For my upcoming test it would be useful to me if you could create a few ciphers that match the 340’s flipped bigram count of 41 at period 15. Thanks.

OK – the generator is running now.

Here’s one that matches Z340 on the following measurements:
– unigram distribution
– bigram repeats at period 1 and period 19 (normal reading direction)
– trigram repeats at period 1
– bigram repeats at period 15 (mirrored reading direction)
– perfect cycle score (L=2)
– pivots
– appearance of pseudo-words "HER", "GOD", and "ZODIAC" among the ciphertext symbols

C;XC)PP6#Y%T8SyL(
jO<k2VUWF51K4l|UB
yZz)/#D3cK8RE|*TO
bzOBK4WE<(F^WHERE
^Md#KytS*-1tPM(P6
FtU64LPk|RJ|*N5P8
cTyK(@*9R2<^|OKHl
^O)1b.cVcO2DJ5OfV
PWl8*@9c<OS)Rd(OK
->WK7|T.WBWRfUCP-
HL3FLP.b1|5FBcJkc
pcPYNPC2D8M@1RqL^
-(A1BOP%dT48:9fzT
CN5;tPGRPS+R*;>9|
3fU8PkO7q&lyL+.-*
P4G_D#7#dCMl)8W(y
F&cEPFP8W1FPPNzZ5
8A;kqMYP5WKV2-DzZ
KckOj<JpptPLZP3FB
cMP:4>#2S|5FYX+M/

It is simple homophonic substitution, so it should solve easily. I should have a few dozen more by tomorrow.

This is gnarly complicated. But I am wondering about some type of subtle double cycling of the key. One that wouldn’t destroy the period 19 repeats ( EDIT or the L=2 cycles ), but which would ( EDIT: destroy the L=3 cycles, and ) make the message polyalphabetic enough so that it is difficult to solve.

That’s a reasonable hypothesis and I would like to see such a cipher. I’m thinking that it might be hard to reconcile subtle polyalphabetism with the absence of L3 cycles.

Here’s another encoding hypothesis where a per 4 row period 19 transposition is applied after encoding. I’m skeptical of this hypothesis but wonder how it looks like for the L3’s.

p105_jarlve_e2.txt

1  2  3  4  5  6  7  8  9  10 11 12 13 14 5  15 1
4  16 17 18 19 20 21 22 23 24 25 26 14 20 27 28 7
29 30 31 32 14 33 34 35 36 37 14 32 38 39 40 41 42
14 43 44 14 2  25 45 46 44 3  47 48 49 14 50 51 52
52 14 6  12 36 53 50 39 54 55 56 2  14 25 20 12 27
30 37 57 48 46 22 8  49 15 43 26 44 38 10 18 31 9
43 16 14 35 58 17 51 18 13 40 19 11 4  34 29 58 42
49 28 53 57 1  58 59 14 10 20 24 57 9  14 16 7  23
5  48 19 18 21 10 59 57 53 29 2  14 38 52 16 1  31
17 23 14 14 2  16 60 38 47 12 5  32 36 18 49 47 14
40 26 39 29 26 29 15 14 4  9  56 31 41 13 15 43 46
56 9  4  54 6  58 13 43 51 49 32 20 52 26 58 19 27
8  61 32 7  52 32 50 51 5  40 42 36 14 19 45 39 41
16 26 14 2  62 56 5  52 25 46 14 62 13 58 20 27 32
38 43 5  44 22 43 44 20 45 34 55 22 14 16 53 28 49
7  21 52 9  14 29 5  10 48 37 54 12 56 47 11 57 18
58 43 35 23 2  62 21 18 12 44 32 6  26 41 20 29 5
8  16 15 4  52 36 55 16 54 39 53 20 55 48 45 58 52
43 24 33 11 14 37 34 30 59 46 31 49 9  22 62 7  63
13 25 40 60 50 14 32 3  25 33 40 17 10 45 1  5  36

Some while ago I talked about an encoding hypothesis that Zodiac didn’t try to cycle but more or less had some kind of window/range in which he tried not to repeat symbols. Per row or per 2 rows, whatever. I made such a cipher. Doranchak could you run them through your cycle measurements please, thanks.

p105_jarlve_e3.txt

1  2  3  4  5  6  7  8  9  10 11 12 13 14 9  9  15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
33 34 35 5  12 22 2  36 37 38 13 39 16 40 1  19 3
41 30 42 23 43 35 26 44 45 46 25 35 47 31 48 29 32
42 49 50 46 30 22 2  25 19 20 45 40 13 8  26 14 44
27 35 28 47 5  32 49 34 35 10 31 12 51 52 36 24 6
35 51 53 44 16 32 54 33 6  24 26 40 50 3  5  52 37
47 31 14 6  41 13 43 10 55 48 49 2  25 22 20 9  48
56 30 31 40 55 25 5  50 33 6  13 45 26 51 3  26 11
7  35 57 13 10 5  39 46 18 54 15 49 35 47 6  33 38
11 51 31 57 13 33 5  58 35 45 3  26 43 47 6  8  56
18 54 48 30 6  1  37 40 10 26 59 27 12 46 24 31 50
34 30 21 56 60 31 48 40 38 4  12 22 23 54 39 8  57
15 53 24 42 29 11 13 27 37 61 54 1  20 8  18 15 25
30 41 37 53 51 49 34 13 10 26 44 48 19 25 14 31 47
55 32 61 38 62 58 33 56 16 43 6  48 15 3  5  12 31
51 40 25 38 48 35 20 9  9  56 16 32 59 17 46 7  26
61 19 23 4  43 8  52 16 24 10 13 5  58 6  53 40 47
31 1  17 14 21 56 42 4  61 12 2  55 32 26 4  63 16
51 13 39 38 37 5  50 23 57 28 7  41 7  46 43 52 30

I woke up and wondered what would happen if I used my new spreadsheet to look at the mirrored 340, vertically flipped 340, and vertically flipped and mirrored 340. Because we have the diagonal row of symbol positions where cycles of at least 6 consecutive alternations start. Both with the 340 and the 408. And you guys were talking about encoding direction lately. So what would we see if I tried those other orientations of the 340?

Upper left, the 340.
Upper right, the 340 mirrored.
Lower left, the 340 vertically flipped.
Lower right, the 340 vertically flipped and mirrored.

I was surprised to see any diagonal rows. None for the bottom two, suggesting that he did not start encoding at the bottom of the message. But those diagonal rows for the mirrored are very interesting. There is a diagonal row in the void area now, but in the opposite direction. And there are a couple of other diagonal row sections. Scroll right to look at them. So it seems as though the 340 has some cycles that start at the top of the message when looking at encoding direction both left right and right left. But the diagonal rows do not exist for the flipped.

The picture only shows the first 34 positions.

Just checking to see if my new spreadsheet is working correctly, here are the last 34 positions of the vertically flipped mirrored 340. As expected, the diagonal row is there, with the void.

I checked the 340 cycles going in eight different directions ( horizontal and vertical from each corner ), minimum of 6 consecutive alternations. Only two of these showed diagonal rows at the beginning of the message, the 340 and mirrored 340. And two showed diagonal rows at the end of the message, vertically flipped and vertically flipped mirrored. Same pattern. None of the vertical cycles showed any diagonal rows.

For my upcoming test it would be useful to me if you could create a few ciphers that match the 340’s flipped bigram count of 41 at period 15. Thanks.

OK – the generator is running now.

OK here’s a full set of 24 generated ciphers (simple homophonic substitution) that share these measurements with the Z340:

– unigram distribution
– bigram repeats at period 1 and period 19 (normal reading direction)
– trigram repeats at period 1
– bigram repeats at period 15 (mirrored reading direction)
– perfect cycle score (L=2)
– pivots
– appearance of pseudo-words such as "HER", "GOD", and "ZODIAC" among the ciphertext symbols

+(z&|l%2d+bLBfzU^
4&yAYD_B+lTzZ)8:^
K+WVcB+;9FN#tp68J
VCSV++(^3p+l<|5F5
zBA%4*E2q4yCb>2U+
R9ELkO#FBc/+.dzO5
DySF>pcO-_2(cfZ64
RNt*3y(PU9yAVc.b#
f^LCNFy^|X+DyMkS9
-lM4dz6-*2tUO@c7-
+OHERALS>G5Dp3qc(
H)M:b.l).|.RH@E+<
jl4O135fRW#2*-bA<
FWKO+Ol#J7t+|^/fB
3<5+;Z2W|z(|+j2H8
BMY2k+lK*|JRYfV^;
*OPK1F7RPLZN+dCDO
/+fCMp<zYcBFNp+TW
VRU2BRTpb#+|T|5FB
c+Xc<2Bl+TkUBF@LJ

