6 20 34 25 4 20 34 25 19 20 34 24 6 20 34 24 17 20 34 23 4 20 34 23 20 20 34 22 17 20 34 22 12 20 34 19 5 20 34 19 2 20 34 19 17 20 34 19 15 20 34 19 14 20 34 19 1 20 34 18 17 5 34 18 17 20 34 18 1 20 34 18 0 20 34 17 8 20 34 17 4 20 34 17 3 20 34 16 9 20 34 16 7 20 34 16 6 20 34 14 12 5 34 11 8 21 34 11 7 21 34 11 2 21 33 30 22 5 33 29 9 40 33 29 8 40 33 29 15 5 33 29 11 20 33 29 10 20 33 27 10 20 33 25 1 20 33 24 12 20 33 23 8 20 33 23 21 20 33 23 17 20 33 23 16 5 33 23 15 17 33 23 13 146 33 23 12 20 33 22 7 5 33 22 5 20 33 22 21 20 33 22 18 20 33 22 1 20 33 22 0 20 33 21 3 20 33 19 18 20 33 19 13 20 33 19 11 20 33 19 10 20 33 19 0 20 33 18 6 20 33 18 16 20 33 18 10 20 33 17 9 20 33 17 5 20 33 17 4 41 33 11 9 21 33 11 4 21 33 11 1 21 32 30 22 88 32 30 19 85 32 30 18 40 32 30 14 56 32 29 27 35 32 29 22 64 32 29 13 20 32 29 12 20 32 28 4 40 32 28 19 20 32 27 9 20 32 27 8 20 32 27 7 20 32 27 20 164 32 27 16 20 32 27 14 20 32 27 13 5 32 27 12 20 32 26 8 20 32 26 6 5 32 26 3 20 32 26 25 20 32 26 24 20 32 26 23 20 32 26 2 20 32 26 0 20 32 25 5 20 32 25 20 20 32 25 19 5 32 24 5 20 32 24 19 20 32 23 5 20 32 23 18 20 32 23 17 5 32 23 17 17 32 23 16 17 32 23 15 5 32 23 14 5 32 23 14 20 32 23 14 17 32 23 13 5 32 23 11 89 32 22 9 41 32 22 7 68 32 22 16 20 32 22 15 86 32 22 14 20 32 21 15 96 32 19 8 20 32 19 16 20 32 19 12 20 32 18 9 20 32 18 3 20 32 18 2 20 32 18 13 20 32 17 2 20 32 17 12 20 32 17 1 41 32 17 0 20 32 16 5 20 32 16 10 20 32 15 2 20 32 12 1 21 32 11 6 21 32 10 6 21 32 10 4 21 31 9 3 21 31 30 9 85 31 30 8 85 31 30 28 76 31 30 25 65 31 30 25 5 31 30 17 40 31 30 16 40 31 30 13 20 31 30 12 56 31 30 10 85 31 29 9 20 31 29 7 56 31 29 28 35 31 29 23 162 31 29 15 85 31 29 14 5 31 29 14 20 31 29 13 56 31 29 13 5 31 29 11 5 31 29 10 40 31 29 0 35 31 28 4 5 31 28 3 40 31 28 26 18 31 28 24 78 31 28 23 78 31 28 2 40 31 28 18 20 31 28 16 20 31 28 1 40 31 27 6 20 31 27 4 40 31 27 24 139 31 27 18 140 31 27 18 126 31 27 17 140 31 27 15 20 31 27 15 140 31 27 14 5 31 27 11 140 31 26 9 20 31 26 5 17 31 26 3 77 31 26 3 17 31 26 24 77 31 26 24 29 31 26 23 29 31 26 2 77 31 26 10 20 31 26 1 40 31 26 1 20 31 25 21 5 31 25 21 20 31 25 20 5 31 25 2 29 31 25 2 20 31 25 18 5 31 25 15 29 31 24 7 20 31 24 4 5 31 24 4 20 31 24 3 68 31 24 22 5 31 24 20 18 31 24 2 17 31 24 18 20 31 24 11 20 31 23 9 20 31 23 6 20 31 23 3 20 31 23 2 20 31 23 19 68 31 23 19 20 31 23 15 68 31 23 13 17 31 23 11 20 31 23 1 31 31 23 1 141 31 22 4 41 31 22 3 41 31 22 15 20 31 20 19 142 31 20 0 142 31 