Zodiackillersite.com

Jarlve wrote:This goes through the typical directional transposition. It stands out that the 340 shows high scores for some of the diagonal transpositions (1627)

To get an idea of significance, I shuffled 10,000 times and ran my implementation of your cycle score:

Min: 809.8
Max: 1697.0
Mean: 1197.3
Std dev: 126.8

Z340's cycle score is 2150.7 (it's different from yours a little for some reason), which is 7.5 std deviations from the mean of shuffles.
Your diagonal cycle score of 1627 is 3.4 std deviations from the mean of shuffles.

Here are the charts for increases of transposed periodic ngrams resulting from symbol merges, at this new link:

http://zodiackillerciphers.com/symbol-m ... transpose/

The previous link still shows the untransposed periodic ngram data if you want to compare them.

Both links include 5-grams now.

Select "shuffle sigma" in the sort by dropdown to view the more significant spikes in the data.

Only one pair of symbols, "(W", produces an increase in transposed 5-grams when merged. Interestingly, the 5-grams appear in the same columns, at transposed period 68 which is a multiple of 17:


(I think that is the equivalent of untransposed period 5)

The same 5-grams appear at periods 69 and 70:





I'm still puzzled about the significance of this. Maybe these are just phantoms. It may be related to your earlier question, Jarlve -- if we are already looking at bigram anomalies at certain periods, then formation of larger-order ngrams might be more likely since there are more building blocks lying around.

And, more generally: Wouldn't we be seeing more convincing spikes if we were merging correctly selected pairs of symbols to form homophones? I.e., newly forming bigrams should be appearing at the anomalous periods. Maybe it's not sufficient to merge a single set of symbol pairs together at a time. We might need to expand the experiment to merge more than two symbols together, or even to consider more than one homophone at once (k sets of symbols, where each set contains m symbols). I'm planning to move away from this exploration for the moment though because I need to work on the cipher type identifier.

Side note: Maybe you've done this already, but here's a list of equivalencies between untransposed and transposed periods:

untransposed period 2 = transposed period 170
untransposed period 4 = transposed period 85
untransposed period 5 = transposed period 68
untransposed period 10 = transposed period 34
untransposed period 11 = transposed period 31
untransposed period 17 = transposed period 20
untransposed period 20 = transposed period 17
untransposed period 31 = transposed period 11
untransposed period 34 = transposed period 10
untransposed period 68 = transposed period 5
untransposed period 85 = transposed period 4
untransposed period 170 = transposed period 2

doranchak wrote:Interesting results, Jarlve. The bump in encoding score for diagonals is curious. There's something that "feels" diagonal about the pivots (namely, a pivot's line of symmetry is a diagonal line). I also noticed that a "Snake" transposition (read line 1 from left to right, line 2 from right to left, line 3 from left to right, etc) has only a small effect on your cycle score (I measured it as 2080.25). I also tried to find operations in my old transposition experiments that produced high repeating bigrams AND high cycle scores. PeriodColumn(2) FlipVertical() Diagonal(1) produces 41 repeating bigrams but kills your cycle score (1164.80).

Is PeriodColumn(2) a transposition/untransposition or transformation/untransformation? I want to take another look at it. I wonder about the discrepancy between our measurements. It seems that in the 340 there are allot of short 2 symbol cycles, what do you think?

doranchak wrote:

Jarlve wrote:This goes through the typical directional transposition. It stands out that the 340 shows high scores for some of the diagonal transpositions (1627)

To get an idea of significance, I shuffled 10,000 times and ran my implementation of your cycle score:

Min: 809.8
Max: 1697.0
Mean: 1197.3
Std dev: 126.8

Z340's cycle score is 2150.7 (it's different from yours a little for some reason), which is 7.5 std deviations from the mean of shuffles.
Your diagonal cycle score of 1627 is 3.4 std deviations from the mean of shuffles.

Thanks doranchak,

I just ran a test with 10000 iterations that for every iteration encodes a plaintext with 18% randomization while matching 340 ioc. And then transposes diagonal 3 and measures. For the 340 this diagonal direction sits at 1627 while the test highest was 1540. I feel this must be something, but what?

Code: Select all

Combinations processed: 10000/10000
Measurements:
- Summed: 10043332.20806184
- Average: 1004.333220806184
- Lowest: 671.0121436408454 (Plaintext(1), Encode: homophonic substitution(3854), Diagonal(TP,3))
- Highest: 1540.956268463562 (Plaintext(1), Encode: homophonic substitution(499), Diagonal(TP,3))


doranchak wrote:I'm still puzzled about the significance of this. Maybe these are just phantoms. It may be related to your earlier question, Jarlve -- if we are already looking at bigram anomalies at certain periods, then formation of larger-order ngrams might be more likely since there are more building blocks lying around.