01 02 03 04 05 06 07 08 09 01 10 11 12 13 03 14 15 
16 04 17 18 19 20 21 12 01 06 22 03 23 24 25 26 15 
27 01 28 29 30 12 01 31 32 33 34 35 36 37 38 25 39 
29 40 41 29 01 01 02 15 42 37 01 06 43 05 44 33 44 
03 12 18 07 16 45 46 08 47 16 17 40 10 48 08 14 01 
49 32 46 11 50 51 35 33 12 30 52 01 53 09 03 51 44 
20 17 41 33 48 37 30 51 54 21 08 02 30 13 23 38 16 
49 34 36 45 42 17 02 55 14 32 17 18 29 30 53 10 35 
13 15 11 40 34 33 17 15 05 56 01 20 17 57 50 41 32 
54 06 57 16 09 03 38 54 45 08 36 14 51 58 30 59 54 
01 51 60 46 49 18 11 41 48 61 44 20 37 42 47 30 02 
60 24 57 26 10 53 06 24 53 05 53 49 60 58 46 01 43 
62 06 16 51 63 42 44 13 49 28 35 08 45 54 10 18 43 
33 28 27 51 01 51 06 35 39 59 36 01 05 15 52 13 12 
42 43 44 01 31 23 08 28 05 03 02 05 01 62 08 60 25 
12 57 19 08 50 01 06 27 45 05 39 49 19 13 29 15 31 
45 51 55 27 63 33 59 49 55 11 23 34 01 09 40 20 51 
52 01 13 40 57 37 43 03 19 30 12 33 34 37 01 22 28 
29 49 14 08 12 49 22 37 10 35 01 05 22 05 44 33 12 
30 01 56 30 43 08 12 06 01 22 50 14 12 33 58 11 39

---

D+#%qzZ(D/8K)ZSKW
NbZ6++:+Z&ZSUZ_ZC
pZA|5F4+@Fj;5f3-q
.@RdLM+S^L+S*|JRy
OZO:+A/LFY+O|z+Tl
X+TGz2WVc.bGJRB#;
FBc|5FBc%cFkRBVHt
7-*tOW5.*_++BKR^D
&3|R/7.b<FHEROp5G
-|z>|G2f)1cd;Jt3-
^BFy*-%)1RbC/Y+BR
TM2^BlHG/5XEV/.+X
dW;+EF%K93CY_+qc<
+T2>D)JljG%dVl44t
NH6P#H)c+k:BT>+y%
H^;f*zt244WOFTp>|
P%9V+TJ#.kFOKclB8
Bd+Wjc2M)-l1^ND|*
O^C|+Y5O1tO<_SBc5
+CNq*%JGZU%3.9p<M

01 02 03 04 05 06 07 08 01 09 10 11 12 07 13 11 14 
15 16 07 17 02 02 18 02 07 19 07 13 20 07 21 07 22 
23 07 24 25 26 27 28 02 29 27 30 31 26 32 33 34 05 
35 29 36 37 38 39 02 13 40 38 02 13 41 25 42 36 43 
44 07 44 18 02 24 09 38 27 45 02 44 25 06 02 46 47 
48 02 46 49 06 50 14 51 52 35 16 49 42 36 53 03 31 
27 53 52 25 26 27 53 52 04 52 27 54 36 53 51 55 56 
57 34 41 56 44 14 26 35 41 21 02 02 53 11 36 40 01 
19 33 25 36 09 57 35 16 58 27 55 59 36 44 23 26 49 
34 25 06 60 25 49 50 32 12 61 52 37 31 42 56 33 34 
40 53 27 43 41 34 04 12 61 36 16 22 09 45 02 53 36 
46 39 50 40 53 47 55 49 09 26 48 59 51 09 35 02 48 
37 14 31 02 59 27 04 11 62 33 22 45 21 02 05 52 58 
02 46 50 60 01 12 42 47 30 49 04 37 51 47 28 28 56 
15 55 17 63 03 55 12 52 02 54 18 53 46 60 02 43 04 
55 40 31 32 41 06 56 50 28 28 14 44 27 46 23 60 25 
63 04 62 51 02 46 42 03 35 54 27 44 11 52 47 53 10 
53 37 02 14 30 52 50 39 12 34 47 61 40 15 01 25 41 
44 40 22 25 02 45 26 44 61 56 44 58 21 13 53 52 26 
02 22 15 05 41 04 42 49 07 20 04 33 35 62 23 58 39

---

%+ZcFJkDYOOXp.GpO
+__Nt>(1pA6BF+:-M
PpJ3+lWUj:z&C%8bf
L(tFU+VL+7UdX+#Hd
BOl-&S.ky*|JR@W|q
zZ)9A|K<<|+KM+Z*K
NWBc/;2PYJ.LB|5FB
cYb34RKLpRF*-.F+5
9+*4+6FBcF#|Dl+tp
-%1cclUy&|>HERfM-
VS<dAb7O3+klTH^E(
#Cq+Z1O7BE/;|TZ2.
KZz;6+XXBDL-*5RM+
2dbM&^yF+p|#l<&Hj
+6CR#K%V/VZ4>|5F+
Vc.by^&4#O2*Y1OSp
c6WK<PM++2XE*(DK/
.OkSJZZz8ZZJEEzJ)
b1>9p<FdBc^cR>t+f
G+4GODzbVMFB.4yK5

01 02 03 04 05 06 07 08 09 10 10 11 12 13 14 12 10 
02 15 15 16 17 18 19 20 12 21 22 23 05 02 24 25 26 
27 12 06 28 02 29 30 31 32 24 33 34 35 01 36 37 38 
39 19 17 05 31 02 40 39 02 41 31 42 11 02 43 44 42 
23 10 29 25 34 45 13 07 46 47 48 06 49 50 30 48 51 
33 03 52 53 21 48 54 55 55 48 02 54 26 02 03 47 54 
16 30 23 04 56 57 58 27 09 06 13 39 23 48 59 05 23 
04 09 37 28 60 49 54 39 12 49 05 47 25 13 05 02 59 
53 02 47 60 02 22 05 23 04 05 43 48 08 29 02 17 12 
25 01 20 04 04 29 31 46 34 48 18 44 61 49 38 26 25 
40 45 55 42 21 37 41 10 28 02 07 29 62 44 63 61 19 
43 35 51 02 03 20 10 41 23 61 56 57 48 62 03 58 13 
54 03 33 57 22 02 11 11 23 08 39 25 47 59 49 26 02 
58 42 37 26 34 63 46 05 02 12 48 43 29 55 34 44 32 
02 22 35 49 43 54 01 40 56 40 03 60 18 48 59 05 02 
40 04 13 37 46 63 34 60 43 10 58 47 09 20 10 45 12 
04 22 30 54 55 27 26 02 02 58 11 61 47 19 08 54 56 
13 10 07 45 06 03 03 33 36 03 03 06 61 61 33 06 52 
37 20 18 53 12 55 05 42 23 04 63 04 49 18 17 02 38 
14 02 60 14 10 08 33 37 40 26 05 23 13 60 46 54 59

---

FzE&c&d-p6l^+V8<j
PLJMV^9.52|MWpk#K
(>)*8CRfpO^JpW<_+
Fb%YS|K^jUV7+F14(
>qW^1*F@MOL+NYB9+
<ZKjFVCCt)27>|2+4
c+KNdG#D72zH);|5F
BcktTTKBfd(>p2;W.
XpW16RJ|*z:-+MV)C
-BtU%NPL|p+A22kf-
HER_UfpFJ(<GFcSyW
B2+-UYA;RzZ3d8/cM
p4C5qB+O+b.cVf^D|
pN^Y6Oy+^TL+c+z-*
b>*-k+8N*<Oz.4CW#
GU|YfMPqFBclbc+yO
(X5lZO;+9_+Lk+++R
D/3/K#BD+R/Mpl@OO
62<.K_Olzp4)c2<+t
z/F^S|lP/5d94z|5F