19 9 20 31 19 7 20 31 18 7 20 31 18 4 20 31 18 16 5 31 18 15 20 31 17 6 31 31 17 3 41 31 17 16 20 31 17 15 20 31 17 1 20 31 17 0 41 31 15 14 20 31 15 1 88 31 15 0 20 31 13 7 21 31 12 11 21 31 12 0 21 31 11 3 21 31 10 5 21 31 10 2 21 30 6 5 6 30 6 4 6 30 6 3 6 30 6 2 6 30 6 1 6 30 6 0 6 30 30 8 100 30 30 26 5 30 30 24 5 30 30 21 88 30 30 21 85 30 30 21 5 30 30 20 5 30 30 19 40 30 30 18 56 30 30 17 56 30 30 14 20 30 30 12 20 30 29 8 35 30 29 7 35 30 29 5 18 30 29 26 35 30 29 24 140 30 29 23 64 30 29 22 76 30 29 21 67 30 29 19 163 30 29 17 139 30 29 16 139 30 29 15 139 30 29 11 85 30 29 10 5 30 28 9 157 30 28 7 40 30 28 6 5 30 28 4 20 30 28 27 96 30 28 27 20 30 28 27 18 30 28 24 18 30 28 23 18 30 28 22 18 30 28 21 20 30 28 13 47 30 28 10 17 30 28 1 95 30 28 1 20 30 28 0 96 30 28 0 20 30 28 0 18 30 27 8 77 30 27 7 29 30 27 6 101 30 27 5 29 30 27 3 47 30 27 21 67 30 27 1 63 30 26 7 5 30 26 4 5 30 26 3 47 30 26 3 45 30 26 25 40 30 26 11 140 30 26 10 140 30 26 0 40 30 25 7 20 30 25 3 29 30 25 3 20 30 25 24 166 30 25 23 20 30 25 17 20 30 25 14 77 30 25 13 5 30 24 21 20 30 24 17 86 30 24 16 20 30 24 15 20 30 24 13 20 30 24 1 20 30 24 1 17 30 24 0 20 30 23 7 20 30 23 18 5 30 23 17 84 30 23 15 20 30 23 12 68 30 23 11 101 30 23 10 89 30 23 10 165 30 22 6 68 30 22 6 5 30 22 5 68 30 22 20 101 30 22 2 86 30 22 16 128 30 22 15 11 30 21 7 5 30 21 5 41 30 21 14 96 30 21 10 41 30 20 3 152 30 20 17 57 30 20 16 5 30 20 15 5 30 20 13 41 30 2 1 10 30 2 0 10 30 19 2 5 30 18 8 20 30 18 5 20 30 18 17 41 30 18 0 41 30 17 7 31 30 17 6 59 30 17 16 41 30 17 15 41 30 17 14 20 30 17 13 5 30 17 12 5 30 17 11 5 30 17 1 66 30 16 7 91 30 16 12 20 30 16 11 20 30 16 0 20 30 15 7 79 30 15 4 20 30 14 8 70 30 14 7 70 30 14 12 70 30 14 1 70 30 10 3 21 30 10 1 21 30 1 0 10
(Note that the result corresponding to your example is highlighted in the above list)
Something interesting: Many of the ones involving high bigram counts use period 20 or period 38.
Here’s one of the best ones (col 16, shift 8, has 39 bigrams at period 20):
HER>pl^ VPk|1LTG 2dNp+B( #O%DWY.< *Kf)By: cM+UZGW( )L#zHJS pp7^l8*V 3pO++RK 2_9M+ztj d|5FP+& 4k/p8R^F lO-*dCk F>2D(#5+ Kq%;2Uc XGV.zL|( G2Jfj#O +_NYz+@L 9d<M+b+ ZR2FBcyA 64K-zlU V+^J+Op7 <FBy-U+ R/5tE|DY BpbTMKO 2<clRJ|* 5T4M.+& BFz69Sy# +N|5FBc (;8RlGFN ^f524b. cV4t++yB X1*:49C E>VUZ5-+ |c.3zBK (Op^.fMq G2RcT+L 16C<+FlW B|)L++) WCzWcPOS HT/()p| FkdW<7tB _YOB*-C c>MDHNpk SzZO8A| K;+
You may want to confirm these results, since there’s a chance of buggy code somewhere! 