Yes, I agree and thought the same. It is more likely for higher order ngrams to appear for periods which have higher repeats.

doranchak wrote:And, more generally: Wouldn't we be seeing more convincing spikes if we were merging correctly selected pairs of symbols to form homophones? I.e., newly forming bigrams should be appearing at the anomalous periods. Maybe it's not sufficient to merge a single set of symbol pairs together at a time. We might need to expand the experiment to merge more than two symbols together, or even to consider more than one homophone at once (k sets of symbols, where each set contains m symbols). I'm planning to move away from this exploration for the moment though because I need to work on the cipher type identifier.

I know that AZdecrypt can create text level ngram repeats at any direction you throw at it with a cipher like the 340. Perhaps the true plaintext direction would allow for a higher maximum formation of ngrams. I'll see about testing this with AZdecrypt.

I'm thinking about scoring this way, a 2-gram repeat scores 1, a 3-gram repeat scores 2, a 4-gram repeat scores 4, a 5-gram repeat scores 8, etc. My reasoning here is that two 2-gram repeats can potentially form a 3-gram repeat, so the score of two 2-gram repeats should be equal to the score of one 3-gram repeats. The score of two 3-gram repeats equals the score of one 4-gram repeat and so forth. What do you think?

doranchak wrote:Side note: Maybe you've done this already, but here's a list of equivalencies between untransposed and transposed periods:

untransposed period 2 = transposed period 170
untransposed period 4 = transposed period 85
untransposed period 5 = transposed period 68
untransposed period 10 = transposed period 34
untransposed period 11 = transposed period 31
untransposed period 17 = transposed period 20
untransposed period 20 = transposed period 17
untransposed period 31 = transposed period 11
untransposed period 34 = transposed period 10
untransposed period 68 = transposed period 5
untransposed period 85 = transposed period 4
untransposed period 170 = transposed period 2

Interesting, it correlates with the factors of 340. That was actually one of the first things I learned about periodical transposition, it is multiplicative. Stacking two period 5 transpositions is equal to a period 25 transposition etc.

340 / 2 = 170
340 / 4 = 85
340 / 5 = 68
340 / 10 = 34
340 / 11 = 30.909090...

Yes, simple multiplication and division going on here. I wonder if we could do fractional periods this way. Period transposition equals the multiplication operation and period untransposition would be division, then what would equal addition, subtraction, and square root operators? The square root of 340 is close to 19 (18.43).

I've added depth bigram stats to AZdecrypt. This looks at stacked combinations of periodic operations, it turned up something interesting. With the 340 the highest peak occurs at untransposed period 181 while it should be at either 1 and/or 19 (assuming 19 is the true direction) given the multiplicative aspect of the operation. For the 340 it is then untransposed period 181 into untransposed period 38. 181 / 38 = untransposed period 4.76 which is close to transposed period 78. It seems that the 340 prefers a fractional period for some reason. Transposition misalignment? Wow, I'm loving this stuff.

doranchak, you'll have to increase your periodic range to 339 since interesting stuff is also happening after 170.