01 02 03 04 05 04 06 07 08 09 10 11 12 13 14 15 16 
17 18 19 20 13 11 21 22 23 24 25 20 26 08 27 28 29 
30 31 32 33 14 34 35 36 08 37 11 19 08 26 15 38 12 
01 39 40 41 42 25 29 11 16 43 13 44 12 01 45 46 30 
31 47 26 11 45 33 01 48 20 37 18 12 49 41 50 21 12 
15 51 29 16 01 13 34 34 52 32 24 44 31 25 24 12 46 
05 12 29 49 06 53 28 54 44 24 02 55 32 56 25 23 01 
50 05 27 52 57 57 29 50 36 06 30 31 08 24 56 26 22 
58 08 26 45 09 35 19 25 33 02 59 07 12 20 13 32 34 
07 50 52 43 40 49 17 18 25 08 12 60 24 24 27 36 07 
55 03 35 38 43 36 08 01 19 30 15 53 01 05 42 61 26 
50 24 12 07 43 41 60 56 35 02 51 62 06 14 63 05 20 
08 46 34 23 47 50 12 37 12 39 22 05 13 36 11 54 25 
08 49 11 41 09 37 61 12 11 57 18 12 05 12 02 07 33 
39 31 33 07 27 12 14 49 33 15 37 02 22 46 34 26 28 
53 43 25 41 36 20 17 47 01 50 05 10 39 05 12 61 37 
30 58 23 10 51 37 56 12 21 38 12 18 27 12 12 12 35 
54 63 62 63 29 28 50 54 12 35 63 20 08 10 48 37 37 
09 24 15 22 29 38 37 10 02 08 46 32 05 24 15 12 52 
02 63 01 11 42 25 10 17 63 23 06 21 46 02 25 23 01

---

+ZW<D+>SNL+Py7j+5
Fz3+yfYc^U+CRk2#Z
SW1O&%9f/7p8+tG2d
94LlDT(6P(*-TbJAW
|5FBc.+5f<|KN|M#c
|5F2yN(|>W2ClT+4+
KpyP#&UA%F48DNY+p
#+;p9p-7zZ)d9/k+F
tB6b.cV14^MRY*EU|
CzLcFBc(l5J3+K>-*
-yZ(L4.p(MK/X2PS-
8q2;++by9t+fAqlB_
cRJ|*Yc_X4Sp.Pd+K
/W2||B+tO269429zB
(zU8JSyzJp<+CZ@fT
^YOWRF+*8O+;f:O:2
5NF(9-4VV)XHVRV)E
.GXEVk12#fz5F^+D>
9M9*+5E2-1(>L4B>j
_HERFlc4EOK5(5(Yb

01 02 03 04 05 01 06 07 08 09 01 10 11 12 13 01 14 
15 16 17 01 11 18 19 20 21 22 01 23 24 25 26 27 02 
07 03 28 29 30 31 32 18 33 12 34 35 01 36 37 26 38 
32 39 09 40 05 41 42 43 10 42 44 45 41 46 47 48 03 
49 14 15 50 20 51 01 14 18 04 49 52 08 49 53 27 20 
49 14 15 26 11 08 42 49 06 03 26 23 40 41 01 39 01 
52 34 11 10 27 30 22 48 31 15 39 35 05 08 19 01 34 
27 01 54 34 32 34 45 12 16 02 55 38 32 33 25 01 15 
36 50 43 46 51 20 56 28 39 21 53 24 19 44 57 22 49 
23 16 09 20 15 50 20 42 40 14 47 17 01 52 06 45 44 
45 11 02 42 09 39 51 34 42 53 52 33 58 26 10 07 45 
35 59 26 54 01 01 46 11 32 36 01 18 48 59 40 50 60 
20 24 47 49 44 19 20 60 58 39 07 34 51 10 38 01 52 
33 03 26 49 49 50 01 36 29 26 43 32 39 26 32 16 50 
42 16 22 35 47 07 11 16 47 34 04 01 23 02 61 18 41 
21 19 29 03 24 15 01 44 35 29 01 54 18 62 29 62 26 
14 08 15 42 32 45 39 56 56 55 58 63 56 24 56 55 57 
51 37 58 57 56 25 28 26 27 18 16 14 15 21 01 05 06 
32 53 32 44 01 14 57 26 45 28 42 06 09 39 50 06 13 
60 63 57 24 15 40 20 39 57 29 52 14 42 14 42 19 46

---

&3z)-tNPpp_dDzBUf
T)X%W2LLWp<RDtU;N
K-*26GM&FAN9tlk+b
Wq|TGpO_(l(&zBBGR
6U)z(.p#&T|&7F<GP
O>4SC&lzO4&O/c5RF
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pB#F<2&YB&&cVH&lM
jNLfD9OV(1EK|kM<|
H:45Ob.cVUkt&9Y&M
-fLZ1@P<c;l&KdRp-
&tLc%7_2.:TU&y>^&
V5d6Azyzb|5F;(>_J
j&5M*kcRHER6.*d7N
yf.K&pA&FE9J4/<EJ
SJHbzZ(8^/kRJ|*Ol
pBJXT|CdkGlO2q|5c
lO#zz*-O&c3Up^J*p
V|t&fW^:L|5FBcRL&
>WM+d(T)yyDBWKpB&

01 02 03 04 05 06 07 08 09 09 10 11 12 03 13 14 15 
16 04 17 18 19 20 21 21 19 09 22 23 12 06 14 24 07 
25 05 26 20 27 28 29 01 30 31 07 32 06 33 34 35 36 
19 37 38 16 28 09 39 10 40 33 40 01 03 13 13 28 23 
27 14 04 03 40 41 09 42 01 16 38 01 43 30 22 28 08 
39 44 45 46 47 01 33 03 39 45 01 39 48 49 50 23 30 
24 46 47 13 30 13 49 33 51 23 28 52 11 18 43 44 12 
09 13 42 30 22 20 01 53 13 01 01 49 54 55 01 33 29 
51 07 21 15 12 32 39 54 40 56 57 25 38 34 29 22 38 
55 58 45 50 39 36 41 49 54 14 34 06 01 32 53 01 29 
05 15 21 59 56 52 08 22 49 24 33 01 25 11 23 09 05 
01 06 21 49 18 43 10 20 41 58 16 14 01 60 44 61 01 
54 50 11 27 31 03 60 03 36 38 50 30 24 40 44 10 62 
51 01 50 29 26 34 49 23 55 57 23 27 41 26 11 43 07 
60 15 41 25 01 09 31 01 30 57 32 62 45 48 22 57 62 
46 62 55 36 03 59 40 63 61 48 34 23 62 38 26 39 33 
09 13 62 17 16 38 47 11 34 28 33 39 20 37 38 50 49 
33 39 42 03 03 26 05 39 01 49 02 14 09 61 62 26 09 
54 38 06 01 15 19 61 58 21 38 50 30 13 49 23 21 01 
44 19 29 35 11 40 16 04 60 60 12 13 19 25 09 13 01

---

bF>_463dz1kWM:#FT
L%69zf@^t+2Vc.bcN
/+ylO&5ROO)cS+R_S
<>*1*|JR+pk.OX>Yd
/T6+|F.zRl+b9z:@+
K^jWJ@M>+^yK+Y(1t
@5|(R(2p<)p7KV4WG
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FBcd^FKc+cW|lY%O)
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-/|A7(J-C_/NybVq-
XL.|Bz9S)b5Dd4Z;&
5t*p+AH<|++:lUUzN
kRl354+W7X/OVKz|J
2z+dM+9E#O+YU|-*|
^GFBcFNHERPWy1qzZ
(8A;C.MLLp/^%OC*-
++p/Y+5<5c+lLRN|5
FSpCKK5pEF2V4BTp/
4c9VO)P<OOj:-M7L.

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 02 16 
17 18 06 19 09 20 21 22 23 24 25 26 27 28 01 27 29 
30 24 31 32 33 34 35 36 33 33 37 27 38 24 36 04 38 
39 03 40 10 40 41 42 36 24 43 11 28 33 44 03 45 08 
30 16 06 24 41 02 28 09 36 32 24 01 19 09 14 21 24 
46 22 47 12 42 21 13 03 24 22 31 46 24 45 48 10 23 
21 35 41 48 36 48 25 43 39 37 43 49 46 26 05 12 50 
40 51 25 27 23 08 31 17 52 14 49 24 53 36 40 41 35 
02 54 27 08 22 02 46 27 24 27 12 41 32 45 18 33 37 
24 13 55 56 11 57 25 09 58 55 24 36 59 06 01 21 32 
52 30 41 60 49 48 42 52 61 04 30 29 31 01 26 62 52 
44 17 28 41 54 09 19 38 37 01 35 51 08 05 57 56 34 
35 23 40 43 24 60 55 39 41 24 24 14 32 59 59 09 29 
11 36 32 07 35 05 24 12 49 44 30 33 26 46 09 41 42 
25 09 24 08 13 24 19 63 15 33 24 45 59 41 52 40 41 
22 50 02 54 27 02 29 55 63 36 53 12 31 10 62 09 57 
48 58 60 56 61 28 13 17 17 43 30 22 18 33 61 40 52 
24 24 43 30 45 24 35 39 35 27 24 32 17 36 29 41 35 
02 38 43 61 46 46 35 43 63 02 25 26 05 54 16 43 30 
05 27 19 26 33 37 53 39 33 33 47 14 52 13 49 17 28