Here are the results for trigrams instead of bigrams (note: your scheme will also produce 4 trigrams at period 5, but only when you shift the added column 9 positions to the left):
trigrams col shift period 5 28 27 105 5 28 26 105 5 28 1 105 5 28 0 105 5 27 21 105 5 27 20 105 5 27 18 105 5 19 6 50 5 19 4 50 5 16 5 108 5 14 5 51 5 13 6 82 4 30 8 100 4 30 7 100 4 30 24 89 4 30 23 89 4 30 21 119 4 30 15 40 4 29 7 40 4 29 26 158 4 29 1 100 4 28 4 105 4 28 3 105 4 28 20 100 4 28 2 105 4 28 13 119 4 28 12 119 4 27 25 165 4 27 23 29 4 27 19 105 4 27 17 105 4 27 16 20 4 26 8 20 4 26 7 20 4 26 6 20 4 26 17 165 4 26 17 120 4 26 16 165 4 25 6 105 4 25 5 105 4 25 2 105 4 24 9 79 4 24 8 79 4 24 17 94 4 24 11 79 4 24 10 79 4 23 4 90 4 23 4 123 4 23 13 20 4 22 8 160 4 22 7 160 4 22 16 106 4 22 15 106 4 22 13 106 4 21 3 121 4 19 7 50 4 19 5 50 4 18 9 5 4 18 14 122 4 18 10 5 4 17 16 41 4 17 15 41 4 17 1 108 4 17 0 41 4 16 4 108 4 16 3 108 4 16 10 123 4 15 8 108 4 14 11 31 4 12 9 104 4 10 5 112 3 9 5 76 3 8 7 3 3 8 7 16 3 8 6 16 3 8 5 16 3 8 4 16 3 8 3 62 3 8 3 109 3 8 2 98 3 8 2 16 3 8 1 98 3 8 0 3 3 8 0 16 3 7 6 33 3 7 4 32 3 7 0 33 3 6 5 6 3 6 4 6 3 6 3 6 3 6 2 6 3 6 1 6 3 6 1 103 3 6 0 6 3 30 8 89 3 30 7 89 3 30 6 89 3 30 6 165 3 30 6 100 3 30 5 89 3 30 5 100 3 30 4 99 3 30 4 89 3 30 4 49 3 30 3 99 3 30 3 89 3 30 29 89 3 30 28 89 3 30 27 89 3 30 27 119 3 30 23 154 3 30 22 92 3 30 22 89 3 30 22 119 3 30 20 102 3 30 2 99 3 30 2 89 3 30 19 138 3 30 19 130 3 30 19 115 3 30 18 5 3 30 18 40 3 30 18 130 3 30 18 115 3 30 17 89 3 30 17 5 3 30 17 40 3 30 17 130 3 30 16 89 3 30 16 79 3 30 16 5 3 30 16 40 3 30 15 89 3 30 15 79 3 30 15 5 3 30 15 48 3 30 14 40 3 30 14 17 3 30 14 158 3 30 13 5 3 30 13 40 3 30 13 17 3 30 12 5 3 30 12 17 3 30 11 5 3 30 11 17 3 30 10 5 3 30 1 89 3 30 0 89 3 3 1 21 3 29 9 89 3 29 9 40 3 29 9 17 3 29 8 89 3 29 8 40 3 29 7 89 3 29 7 158 3 29 6 40 3 29 6 105 3 29 3 17 3 29 28 89 3 29 28 49 3 29 28 158 3 29 28 100 3 29 27 89 3 29 27 49 3 29 27 158 3 29 26 89 3 29 25 89 3 29 24 89 3 29 24 122 3 29 23 89 3 29 23 122 3 29 23 119 3 29 22 89 3 29 22 165 3 29 22 122 3 29 21 89 3 29 21 165 3 29 21 122 3 29 2 89 3 29 2 158 3 29 2 100 3 29 18 79 3 29 18 154 3 29 17 154 3 29 17 138 3 29 16 92 3 29 16 89 3 29 16 154 3 29 16 138 3 29 15 92 3 29 15 89 3 29 15 5 3 29 15 154 3 29 14 92 3 29 14 5 3 29 14 154 3 29 13 92 3 29 13 5 3 29 12 5 3 29 11 5 3 29 1 89 3 29 1 158 3 29 0 89 3 29 0 49 3 29 0 158 3 29 0 100 3 28 9 122 3 28 8 5 3 28 6 5 3 28 5 5 3 28 5 116 3 28 5 105 3 28 4 5 3 28 3 5 3 28 25 19 3 28 25 158 3 28 25 105 3 28 24 19 3 28 24 158 3 28 24 105 3 28 23 19 3 28 23 158 3 28 22 158 3 28 21 49 3 28 21 100 3 28 2 5 3 28 17 89 3 28 15 122 3 28 14 122 3 28 14 119 3 28 13 122 3 28 12 122 3 28 11 122 3 28 10 122 3 27 9 99 3 27 8 99 3 27 26 105 3 27 25 5 3 27 25 139 3 27 25 105 3 27 24 5 3 27 24 139 3 27 24 120 3 27 24 105 3 27 23 44 3 27 23 139 3 27 23 105 3 27 22 44 3 27 22 105 3 27 21 44 3 27 17 20 3 27 16 105 3 27 15 20 3 27 15 105 3 27 14 105 3 27 13 20 3 27 13 105 3 27 12 5 3 27 12 20 3 27 10 99 3 27 0 105 3 26 9 5 3 26 9 20 3 26 9 105 3 26 8 5 3 26 8 105 3 26 7 105 3 26 6 5 3 26 6 105 3 26 5 5 3 26 5 20 3 26 5 105 3 26 4 5 3 26 4 20 3 26 4 105 3 26 3 5 3 26 3 105 3 26 22 105 3 26 21 105 3 26 20 105 3 26 19 105 3 26 18 165 3 26 18 120 3 26 18 105 3 26 17 105 3 26 16 39 3 26 16 163 3 26 16 120 3 26 16 105 3 26 15 44 3 26 15 39 3 26 15 165 3 26 15 163 3 26 15 105 3 26 14 44 3 26 14 165 3 26 14 163 3 26 14 105 3 26 13 165 3 26 13 105 3 26 12 165 3 26 12 105 3 26 11 96 3 26 11 60 3 26 11 105 3 26 10 105 3 25 8 105 3 25 7 165 3 25 7 105 3 25 6 79 3 25 5 159 3 25 4 105 3 25 3 105 3 25 24 2 3 25 23 94 3 25 22 94 3 25 21 5 3 25 20 5 3 25 20 20 3 25 2 5 3 25 19 5 3 25 19 20 3 25 16 67 3 25 16 166 3 25 15 166 3 25 15 120 3 25 14 166 3 25 13 166 3 25 12 9 3 25 11 9 3 25 1 105 3 25 0 2 3 24 7 79 3 24 6 166 3 24 4 166 3 24 3 5 3 24 3 100 3 24 23 165 3 24 2 5 3 24 17 2 3 24 15 94 3 24 15 83 3 24 15 67 3 24 15 41 3 24 14 67 3 24 14 41 3 24 13 67 3 24 12 79 3 24 12 165 3 24 12 123 3 24 11 20 3 24 11 165 3 24 10 165 3 24 0 165 3 23 9 57 3 23 5 90 3 23 5 143 3 23 4 143 3 23 3 90 3 23 3 123 3 23 22 123 3 23 21 123 3 23 20 5 3 23 2 90 3 23 2 123 3 23 19 5 3 23 19 10 3 23 17 5 3 23 16 5 3 23 15 5 3 23 14 20 3 23 12 20 3 23 11 90 3 23 10 90 3 23 10 55 3 23 1 123 3 23 0 123 3 22 9 90 3 22 9 160 3 22 8 90 3 22 7 5 3 22 7 20 3 22 6 5 3 22 6 160 3 22 5 5 3 22 5 160 3 22 3 166 3 22 21 90 3 22 21 3 3 22 20 26 3 22 20 20 3 22 2 90 3 22 2 166 3 22 17 100 3 22 16 90 3 22 15 90 3 22 14 106 3 22 12 106 3 22 11 50 3 22 11 5 3 22 11 106 3 22 10 50 3 22 10 160 3 22 1 90 3 22 0 90 3 22 0 3 3 21 9 121 3 21 9 106 3 21 8 165 3 21 8 121 3 21 8 106 3 21 7 121 3 21 7 106 3 21 6 106 3 21 5 34 3 21 5 106 3 21 5 100 3 21 4 106 3 21 4 100 3 21 3 106 3 21 20 5 3 21 20 160 3 21 20 106 3 21 2 121 3 21 2 106 3 21 19 57 3 21 19 160 3 21 19 106 3 21 18 5 3 21 18 166 3 21 18 106 3 21 16 34 3 21 16 115 3 21 15 115 3 21 14 115 3 21 13 121 3 21 13 115 3 21 12 121 3 21 12 106 3 21 11 121 3 21 11 106 3 21 10 121 3 21 10 106 3 21 1 160 3 21 1 106 3 21 0 5 3 21 0 160 3 21 0 106 3 20 9 26 3 20 8 2 3 20 7 13 3 20 5 13 3 20 19 50 3 20 18 155 3 20 18 124 3 20 17 5 3 20 17 124 3 20 16 5 3 20 15 5 3 20 12 95 3 20 12 49 3 20 12 30 3 20 11 30 3 20 10 58 3 20 10 49 3 20 10 106 3 20 0 50 3 2 1 10 3 2 0 10 3 19 8 5 3 19 7 80 3 19 7 167 3 19 6 80 3 19 6 167 3 19 5 107 3 19 4 107 3 19 3 50 3 19 3 107 3 19 2 100 3 19 17 161 3 19 15 49 3 19 15 122 3 19 13 91 3 19 12 91 3 19 12 5 3 19 11 91 3 19 10 91 3 19 1 100 3 18 8 107 3 18 7 68 3 18 7 107 3 18 6 91 3 18 6 107 3 18 