---

^7M2J.b|5FBcPW^*8
T+<XpT.ZV>6b2+LWC
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C(|;YW#*-9pkLqM+O
2>N+_W+|VlHERVjAP

01 02 03 04 05 06 07 08 09 10 11 12 13 14 01 15 16 
17 18 19 20 21 17 06 22 23 24 25 07 04 18 26 14 27 
28 29 30 31 32 33 12 11 34 18 35 23 36 37 05 16 02 
38 39 30 07 06 12 23 40 18 41 18 10 32 18 28 01 13 
32 42 43 11 03 37 32 39 01 44 18 26 45 15 46 19 18 
47 48 47 49 47 46 06 47 19 50 19 51 08 52 53 54 04 
52 38 31 55 35 21 56 08 09 10 32 10 17 52 19 01 55 
36 57 34 58 29 18 10 11 12 10 38 33 43 03 59 32 45 
54 53 55 18 31 43 24 56 42 31 57 23 58 21 11 38 29 
18 60 43 20 04 31 18 25 11 43 55 04 57 34 05 27 11 
59 33 27 32 25 18 16 05 18 58 31 45 08 10 61 43 59 
26 31 25 61 56 47 62 21 40 33 21 52 01 32 10 33 21 
39 04 41 46 33 22 63 02 16 48 38 18 55 34 42 15 50 
57 32 43 05 27 35 18 18 23 08 18 28 03 38 44 04 40 
19 38 24 08 11 04 11 39 18 31 25 14 42 42 13 44 17 
46 05 08 15 11 53 34 17 04 08 10 20 18 26 11 55 08 
50 21 39 39 36 53 14 25 26 53 49 33 57 45 40 59 15 
11 17 43 01 43 62 17 21 03 18 54 29 17 21 40 56 41 
27 45 08 48 58 14 31 15 59 49 21 39 26 50 03 18 32 
04 24 40 18 56 14 18 08 23 43 35 51 46 23 60 28 13

---

7;z6CL2+8++U4T/p<
((j)LZlUP|8T1:.+>
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01 02 03 04 05 06 07 08 09 08 08 10 11 12 13 14 15 
16 16 17 18 06 19 20 10 21 22 09 12 23 24 25 08 26 
16 08 27 28 29 30 10 31 14 24 32 33 10 07 34 08 35 
35 36 35 37 38 35 08 36 08 35 39 25 13 40 08 16 23 
41 42 43 14 15 14 44 37 45 20 12 08 31 07 46 33 08 
47 44 22 08 06 45 07 48 22 14 49 43 36 50 35 16 04 
51 29 33 25 30 12 24 08 30 35 25 29 52 34 49 40 08 
53 39 46 46 08 47 15 49 35 06 30 07 21 22 23 22 40 
36 50 35 05 31 51 02 33 25 45 43 14 08 45 37 30 03 
54 50 10 12 15 34 55 28 29 56 47 08 57 16 27 41 03 
37 57 46 03 19 16 09 24 58 35 11 01 51 08 20 40 37 
06 59 11 53 52 50 06 03 24 16 54 60 26 33 41 30 46 
36 13 08 42 23 34 50 39 49 43 08 58 08 47 55 15 07 
51 01 21 20 40 57 03 05 60 53 52 54 50 17 61 33 05 
53 08 42 17 20 43 62 37 05 32 33 14 22 27 47 63 24 
62 62 08 03 44 60 59 47 50 11 27 03 50 20 14 15 54 
23 26 39 41 34 54 31 62 07 03 45 22 38 47 10 42 22 
14 63 14 55 47 19 50 09 07 62 22 12 29 22 25 22 40 
36 32 10 25 35 13 35 12 01 52 38 20 43 08 53 07 21 
41 50 03 10 48 17 46 56 11 10 47 18 62 58 24 51 07

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01 02 03 04 05 06 02 07 08 09 10 11 12 13 14 15 16 
17 12 17 18 19 02 20 21 18 22 23 05 24 25 26 27 28 
07 14 29 30 31 07 32 33 34 22 03 35 36 17 29 31 37 
38 39 40 20 41 08 02 42 05 43 37 40 10 44 45 09 32 
01 16 25 10 26 46 47 24 12 45 20 15 48 49 14 48 50 
06 38 51 18 19 02 37 12 19 22 19 31 46 42 12 28 52 
13 41 03 18 25 24 16 45 33 37 40 05 51 25 27 44 12 
14 02 05 26 29 12 35 20 51 32 28 53 52 05 10 14 01 
35 48 31 05 51 43 19 49 51 18 47 39 54 33 29 41 55 
25 05 44 50 07 05 51 36 34 05 23 03 19 12 55 53 25 
29 56 05 02 05 44 18 06 01 42 35 22 57 44 54 48 30 
20 51 43 34 22 58 02 05 59 05 59 44 44 59 08 05 05 
22 09 59 60 49 47 17 41 32 05 61 18 34 51 18 56 21 
26 35 15 05 34 01 37 38 27 62 22 38 36 19 39 61 24 
44 12 17 18 57 14 25 33 02 46 27 21 20 05 41 17 50 
16 38 39 12 32 34 23 07 36 43 33 51 01 34 63 02 60 
29 36 32 42 16 19 22 37 22 08 50 56 05 62 05 44 43 
34 34 11 18 30 42 45 40 06 14 34 21 28 03 60 58 23 
05 36 05 31 51 50 17 05 11 50 24 32 60 45 34 28 22 
33 45 04 50 57 56 02 42 29 02 23 27 35 38 14 62 14

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01 02 03 04 05 06 07 08 09 10 11 02 12 13 05 14 15 
16 17 18 15 19 02 20 21 22 23 24 25 26 04 25 27 28 
29 30 31 32 33 34 10 35 36 37 38 02 22 11 39 40 13 
14 41 32 07 40 26 15 34 36 22 02 27 42 04 43 44 45 
10 19 33 40 14 46 41 02 18 20 47 48 35 06 49 23 38 
40 06 10 50 51 52 53 37 54 44 54 12 04 55 21 43 06 
21 48 48 48 21 09 09 03 40 39 14 24 10 17 56 53 14 
57 42 10 50 58 45 07 39 13 11 59 46 54 08 10 09 32 
36 21 20 10 42 10 54 60 46 27 26 02 03 57 05 55 37 
02 24 07 13 26 10 61 36 05 47 46 18 01 61 10 09 30 
21 38 49 16 52 45 54 42 21 46 11 01 48 18 10 23 21 
10 61 07 26 30 37 56 58 41 52 53 01 18 47 50 21 21 
56 02 40 03 14 54 22 07 62 63 23 40 32 10 16 28 10 
26 01 40 15 42 58 07 20 38 10 44 26 42 01 02 21 38 
55 63 52 50 07 37 46 17 10 25 32 25 31 05 01 48 11 
44 10 22 10 56 10 62 29 51 42 37 11 32 29 26 44 01 
62 28 07 13 26 01 40 56 10 20 44 55 27 10 25 34 10 
09 03 51 28 14 27 25 27 52 36 61 11 20 13 01 50 25 
31 40 15 09 34 01 26 03 11 12 42 10 39 31 51 16 62 
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01 02 03 04 05 06 07 08 09 10 08 11 08 12 08 13 14 
15 16 13 17 18 14 14 19 20 21 22 23 24 19 25 05 08 
26 27 08 28 29 30 04 31 32 05 08 33 20 34 11 20 35 
36 37 38 22 39 28 27 25 14 39 40 08 41 41 36 18 17 
17 26 39 42 17 20 32 14 28 16 14 43 35 36 37 44 22 
09 22 33 45 10 09 23 46 41 36 28 02 32 03 47 01 08 
44 41 20 05 08 30 21 01 11 18 08 36 15 38 48 39 36 
03 45 08 39 40 14 49 39 20 02 17 33 28 50 39 43 51 
07 21 35 25 15 44 52 39 22 53 36 32 39 23 08 49 25 
28 17 50 53 54 41 29 55 08 05 19 12 01 24 48 07 03 
02 36 47 56 05 22 57 58 52 57 16 27 43 37 55 31 02 
51 04 24 29 35 25 08 05 22 59 48 37 19 27 20 60 15 
41 54 54 50 30 58 49 29 56 55 36 12 43 08 53 27 08 
39 08 05 35 03 06 06 10 61 16 24 34 52 37 57 08 41 
53 05 48 41 15 27 20 42 34 44 61 11 03 02 21 24 49 
53 39 38 54 30 45 29 04 20 51 21 60 37 29 28 06 34 
19 57 50 28 56 02 28 22 62 52 03 37 17 38 63 46 08 
39 18 11 05 32 47 14 61 01 55 57 10 20 34 14 43 35 
25 57 44 22 62 08 14 53 62 22 26 15 50 44 63 08 08 
47 01 35 30 41 28 06 56 04 37 50 20 51 10 21 08 25