5 91 3 18 5 169 3 18 5 107 3 18 4 91 3 18 4 168 3 18 4 107 3 18 3 91 3 18 3 168 3 18 3 107 3 18 2 91 3 18 2 107 3 18 17 122 3 18 17 107 3 18 16 91 3 18 16 80 3 18 16 122 3 18 16 107 3 18 15 122 3 18 15 107 3 18 15 102 3 18 13 91 3 18 13 122 3 18 12 91 3 18 11 91 3 18 11 5 3 18 1 107 3 18 0 122 3 18 0 107 3 17 8 5 3 17 4 125 3 17 3 30 3 17 3 125 3 17 2 20 3 17 2 162 3 17 16 123 3 17 16 108 3 17 15 108 3 17 10 168 3 17 1 41 3 17 0 123 3 17 0 108 3 16 9 119 3 16 7 23 3 16 7 119 3 16 6 22 3 16 6 2 3 16 4 61 3 16 12 149 3 16 11 123 3 16 10 119 3 15 9 92 3 15 9 15 3 15 9 145 3 15 8 92 3 15 8 168 3 15 7 92 3 15 7 168 3 15 7 15 3 15 7 108 3 15 6 15 3 15 6 108 3 15 5 15 3 15 4 15 3 15 3 15 3 15 2 92 3 15 2 15 3 15 14 15 3 15 13 15 3 15 12 15 3 15 11 15 3 15 11 102 3 15 10 145 3 15 10 126 3 15 1 92 3 15 1 15 3 15 0 15 3 14 9 10 3 14 4 51 3 14 3 51 3 14 2 51 3 14 13 95 3 14 13 50 3 14 13 109 3 14 12 95 3 14 11 20 3 14 11 124 3 14 10 50 3 14 10 30 3 14 1 50 3 14 0 95 3 14 0 50 3 14 0 109 3 13 8 31 3 13 5 109 3 13 4 96 3 13 3 96 3 13 11 121 3 12 4 94 3 12 2 110 3 12 11 16 3 12 11 110 3 12 1 110 3 12 0 16 3 12 0 110 3 11 9 168 3 11 9 111 3 11 8 111 3 11 6 51 3 11 4 52 3 11 2 51 3 11 2 111 3 11 10 168 3 11 10 111 3 11 1 168 3 11 1 111 3 11 0 168 3 11 0 111 3 10 7 128 3 10 6 128 3 10 4 112 3 10 2 128 3 10 2 107 3 10 1 54 3 1 0 10
And quadgrams:
quadgrams col shift period 3 28 27 105 3 28 1 105 3 28 0 105 3 27 21 105 3 27 20 105 2 29 24 122 2 29 23 122 2 29 22 122 2 29 21 122 2 28 26 105 2 28 15 122 2 28 14 122 2 28 13 122 2 28 12 122 2 28 11 122 2 28 10 122 2 27 26 105 2 27 25 105 2 27 24 105 2 27 23 105 2 27 22 105 2 27 19 105 2 27 18 105 2 27 17 105 2 27 16 105 2 27 15 105 2 27 14 105 2 27 13 105 2 27 0 105 2 26 9 105 2 26 8 105 2 26 7 105 2 26 6 105 2 26 5 105 2 26 4 105 2 26 3 105 2 26 22 105 2 26 21 105 2 26 20 105 2 26 19 105 2 26 18 105 2 26 17 105 2 26 16 105 2 26 15 105 2 26 14 105 2 26 13 105 2 26 12 105 2 26 11 105 2 26 10 105 2 25 8 105 2 25 7 105 2 25 6 105 2 25 5 105 2 25 4 105 2 25 3 105 2 25 2 105 2 24 12 123 2 23 4 123 2 23 3 123 2 23 22 123 2 23 21 123 2 23 2 123 2 23 1 123 2 23 0 123 2 22 16 106 2 22 15 106 2 22 14 106 2 22 13 106 2 22 12 106 2 22 11 106 2 21 9 106 2 21 8 106 2 21 7 106 2 21 6 106 2 21 5 106 2 21 4 106 2 21 3 106 2 21 20 106 2 21 2 106 2 21 19 106 2 21 18 106 2 21 12 106 2 21 11 106 2 21 10 106 2 21 1 106 2 21 0 106 2 20 18 124 2 20 17 124 2 18 8 107 2 18 7 107 2 18 6 107 2 18 5 107 2 18 4 107 2 18 3 107 2 18 2 107 2 18 17 107 2 18 16 107 2 18 15 107 2 18 1 107 2 18 0 107 2 17 4 125 2 17 3 125 2 15 8 108 2 15 7 108 2 15 6 108 2 14 13 50 2 14 13 109 2 14 1 50 2 14 0 50 2 14 0 109 2 12 2 110 2 12 11 110 2 12 1 110 2 12 0 110 2 11 9 111 2 11 8 111 2 11 2 111 2 11 10 111 2 11 1 111 2 11 0 111 2 10 5 112
Col 28 shift 0 produces 3 repeated quadgrams at period 105. First, here’s what the inserted column looks like:
[HER>pl^VPk|1LTG2dNp+B(#O%DW ] [Y.<*Kf)By:cM+UZGW()L#zHJSpp ] [7^l8*V3pO++RK2_9M+ztjd|5FP+ ] [&4k/p8R^FlO-*dCkF>2D(#5+Kq% ] [;2UcXGV.zL|(G2Jfj#O+_NYz+@L ] [9d<M+b+ZR2FBcyA64K-zlUV+^J+ ] [Op7<FBy-U+R/5tE|DYBpbTMKO2< ] [clRJ|*5T4M.+&BFz69Sy#+N|5FB ] [c(;8RlGFN^f524b.cV4t++yBX1* ] [:49CE>VUZ5-+|c.3zBK(Op^.fMq ] [G2RcT+L16C<+FlWB|)L++)WCzWc ] [POSHT/()p|FkdW<7tB_YOB*-Cc> ] [MDHNpkSzZO8A|K;+]
Then rewritten at period 105, you get something like this:
H#F)E5zpR+6|>K9F pqSkl%yd^ #WV;+< P2N7kU|t|c5B1XF_ LGBYTV OG.cB2z(* dL;-N|8Cp(Rc+Gl> B2G (JFM#fNDOj^H %#fNDO5pW+2k _4S YNbz.Y.Z<zcO*+V8 K@4AfLt|) +KB9+; ydy+:<BcMXM+1+b* U+ ZZ:GR4W29(FC) BELc>#yVzAUH6ZJ4 5SK-p-+pz| lc7U. ^V3l+z8^B*JKV+(3 OpOpOp^+7.+<fRF MKBq2y _-G9U2M+R +Rcz/Tt5+jtLdE1| |65DCFY<PB++pF b l&TW4MBkK|/O)p2L 8<+R +^c)FlWlRCO Jz-|W**cd5 CTPk4 OFMS>.H2+TD&/(B(
Visualization of the quadgrams:
Bizarre!
You added a symbol at every 18th position. When you add a symbol you change the bigrams around it.
Below: DH, EI, FJ and GK were period 4 bigrams before you added the X. Now they are period 5 bigrams.
Looking at it on a 17 x 20 grid, these are the period 4 to period 5 comparison "distortion zones". But you could compare any two periods, not just 4 and 5. Below the light yellow shaded cells are period 4 bigrams with symbols that match period 5 bigrams. A lot of them are in the new distortion zones that you created.
One example, 19 and 51 are a period 4 bigram in row 9, and period 5 bigram in row 10. You put the new symbols where the short vertical red lines are. Now 19 and 51 are a period 5 bigram, and also a repeat. The 19 – 51 period 5 bigram on row 10 is not affected.
There are actually 50 count period 4 bigrams in the message that have symbols matching period 5 bigrams, and they seem to be distributed somewhat uniformly. I think that maybe there is a big change in period 5 repeats because of that.
The period 19 repeat count doesn’t change because with adding a new symbol every 18th position, all or most of the period 19 repeats are shifted relative to each other. And maybe you destroyed a few and created a few in the process, making it a wash.
I tried millions of period 15/19 line randomizations and the 340 just managed to touch a 21000+ score but your test cipher scored 21700+. I think the 21000 would be close to what is expected from a random string with so many randomizations.
Mr. Lowe, it sounds like Jarlve tried the equivalent of the scytale and rearranged the columns ( rows ) millions of times, thinking that Zodiac may have done the same. It doesn’t seem to have worked. I like the scytale idea the best, but he must have used some other cipher step besides just transposition and homophonic substitution.