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01 02 03 04 05 06 07 01 08 09 10 11 12 13 14 15 16 
13 17 18 13 19 20 13 06 21 07 08 22 23 24 06 13 16 
25 26 27 19 08 28 29 05 03 30 30 13 31 02 32 33 34 
13 09 35 11 32 36 37 12 38 20 30 27 13 36 01 02 25 
12 39 40 40 03 21 41 39 27 39 40 11 35 42 28 43 44 
45 02 46 33 30 24 08 08 47 32 37 40 12 48 16 24 46 
49 36 27 48 50 43 44 49 36 35 13 30 44 19 08 40 13 
36 05 44 14 48 49 39 08 13 43 44 49 01 02 13 05 09 
44 04 13 28 42 51 43 29 52 30 01 39 33 51 31 13 53 
30 20 29 38 07 49 43 25 44 53 54 55 31 18 25 09 05 
28 31 54 03 37 50 13 24 24 47 41 56 12 21 55 57 28 
38 48 30 01 52 19 49 17 58 48 02 09 43 20 13 12 10 
35 48 30 46 54 44 04 05 49 59 60 13 45 42 36 03 36 
33 61 32 57 09 23 62 49 40 37 49 36 14 54 44 21 29 
42 48 41 09 25 55 20 59 54 38 17 47 08 13 03 22 10 
48 09 01 44 05 36 13 60 62 07 38 58 26 11 28 04 13 
41 06 44 57 07 55 28 44 27 11 63 15 34 56 58 48 24 
09 13 49 26 42 10 13 26 17 46 06 06 39 46 31 08 21 
45 03 13 27 61 43 46 51 52 26 26 23 30 36 33 22 43 
16 39 03 48 50 43 58 38 35 07 22 43 60 13 26 37 36

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01 02 03 04 05 06 07 08 09 10 07 11 12 13 14 15 16 
17 11 18 19 20 21 11 22 23 13 06 24 25 20 26 13 27 
28 29 24 30 11 31 05 32 33 09 34 35 13 06 36 37 13 
38 39 40 14 21 26 41 32 13 35 42 04 24 43 44 45 25 
46 03 29 47 13 48 49 13 31 50 20 01 17 49 13 51 05 
24 52 22 31 53 54 51 29 24 07 28 45 37 55 52 13 02 
11 31 14 53 56 33 51 38 10 13 15 08 17 43 56 16 48 
26 25 19 51 41 52 19 06 34 37 56 13 15 57 32 58 13 
31 33 59 13 30 19 14 47 27 13 24 29 31 20 54 48 38 
59 52 13 60 16 06 55 61 16 49 23 36 43 32 43 28 59 
17 33 37 08 51 34 38 07 56 07 54 47 39 18 25 50 25 
03 13 25 55 12 13 13 44 31 53 53 53 01 25 10 62 40 
63 16 02 43 23 30 05 51 61 19 07 20 20 16 63 25 09 
63 13 06 02 08 57 04 34 03 36 07 28 16 05 09 20 59 
31 20 22 49 07 19 08 14 03 58 15 25 63 63 31 16 41 
17 19 02 47 07 39 57 25 03 03 30 38 25 40 60 27 13 
09 02 13 52 07 09 03 10 11 18 19 07 44 11 54 45 07 
20 01 09 08 46 44 16 51 37 28 08 48 59 37 05 11 04 
56 33 27 55 62 59 20 48 13 14 60 63 10 17 40 51 16 
17 11 55 31 44 19 52 38 29 23 11 03 54 43 24 13 06

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01 02 03 04 05 06 06 07 08 05 09 10 11 12 07 13 14 
15 16 17 18 19 20 21 11 05 22 12 23 24 25 05 09 26 
27 28 29 30 24 31 01 02 32 33 34 28 25 24 07 32 09 
35 04 36 05 37 05 03 38 39 19 40 40 28 23 10 30 05 
22 20 41 22 14 42 43 42 44 24 45 26 09 46 14 34 40 
04 44 12 47 05 22 48 21 11 40 02 36 18 05 28 25 38 
05 25 05 15 08 25 01 25 17 12 19 22 06 13 12 27 49 
17 50 39 51 22 05 24 20 52 07 13 53 38 12 37 48 54 
43 42 55 47 56 06 31 05 36 57 05 05 33 35 35 05 05 
05 32 02 09 58 11 11 34 38 40 29 01 06 59 23 27 19 
16 56 37 35 12 12 21 04 46 49 54 53 11 43 05 51 16 
17 26 02 60 58 29 41 08 45 09 39 45 50 57 49 12 07 
34 52 61 42 38 25 03 44 03 45 46 38 45 20 16 01 01 
55 32 28 02 15 06 26 35 44 61 49 16 03 62 02 18 30 
48 06 04 25 40 36 02 32 43 49 58 43 53 60 20 63 15 
60 12 03 16 15 20 01 59 26 43 02 14 05 25 09 24 01 
56 33 45 30 49 45 47 15 52 17 01 61 58 48 32 20 09 
05 05 58 09 05 25 14 29 47 09 05 13 06 49 45 52 11 
02 28 57 07 35 38 34 06 62 42 06 11 39 47 29 03 29 
28 08 46 11 02 28 55 11 55 57 43 37 11 08 45 52 11

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01 02 03 01 04 05 05 06 07 08 09 10 11 12 13 14 15 
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 22 31 
13 32 33 04 34 07 35 36 37 27 11 38 39 30 40 10 17 
41 33 17 31 27 28 23 39 18 15 24 42 23 43 39 38 39 
42 44 45 07 27 13 46 12 40 47 26 46 05 44 15 05 06 
24 46 22 06 28 14 05 19 30 38 48 30 40 49 25 05 11 
37 10 13 27 15 50 40 51 38 20 18 42 30 17 27 43 29 
42 17 04 26 41 52 37 21 37 17 20 35 48 25 17 53 21 
05 23 29 11 40 50 51 37 18 17 12 04 38 45 15 17 27 
47 54 23 27 55 30 10 52 23 31 23 38 53 22 01 05 47 
43 14 36 24 14 05 52 41 26 30 25 24 31 37 48 19 37 
56 37 05 08 49 05 01 20 35 11 44 50 26 38 57 14 42 
47 15 58 26 31 17 05 09 45 10 28 11 59 51 53 33 10 
01 49 25 02 46 05 60 38 05 12 61 38 40 02 54 51 30 
36 53 22 11 05 19 17 55 57 62 29 13 14 61 52 47 40 
05 28 60 63 35 07 55 07 45 01 44 29 04 11 23 15 13 
24 62 37 39 05 24 05 11 23 26 24 05 05 49 33 32 25 
11 58 02 19 57 44 08 05 25 23 27 21 20 47 35 33 32 
27 37 19 17 16 18 48 56 56 46 05 14 32 05 36 24 31 
37 44 05 59 28 54 07 20 12 30 25 24 08 03 61 44 34

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01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 
18 16 16 19 16 20 21 19 22 23 24 25 15 26 27 18 16 
03 28 15 16 29 30 01 16 26 31 18 32 33 34 10 04 06 
12 02 16 29 35 13 36 01 07 33 37 32 38 30 29 39 20 
14 08 29 33 40 02 19 21 25 07 28 38 10 41 08 16 42 
43 32 28 28 26 38 44 04 35 23 45 46 12 23 38 07 15 
46 47 48 37 29 49 50 12 44 25 51 03 52 53 34 11 54 
55 16 32 01 54 07 15 30 36 16 26 52 35 31 32 56 23 
21 54 07 52 45 23 15 30 20 56 14 53 29 31 50 42 38 
19 57 26 36 36 17 52 57 23 04 16 34 06 44 15 30 19 
58 47 12 12 37 34 59 02 16 38 26 41 36 16 12 56 10 
45 52 47 01 54 07 41 52 10 30 21 01 60 42 43 29 54 
58 29 38 55 13 07 10 40 13 52 01 16 44 61 53 19 05 
05 62 58 62 27 57 27 62 05 58 60 10 27 21 56 13 01 
09 55 24 10 41 16 07 15 63 38 42 35 63 11 07 41 28 
07 41 52 41 17 01 16 14 16 63 48 62 33 04 31 15 03 
37 24 16 13 10 14 26 20 45 16 10 33 12 35 20 05 59 
16 29 31 41 47 25 28 16 50 16 42 51 07 24 01 23 52 
55 47 59 47 30 57 63 52 29 15 57 39 49 42 50 25 16 
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01 02 03 04 05 06 07 08 09 10 11 12 02 13 14 15 16 
17 18 19 20 21 22 23 24 03 09 04 17 16 25 10 19 03 
16 07 26 27 01 28 29 01 30 31 13 03 17 26 32 33 11 
34 35 33 36 37 14 38 29 39 12 40 15 41 02 08 06 21 
11 30 32 42 29 43 20 03 07 03 44 28 03 21 45 46 03 
12 01 12 32 47 14 05 18 15 39 36 04 48 34 13 33 01 
14 30 39 22 07 49 39 50 47 51 47 20 05 09 51 12 38 
09 08 03 22 34 52 12 49 31 10 04 05 43 10 40 31 20 
53 48 12 51 31 54 45 14 33 51 15 39 11 04 43 22 03 
34 20 03 21 50 49 14 20 25 43 47 42 03 27 55 03 50 
23 56 32 44 57 14 28 07 50 10 19 36 15 05 03 46 23 
48 58 50 47 49 29 59 17 28 53 07 01 31 47 25 01 22 
06 60 43 44 34 27 61 60 03 15 28 24 21 08 59 62 52 
26 60 51 47 14 33 18 58 22 63 39 01 08 08 40 53 03 
45 61 57 23 20 51 46 47 01 07 52 31 47 04 46 51 63 
39 48 44 13 11 03 28 38 22 57 30 06 31 16 51 47 11 
20 23 18 42 41 33 09 14 17 51 22 33 59 54 39 33 05 
14 03 22 03 39 10 19 37 50 03 04 16 54 25 33 01 29 
27 02 17 10 09 42 24 29 56 03 40 30 55 32 03 45 25 
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01 02 03 04 05 06 07 08 09 10 01 04 11 12 13 04 04 
14 15 04 15 16 04 04 04 11 17 18 19 20 21 13 22 23 
24 25 26 27 28 29 30 31 04 29 32 33 34 35 36 25 37 
03 06 38 39 19 19 19 37 40 33 36 18 41 31 05 42 02 
43 44 24 39 04 39 16 45 11 04 08 46 19 47 27 48 03 
11 31 47 49 23 26 10 50 34 20 46 51 36 33 18 46 40 
36 07 04 08 35 30 11 23 34 02 06 18 33 31 19 08 05 
06 26 32 30 12 11 43 29 19 06 23 52 45 05 06 38 24 
11 27 03 46 09 06 50 07 22 10 11 04 32 11 30 53 33 
12 42 44 46 09 06 18 33 10 02 18 04 46 31 31 54 12 
55 51 17 04 47 25 11 24 24 45 32 46 25 01 56 52 04 
57 10 13 54 20 46 58 53 04 24 59 08 48 60 60 38 13 
04 61 41 49 57 29 60 33 40 35 05 52 55 01 04 47 62 
60 41 17 30 60 25 12 04 53 48 24 04 08 37 17 20 31 
25 34 33 50 31 46 44 61 53 60 35 17 33 48 27 60 57 
49 28 53 60 39 13 38 22 47 55 08 33 56 58 20 34 21 
03 09 18 42 39 04 62 60 37 43 04 33 26 19 48 06 40 
23 03 01 04 48 59 08 61 19 32 60 46 17 39 14 05 18 
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01 02 03 04 05 06 07 08 09 10 11 08 12 13 14 15 16 
17 07 18 19 20 13 14 04 21 12 22 23 24 25 26 09 02 
04 09 27 08 28 29 09 25 22 07 30 31 32 02 33 28 34 
35 34 10 08 15 25 27 36 10 37 38 39 16 05 40 41 04 
10 14 06 16 08 38 25 40 21 22 14 15 07 08 18 25 41 
08 16 42 09 17 18 29 43 25 34 09 25 09 37 44 45 34 
46 47 48 28 29 16 25 49 16 18 31 50 04 33 28 20 19 
34 51 08 23 39 41 49 10 18 27 18 34 22 49 18 10 41 
52 53 12 42 03 54 08 35 09 04 18 15 22 48 17 50 08 
43 41 23 42 40 05 39 09 04 18 06 10 48 17 55 08 43 
40 30 22 27 19 05 39 09 02 32 03 51 56 08 03 32 24 
49 52 57 58 03 38 59 08 05 28 46 03 05 60 61 43 45 
48 47 54 03 26 41 06 18 03 35 48 51 44 05 56 48 13 
60 23 48 12 08 28 24 42 04 02 05 08 10 54 32 48 39 
13 24 38 54 36 31 57 58 07 11 50 46 56 25 46 58 19 
46 30 20 08 62 24 22 03 04 08 10 44 43 54 48 62 60 
18 54 08 53 47 60 08 35 13 39 53 05 24 08 50 45 48 
53 05 59 36 50 62 54 20 12 32 60 12 50 40 26 57 49 
43 44 08 07 23 41 42 63 09 31 26 08 47 36 24 13 01 
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p+f%kpd1#OEjD62&|
G_DLK2G+*Ac<+5A|l
L2z+MG|FLAVOS2+KC
MOG6+p%U7)OX6q^*A
p<>bf>O69U)W+44+c
.UKFBczjRtF275.+d
UlZpR4(PH_H444HR@
TVO8JbCdZ^y<l+Y+y
-+SM|5FTkt1-*U8^-
PCWK*|JRyFSR|lULT
ckyU#4d3F</(9NMGY
OtZ:lF5+8^CP#+P6P
fc|+6U*43b|^cqVUZ
bz*-J^tD1W5>F8O+.
.:2#|5FBc)F*LR8+/
c+^p6+cRWOS|pN4bz
Vc.b+lWKVHERj+TV#
zZ(9A;kYG.F|Mzj+z

01 02 03 04 05 06 07 08 09 10 06 11 04 12 13 11 14 
15 16 17 18 19 20 21 22 23 24 17 25 26 02 11 08 27 
11 02 28 29 30 11 31 32 25 12 15 33 34 35 36 09 16 
37 38 34 26 24 36 37 02 39 40 41 42 02 43 40 16 44 
26 36 45 02 08 37 16 46 26 40 47 12 27 36 02 24 05 
08 12 37 35 02 11 29 48 03 49 12 13 35 50 14 39 40 
11 42 06 51 28 06 12 35 07 48 49 52 02 53 53 02 41 
22 48 24 46 54 41 45 33 17 55 46 36 03 43 22 02 31 
48 44 56 11 17 53 57 58 19 38 19 53 53 53 19 17 18 
21 47 12 59 01 51 05 31 56 14 60 42 44 02 10 02 60 
61 02 27 08 16 43 46 21 30 55 32 61 39 48 59 14 61 
58 05 52 24 39 16 01 17 60 46 27 17 16 44 48 26 21 
41 30 60 48 25 53 31 23 46 42 04 57 07 62 08 37 10 
12 55 56 20 44 46 43 02 59 14 05 58 25 02 58 35 58 
28 41 16 02 35 48 39 53 23 51 16 14 41 50 47 48 56 
51 45 39 61 01 14 55 34 32 52 43 06 46 59 12 02 22 
22 20 36 25 16 43 46 54 41 49 46 39 26 17 59 02 04 
41 02 14 11 35 02 41 17 52 12 27 16 11 62 53 51 45 
47 41 22 51 02 44 52 24 47 19 15 17 33 02 21 47 25 
45 56 57 07 40 63 30 10 37 22 46 16 08 45 33 02 45

---

lk|t|7XA#TPK&|/FG
|lt(V|9/1WB-l|d9W
;DJG|W.##U6FBc(MN
A|p%y|W/4:|5FBc|)
F+;Ll|YfG+><YONU8
zfNH-*TZR%:ARzRbB
|GB1<lYHERLDYt8Jl
(Mj><f.FA9/pU4yN+
TlZ(CW+|2p^VLzFM+
YR(3V#UUWN29<VRB|
-qc3_t<j.D4z2#;+-
^zZ#7A/kX)K#OpFB|
#t*|Rz2|5PES8y:cY
+(F+J#+j%Lz17*-Y%
qzHN|My>K2#lD|OTB
bR1p*|JR4GOdDU<JH
.f(5Bzj@|>|5FyV.)
cCt&+WB(CYJBHz8S6
Vc.b|^lU>_S<4Gtp+
qEl7*7+fDb9cc*c4K