Thanks doranchak, that’s quite allot to take in. The period 20 majority is easy to explain (I think) because adding a column causes the period to shift from 19 to 20. And then 38 possibly should have been 39 or 40 in a properly aligned period transposition scheme. Could you please test that with the following cipher, it has a clear peak at 19 and 38. To refresh our memory, period 38 is period 2 untransposed and the 408 also has an increased count here. So I’m thinking that the 38 thing could possibly be another indication of the misalignment thing. But, the emerging of period 5 bigrams remains a mystery.
XF.V!O1NGE4;TPZ4F KFJE:JDU@&I$,=-T: P!@HY5%JB>VCU5+N' $XT5I5;[QV3,G4>E: DWO@YB'[!.%$ZT1PQ X)D+9W,&M;U=)!G# VP4!S3O[1CY-%H&SU NI:ZV>X'CZ2G2E<VI OQ=DMY->4B%+!ATAJ >3KF'[)#TX,DS9;UA BVO!9H9JX<2$1Y%XV JB.:=DM5+K2YC)MQ# 5<[.S)-11@4E$:AV OKTJ2&YWN@G.MIU)F BZ=F[!CAK!&>H-C;& ET.#'!$9U$<N.P%H3 XCRQZ4,39SV+>W5[: GIJ'WQZP[E1OS&ZK, :41<PT!BH>F#<YCA HD;,@==E335FSNJK#
Okay let me go back to the period 15, 19 misalignment (somehow) hypothesis for the 340 with some visuals to show that this is not unlikely at all. I present you the smoking gun (bigrams c*(c-1)), graphs on top are the normal 340, graphs at the bottom are the mirrored 340. For the normal 340 period 39 has right shifted one position (should have been period 38). At the bottom period 29 has left shifted one position (should have been period 30).
There are actually 50 count period 4 bigrams in the message that have symbols matching period 5 bigrams, and they seem to be distributed somewhat uniformly. I think that maybe there is a big change in period 5 repeats because of that.
Thanks!
This is Scytale by rows using 19 periods in flat pack read in rows from left to right 1, 19,37, 44, through to 4. . It ends up being a period 18 row then two 17 period rows and then 16, 18 period rows… This is how a Scytale works I will post up the paper set up next.. It’s a bit tacky but what the..
This is asumming that 19 is the smoking gun and that he started at 1..
This Is a hand made Scytale turned flat pack for viewing ,,starting point top left number 1 read from left to right
All the period 19s line up perfectly!
I noticed that reversing large strings in the 340 doesn’t necessarily reduce cycle-scores so I ran a test that checks all possible strings with my m_s2_cycles measurement. An example of what I mean: "ABCABCABCABC" becomes "ABCCBACBAABC". I ran the test 5 times in a row for both the 340 and smokie9, each step building on the improved cipher string.
Two interesting questions here. Why is the 340 (much) more moldable in this regard than the smokie9? And why are the range of the first 3 steps reasonably similar for both ciphers?
340 base: 2152
1: Reverse string from position 221 to 288: 2350
2: Reverse string from position 272 to 317: 2551
3: Reverse string from position 4 to 166: 2756
4: Reverse string from position 85 to 208: 2945
5: Reverse string from position 52 to 97: 3061
HER<7pO+J^+VUlz-K 46AycBF2RZ+b+M<d9 L@+zYN_+O#jfJ2G(| 5T4M.+&BFz69Sp8R^ FlO-*dCkF>2D(#5+K q%;2UcXGV.zL*|JRl c<2OKMTbpBYD|Et5/ R+U-yBF>pl^VPk|1L TG2dNp+B(#O%DWY.< *Kf)By:cM+UZGW()L #zHJSpp7^l8*V3pO+ +RK2_9M+ztjd|5FP+ &4k/y#+N|5FBc(;8) |BWlF+<C61L+TcR2G qMf.^pO(KBz3.c|+- 5ZUV>EC94:*1XBy+Y _Bt7<WdkF|p)(/THS OPcWzCW)++LRlGFN^ f524b.cV4t+OB*-Cc >MDHNpkSzZO8A|K;+
smokie9 base: 2191
1: Reverse string from position 210 to 254: 2306
2: Reverse string from position 263 to 302: 2444
3: Reverse string from position 2 to 146: 2530
4: Reverse string from position 70 to 134: 2646
5: Reverse string from position 126 to 146: 2732
+D!>A(Z0%G%ETQ7.2 )5M>-4PT#34J^:,4U BYX>=$3K;*3#2AWZ 3+Q]'9JN!"7T4P%^) GBUA;3[LK,!P+'BU> &HFY3D).EY!<$:@03 '?2QIW3NTG_'3KR43 )4ZJA.#(%5-DBW127 !4;=&][BUW:.+BXSI 3),E34K^"TDWO33J Y03YG%>2I+]3#U4Q) 1U)ZJP](/KL)+BC9 6V_^WF',BGPAU-#*@ 36!7B'O;TQW54>DB! %)X3$UKBZT8^WJB?' !RU4:EK>U4<BHB23U MB%.33F-&"WGG(PQZ 3Y>Y1V0X^CL>)A!UJ @K6+Q^BI=4T3D-!,% ;><P_]Q9.57UW33O
I have reversed portions of the 340 to see what would happen to the cycle scores. If I remember correctly, I think that I was trying to figure out if the transposition changed directions like a snake. And I do remember that reversing some of the rows actually increased cycle scores but decreased the number of period 19 repeats. I am not sure why your testing showed what it did.