01 02 03 04 03 05 06 07 08 09 10 11 12 03 13 14 15 
03 01 04 16 17 03 18 13 19 20 21 22 01 03 23 18 20 
24 25 26 15 03 20 27 08 08 28 29 14 21 30 16 31 32 
07 03 33 34 35 03 20 13 36 37 03 38 14 21 30 03 39 
14 40 24 41 01 03 42 43 15 40 44 45 42 46 32 28 47 
48 43 32 49 22 50 09 51 52 34 37 07 52 48 52 53 21 
03 15 21 19 45 01 42 49 54 52 41 25 42 04 47 26 01 
16 31 55 44 45 43 27 14 07 18 13 33 28 36 35 32 40 
09 01 51 16 56 20 40 03 57 33 58 17 41 48 14 31 40 
42 52 16 59 17 08 28 28 20 32 57 18 45 17 52 21 03 
22 60 30 59 61 04 45 55 27 25 36 48 57 08 24 40 22 
58 48 51 08 05 07 13 02 06 39 11 08 46 33 14 21 03 
08 04 50 03 52 48 57 03 38 10 54 62 47 35 37 30 42 
40 16 14 40 26 08 40 55 34 41 48 19 05 50 22 42 34 
60 48 49 32 03 31 35 44 11 57 08 01 25 03 46 09 21 
53 52 19 33 50 03 26 52 36 15 46 23 25 28 45 26 49 
27 43 16 38 21 48 55 63 03 44 03 38 14 35 17 27 39 
30 56 04 12 40 20 21 16 56 42 26 21 49 48 47 62 29 
17 30 27 53 03 58 01 28 44 61 62 45 36 15 04 33 40 
60 54 01 05 50 05 40 43 25 53 18 30 30 50 30 36 11

---

.B<O4621CVV-DE.;Y
PMAFOW+fC)Lj|5FBc
N+SS.Y+O8dtk&/+K^
;X+8|LG2DTY+*clMP
L91DOq4LqD/c/B/5_
k_CZDYDcD+XtRJ|*+
Gz<b.cVPFd8BC*#|2
qPtfX+c|YLPRHERJ+
V2RF@k.2_+2BWUGRJ
-t8^U(b(<yf&+N+p-
>.>J7Njk.<X;z%+6C
A2OF*-8k43N)PB).T
.+G@|O3|WU_(4yRb+
StcB(9-*KkMX6z@yO
/(zT&4U)tBc+zZ#7A
|CUf97F<L6GNH4-Sy
N:B^:B*3O)L2|5FBc
c+bzdN4zBKO#+/tpU
8+|fFC4+_S.c+94AM
5(4+lzH@T+VOFdRzK

01 02 03 04 05 06 07 08 09 10 10 11 12 13 01 14 15 
16 17 18 19 04 20 21 22 09 23 24 25 26 27 19 02 28 
29 21 30 30 01 15 21 04 31 32 33 34 35 36 21 37 38 
14 39 21 31 26 24 40 07 12 41 15 21 42 28 43 17 16 
24 44 08 12 04 45 05 24 45 12 36 28 36 02 36 27 46 
34 46 09 47 12 15 12 28 12 21 39 33 48 49 26 42 21 
40 50 03 51 01 28 10 16 19 32 31 02 09 42 52 26 07 
45 16 33 22 39 21 28 26 15 24 16 48 53 13 48 49 21 
10 07 48 19 54 34 01 07 46 21 07 02 20 55 40 48 49 
11 33 31 38 55 56 51 56 03 57 22 35 21 29 21 58 11 
59 01 59 49 60 29 25 34 01 03 39 14 50 61 21 06 09 
18 07 04 19 42 11 31 34 05 62 29 23 16 02 23 01 41 
01 21 40 54 26 04 62 26 20 55 46 56 05 57 48 51 21 
30 33 28 02 56 44 11 42 37 34 17 39 06 50 54 57 04 
36 56 50 41 35 05 55 23 33 02 28 21 50 47 52 60 18 
26 09 55 22 44 60 19 03 24 06 40 29 53 05 11 30 57 
29 63 02 38 63 02 42 62 04 23 24 07 26 27 19 02 28 
28 21 51 50 32 29 05 50 02 37 04 52 21 36 33 58 55 
31 21 26 22 19 09 05 21 46 30 01 28 21 44 05 18 17 
27 56 05 21 43 50 53 54 41 21 10 04 19 32 48 50 37

---

fW&MYM_+Z4;zHSfES
@(+;k9RKDlzz+%3#C
2|yOW+N*t1^/45U>7
K.3+UA<Bf2+p*2z-*
p:<#4XpGT;dUDjpf|
y_jPl2+l^Vc.bKUc+
+(3Z1|5FBc;-yDRM(
N18OO|GF@.R^<qWz4
X#clL%Wc|b2)+K)+*
42(+GkF+cLFBc.lzC
-#H>||5FD)|67/5)-
KG<2DqF:84X|c)TpB
;+zOFj_9.CU+L&3>&
d&1OEE7&+*|JR_J-+
qftpWAfM1|q2(Bp+;
KT2(54BN+J+DYFKMU
cZz%L84HER8;M1+G#
dO5KBfFR|yty+2JMz
KX291+CZ*-FTBEX+9
PPTR>|#jzZ49/7cBE

01 02 03 04 05 04 06 07 08 09 10 11 12 13 01 14 13 
15 16 07 10 17 18 19 20 21 22 11 11 07 23 24 25 26 
27 28 29 30 02 07 31 32 33 34 35 36 09 37 38 39 40 
20 41 24 07 38 42 43 44 01 27 07 45 32 27 11 46 32 
45 47 43 25 09 48 45 49 50 10 51 38 21 52 45 01 28 
29 06 52 53 22 27 07 22 35 54 55 41 56 20 38 55 07 
07 16 24 08 34 28 37 57 44 55 10 46 29 21 19 04 16 
31 34 58 30 30 28 49 57 15 41 19 35 43 59 02 11 09 
48 25 55 22 60 23 02 55 28 56 27 61 07 20 61 07 32 
09 27 16 07 49 17 57 07 55 60 57 44 55 41 22 11 26 
46 25 12 39 28 28 37 57 21 61 28 62 40 36 37 61 46 
20 49 43 27 21 59 57 47 58 09 48 28 55 61 50 45 44 
10 07 11 30 57 52 06 18 41 26 38 07 60 03 24 39 03 
51 03 34 30 14 14 40 03 07 32 28 63 19 06 63 46 07 
59 01 33 45 02 42 01 04 34 28 59 27 16 44 45 07 10 
20 50 27 16 37 09 44 31 07 63 07 21 05 57 20 04 38 
55 08 11 23 60 58 09 12 14 19 58 10 04 34 07 49 25 
51 30 37 20 44 01 57 19 28 29 33 29 07 27 63 04 11 
20 48 27 18 34 07 26 08 32 46 57 50 44 14 48 07 18 
53 53 50 19 39 28 25 52 11 08 09 18 36 40 55 44 14

Not much to report tonight. I put some of the cyclic smokie messages into my new spreadsheet and didn’t see any diagonal rows. But then I realized that I am going to have to re-number any message that I put into the spreadsheet so that the first symbol is 1, second symbol is 2, etc. That way I can look for patterns, like diagonal rows. So I am going to make a new spreadsheet that re-numbers any message that I want to examine.

OK here’s a full set of 24 generated ciphers (simple homophonic substitution) that share these measurements with the Z340:

– unigram distribution
– bigram repeats at period 1 and period 19 (normal reading direction)
– trigram repeats at period 1
– bigram repeats at period 15 (mirrored reading direction)
– perfect cycle score (L=2)
– pivots
– appearance of pseudo-words such as "HER", "GOD", and "ZODIAC" among the ciphertext symbols

I left out some other things all those generated ciphers have in common with Z340:

– In Z340, the two occurrences of trigram "|5F" (vertical bar, filled circle, F) appear in the same columns. Same is true of generated ciphers.
– In Z340, one of the "|5F" trigrams intersects with trigram "FBc" which also repeats elsewhere in the cipher. Same is true of generated ciphers.
– Generated ciphers have the same fold marks in the middle on the left and right sides
– Generated ciphers have similar "box corner" patterns

I started generating ciphers that have columnar transposition done on the plaintext prior to encipherment. Key lengths are between 2 and 20. They are not keyed by words or phrases. Instead, it is just the random ordering of columns. For example, the key {4,1,3,2} has length 4 and specifies the order in which the columns are transcribed.

If the key length divides evenly into 340, then the columnar transposition is regular. Otherwise it is irregular (no nulls or spaces inserted). The generated ciphers still have many of the same characteristics as the Z340.

Here’s the first one. Its key length is only 3. Can you crack it? Should be easy with such a small key.