I plan to continue working on the 340, and have several projects in mind, not necessarily in order:
1. Figure out a way to use the period x repeats to determine plaintext message direction so that we have another way to evaluate and compare un-transpositions. I don’t know how to do it yet.
2. Finish my analysis of smokie18e, where I need to identify period 19 repeats where there is A19B and A19C and B and C cycle together. Also make a spreadsheet that does that automatically for messages for comparison. The 340 has astronomically improbable situations like this. But the high count symbols in any of the messages contribute to some of the situations that are not quite as improbable, and I am thinking that these period 19 repeats are not good ones to use for comparisons.
3. Use the analysis above and see if I can find out if the + is polyalphabetic by breaking it down into two or more new symbols that cycle well with other other symbols.
4. Make my scytale spreadsheet correct at the lower right hand corner. Figure out ways to compare scytale messages with the 340 to determine if the 340 is a scytale, among other things. Make scytale messages and rearrange the columns to see if I can emulate 340 stats. See if I can use Jarlve’s program ( although he already did ) to solve practice messages like this. Maybe expand symbols at the beginning and end of each un-transposed row.
5. Convert the columns into rows after a scytale untransposition so that the period 19 repeats are all horizontal period 1 repeats. Take a fresh look at the symbols and how they relate to each other. Maybe look at period 1, 2, 3 and 4 etc. repeats to see if I can identify any likely words and symbol assignments. Maybe trying to solve manually will give insight into what the problem is.
6. Work on the heatmap some more. Try to figure out if certain symbols in the 340 are added nulls causing misalignment. Perhaps the same exact symbol deleted in all places would repair the 340. Probably a long shot, but maybe make practice messages and see if I can identify the nulls. Work on misalignment some more.
And other things.
Skokie.. I have performed the task of the scytale in period 19 both physically and on excel it is a few posts back. It has never been tested in that format. Period 19’s end up perfect and I believe period 15 (unchecked) do as well ..all I have to do is rotate it on excel but still only have the iPad.. No rotation available.. I will have to manually copy and type.. I do not believe the format that I have presented has ever been tested.. The scytale acts perfectly for the 19s. One must note it changes course at about the 8th line as the periods run through the side lines and then change through the bottom lines. I would urge you to make one.. It’s interesting to see how they work
@smokie, that are some worthy points to explore.
I don’t see how Scytale is different from other things that we have explored.
@smokie, that are some worthy points to explore.
I don’t see how Scytale is different from other things that we have explored.
I don’t either; the result is the same. But the method of construction is something that Zodiac could have learned in the Boy Scouts or from reading comic books or a basic cryptography book, and it is a little bit different.
Figuring out the direction of the plaintext, that would be interesting. I have been thinking about it, and think that it may not be possible with 63 symbol diffusion. But with 1:1 substitution it would likely be possible to make an educated guess. TH and HE are often the most common bigrams, with E T H in order of frequency. So if you have AB as the most common period 1 bigram and A is more frequent than B, and you have BC as the second most frequent bigram and C is much more frequent than A, then the direction of the plaintext would be from left to right.
No doubt it’s been done before, but I could not find anything on the internet about a comprehensive or detailed way to incorporate more letters and symbols into a direction analysis. I would like to make some tables of symbol relationships in period 1 – 4 bigrams. I need some time to mull things over for a while.
Hey Jarlve, could you make me a scytale-like message with a period of 19, and use one particular symbol as an added null. Use the same symbol several times. Then I will work on my heatmap and try to rank the symbols in order of how likely they are to be the null. See if I can figure out which symbol is the null.