C;XO^z-7Y(SG5DYk>
AUFcK2ypW<TXf847y
Wc<p>2pEVXT9#6LjW
9OpHER;b.2-*Xc)l%
FTB<:O3.dcK|5FBcM
pK/fU)1c>X(zLcT/X
28pOb.cVO;X5N/2L_
2JfY/<XXk1MX9T&t|
TBO>P9#dFNzd4zK<)
-EX+ZBpB|C6kWKOW-
YRL#@7G*^UXRcBXO.
MSXz7)f:@jyPz>%lf
XNOX3G2&L>X2|X+|q
3()zk_NRO8t|5FC*-
NJ6qU4BJz)W1lf<X8
|Hp&//L|*^dzX3VX)
XPAyRJ|*(dzZ_77|k
qXO4MCY+/jM&5G2GK
GFPB9l5(-O#FXWl#F
WpU:FBcdTBBdKq*2+

01 02 03 04 05 06 07 08 09 10 11 12 13 14 09 15 16 
17 18 19 20 21 22 23 24 25 26 27 03 28 29 30 08 23 
25 20 26 24 16 22 24 31 32 03 27 33 34 35 36 37 25 
33 04 24 38 31 39 02 40 41 22 07 42 03 20 43 44 45 
19 27 46 26 47 04 48 41 49 20 21 50 13 19 46 20 51 
24 21 52 28 18 43 53 20 16 03 10 06 36 20 27 52 03 
22 29 24 04 40 41 20 32 04 02 03 13 54 52 22 36 55 
22 56 28 09 52 26 03 03 15 53 51 03 33 27 57 58 50 
27 46 04 16 59 33 34 49 19 54 06 49 30 06 21 26 43 
07 31 03 60 61 46 24 46 50 01 35 15 25 21 04 25 07 
09 39 36 34 62 08 12 42 05 18 03 39 20 46 03 04 41 
51 11 03 06 08 43 28 47 62 37 23 59 06 16 45 44 28 
03 54 04 03 48 12 22 57 36 16 03 22 50 03 60 50 63 
48 10 43 06 15 55 54 39 04 29 58 50 13 19 01 42 07 
54 56 35 63 18 30 46 56 06 43 25 53 44 28 26 03 29 
50 38 24 57 52 52 36 50 42 05 49 06 03 48 32 03 43 
03 59 17 23 39 56 50 42 10 49 06 61 55 08 08 50 15 
63 03 04 30 51 01 09 60 52 37 51 57 13 12 22 12 21 
12 19 59 46 33 44 13 10 07 04 34 19 03 25 44 34 19 
25 24 18 47 19 46 20 49 27 46 46 49 21 63 42 22 60 

Doranchak could you run them through your cycle measurements please, thanks.

OK —

jarlve nonrepeat 1:

z340: 4462
p105_jarlve_e2.txt: 4217
p105_jarlve_e3.txt: 5139

jarlve nonrepeat 2:

z340: 1599
p105_jarlve_e2.txt: 1538
p105_jarlve_e3.txt: 2077

perfect cycle score (L=2):

z340: 247.85
p105_jarlve_e2.txt: 222.91
p105_jarlve_e3.txt: 267.11

perfect cycle score (L=3):

z340: 62.36
p105_jarlve_e2.txt: 65.71
p105_jarlve_e3.txt: 50.72

jarlve m_2s_cycles:

z340: 2150.72
p105_jarlve_e2.txt: 2196.20
p105_jarlve_e3.txt: 2006.21

Thanks doranchak,

These 24 ciphers from your previous generator are somewhat final right? I want to run some tests but it may take a very long time.

Some while ago I talked about an encoding hypothesis that Zodiac didn’t try to cycle but more or less had some kind of window/range in which he tried not to repeat symbols. Per row or per 2 rows, whatever.

I’m strongly in favor of this hypothesis now, it is by far the simplest and can explain everything we’ve seen about the encoding. The randomization. No L3/L4’s because they weren’t there to begin with. Cycles occuring all over the cipher at various starting positions. The frequencies of unique strings peaking strongly at a length of 17 is also a sign in this direction. The "+" and "p" symbol would then more likely be 1:1 substitutes and we are left with transposition.

The other options are that he randomized about 25% which seems far fetched in respect to the L3/L4’s and just in general seems like a weird thing to do. Or that it is transposition after encoding which would then needed to be thorough and would have disturbed various things of which I haven’t seen the faintest clue. Thorough polyalphabetism is also unlikely and partial polyalphabetism would not destroy the L3/L4’s unless it’s very specific and engineered.

Doranchak and smokie what do you think? Agree with me and we can leave the encoding behind us.

I started generating ciphers that have columnar transposition done on the plaintext prior to encipherment.

I have tons of work left with (regular) columnar and diagonal transposition so won’t indulge with keyed columnar transposition for the moment. The 340’s bigram peak is eerily strong, it seems most likely to me that we’ve overlooked something.

Thanks doranchak,
These 24 ciphers from your previous generator are somewhat final right? I want to run some tests but it may take a very long time.

I suppose they are somewhat final, unless you can think of Z340 similarity measurements that they need to incorporate that I haven’t already included.

Doranchak and smokie what do you think? Agree with me and we can leave the encoding behind us.

I don’t fully understand the hypothesis yet. Randomizing the cycles alone is not enough to defeat solvers like azdecrypt. So are you saying Z applied different keys every so often?

What do you mean by "The "+" and "p" symbol would then more likely be 1:1 substitutes and we are left with transposition"? Are you saying once 1:1 substitutes are ruled out, then we should look at transposition?

I might need to see an example of how to apply your hypothesis.

I have tons of work left with (regular) columnar and diagonal transposition so won’t indulge with keyed columnar transposition for the moment

What is the difference between columnar and keyed columnar? Or are you talking about regular vs irregular? I do have some regular columnar transposition ciphers I can produce.

I’m planning to let my generator create some more columnar transposition ciphers, then I will make some scytale ciphers. Would you like me to try out your diagonal scheme with my generator, to make the generated ciphers match the z340 stats?

I don’t fully understand the hypothesis yet. Randomizing the cycles alone is not enough to defeat solvers like azdecrypt. So are you saying Z applied different keys every so often?

Okay,

The hypothesis is about how he applied homophonic substitution. He created a key as normally, as he did with the 408. Then instead of cycling and thus keeping track of which symbol in the cycle should be used next he picked a random symbol from that cycle that was not repeated in his window. And with window I mean a particular range, for instance one row, or a couple of rows, or the last x-number of symbols. And just that for the whole cipher.

Something in this manner. So, if he did that, any symbol that is repeated at close range ("+" and "p") should be 1:1 substitutes. This encoding style seems to fit observations very well.

What is the difference between columnar and keyed columnar? Or are you talking about regular vs irregular? I do have some regular columnar transposition ciphers I can produce.

With unkeyed CT or ICT you take off the columns in order, for example from 1 to 17 or from 17 to 1. With keyed CT or ICT you take off the columns in random order 14,1,7,6,… this especially is what makes it difficult. Since you now have to go through 17! permutations.

I should be able to crack any unkeyed CT or ICT with AZdecrypt right now assuming there hasn’t been fooled with differences between inscription and transcription rectangles and directions. And that’s what I’m working on now, assuming there has.

I’m planning to let my generator create some more columnar transposition ciphers, then I will make some scytale ciphers. Would you like me to try out your diagonal scheme with my generator, to make the generated ciphers match the z340 stats?

That would be great, but let’s wait with that until I’ve taken a look at those other 24 ciphers.

The hypothesis is about how he applied homophonic substitution. He created a key as normally, as he did with the 408. Then instead of cycling and thus keeping track of which symbol in the cycle should be used next he picked a random symbol from that cycle that was not repeated in his window. And with window I mean a particular range, for instance one row, or a couple of rows, or the last x-number of symbols. And just that for the whole cipher.

Something in this manner. So, if he did that, any symbol that is repeated at close range ("+" and "p") should be 1:1 substitutes. This encoding style seems to fit observations very well.

Thanks for clarifying – I think I understand now. My hunch is that even if the cycling is weakened this way, it shouldn’t really affect azdecrypt’s ability to find solutions. However, with 1:1 substitutes thrown in, you have already ruled that out, up to some multiplicity limit. Is this fair to say?

With unkeyed CT or ICT you take off the columns in order, for example from 1 to 17 or from 17 to 1. With keyed CT or ICT you take off the columns in random order 14,1,7,6,… this especially is what makes it difficult. Since you now have to go through 17! permutations.

Oh, ok. In my mind, unkeyed CT is simply a more trivial case of keyed CT, so successful cryptanalysis of the latter will effectively rule out both.

Also, my generated ciphers allow for keys up to length 20 so you’d have to go through 20! permutations.

I was thinking of asking George Lasry if he had ideas of how to solve columnar when it’s combined with homophonic substitution, since he has solved long-keyed columnar transposition ciphers as well as double transposition ciphers.

That would be great, but let’s wait with that until I’ve taken a look at those other 24 ciphers.

OK – sounds good.