Code: Select all

Periodical: (transposition, untransposition)
--------------------------------------------------
Period 1: 37, 37
Period 2: 37, 30
Period 3: 34, 34
Period 4: 37, 30
Period 5: 33, 37
Period 6: 37, 30
Period 7: 33, 34
Period 8: 31, 32
Period 9: 37, 32
Period 10: 32, 32
Period 11: 34, 37
Period 12: 29, 31
Period 13: 37, 30
Period 14: 32, 31
Period 15: 33, 29
Period 16: 31, 35
Period 17: 36, 35
Period 18: 40, 36
Period 19: 33, 41
Period 20: 35, 36
Period 21: 34, 29
Period 22: 33, 32
Period 23: 31, 33
Period 24: 30, 33
Period 25: 31, 34
Period 26: 33, 33
Period 27: 31, 33
Period 28: 35, 30
Period 29: 30, 31
Period 30: 36, 35
Period 31: 37, 34
Period 32: 32, 34
Period 33: 32, 31
Period 34: 32, 32
Period 35: 33, 34
Period 36: 32, 31
Period 37: 40, 31
Period 38: 34, 37
Period 39: 30, 33
Period 40: 31, 31
Period 41: 29, 31
Period 42: 32, 29
Period 43: 31, 36
Period 44: 33, 30
Period 45: 31, 36
Period 46: 32, 34
Period 47: 30, 31
Period 48: 32, 31
Period 49: 32, 31
Period 50: 31, 36
Period 51: 30, 31
Period 52: 32, 31
Period 53: 31, 34
Period 54: 35, 30
Period 55: 33, 36
Period 56: 34, 34
Period 57: 32, 37
Period 58: 33, 30
Period 59: 32, 34
Period 60: 31, 29
Period 61: 32, 32
Period 62: 30, 34
Period 63: 33, 32
Period 64: 30, 30
Period 65: 32, 31
Period 66: 33, 32
Period 67: 33, 31
Period 68: 37, 33
Period 69: 34, 32
Period 70: 34, 31
Period 71: 35, 32
Period 72: 33, 32
Period 73: 33, 32
Period 74: 32, 33
Period 75: 33, 31
Period 76: 32, 32
Period 77: 34, 30
Period 78: 34, 29
Period 79: 32, 30
Period 80: 32, 30
Period 81: 33, 35
Period 82: 32, 32
Period 83: 33, 35
Period 84: 33, 34
Period 85: 30, 37
Period 86: 32, 31
Period 87: 35, 33
Period 88: 31, 29
Period 89: 32, 32
Period 90: 34, 31
Period 91: 34, 33
Period 92: 31, 33
Period 93: 31, 31
Period 94: 32, 32
Period 95: 31, 31
Period 96: 30, 33
Period 97: 32, 31
Period 98: 33, 32
Period 99: 33, 32
Period 100: 33, 30
Period 101: 33, 35
Period 102: 32, 38
Period 103: 29, 31
Period 104: 31, 35
Period 105: 34, 30
Period 106: 34, 31
Period 107: 33, 32
Period 108: 31, 33
Period 109: 34, 32
Period 110: 33, 33
Period 111: 34, 33
Period 112: 32, 35
Period 113: 33, 32
Period 114: 34, 37
Period 115: 35, 35
Period 116: 34, 35
Period 117: 32, 32
Period 118: 32, 32
Period 119: 33, 34
Period 120: 34, 33
Period 121: 34, 31
Period 122: 33, 33
Period 123: 33, 34
Period 124: 32, 35
Period 125: 31, 34
Period 126: 32, 33
Period 127: 31, 33
Period 128: 30, 32
Period 129: 30, 32
Period 130: 31, 31
Period 131: 30, 34
Period 132: 32, 29
Period 133: 32, 35
Period 134: 30, 29
Period 135: 35, 35
Period 136: 31, 32
Period 137: 34, 30
Period 138: 32, 30
Period 139: 33, 32
Period 140: 33, 33
Period 141: 34, 32
Period 142: 33, 30
Period 143: 32, 33
Period 144: 35, 33
Period 145: 35, 31
Period 146: 33, 36
Period 147: 34, 32
Period 148: 33, 31
Period 149: 35, 32
Period 150: 35, 33
Period 151: 34, 33
Period 152: 34, 33
Period 153: 34, 31
Period 154: 32, 34
Period 155: 36, 35
Period 156: 33, 34
Period 157: 32, 32
Period 158: 33, 39
Period 159: 33, 34
Period 160: 32, 33
Period 161: 35, 33
Period 162: 33, 31
Period 163: 32, 34
Period 164: 32, 35
Period 165: 30, 33
Period 166: 35, 33
Period 167: 33, 36
Period 168: 32, 38
Period 169: 34, 38
Period 170: 30, 37
Period 171: 32, 38
Period 172: 30, 38
Period 173: 33, 39
Period 174: 31, 40
Period 175: 32, 37
Period 176: 31, 38
Period 177: 30, 36
Period 178: 31, 38
Period 179: 30, 38
Period 180: 31, 38
Period 181: 29, 43 <---
Period 182: 31, 38
Period 183: 32, 36
Period 184: 30, 35
Period 185: 30, 36
Period 186: 30, 34
Period 187: 32, 35
Period 188: 30, 38
Period 189: 30, 35
Period 190: 32, 35
Period 191: 31, 33
Period 192: 34, 33
Period 193: 33, 38
Period 194: 36, 33
Period 195: 31, 34
Period 196: 33, 34
Period 197: 29, 34
Period 198: 34, 32
Period 199: 31, 32
Period 200: 34, 29
Period 201: 31, 35
Period 202: 30, 35
Period 203: 31, 33
Period 204: 31, 33
Period 205: 33, 32
Period 206: 29, 34
Period 207: 29, 32
Period 208: 30, 34
Period 209: 32, 34
Period 210: 31, 33
Period 211: 30, 31
Period 212: 32, 31
Period 213: 31, 32
Period 214: 31, 33
Period 215: 31, 33
Period 216: 31, 34
Period 217: 32, 33
Period 218: 31, 30
Period 219: 31, 33
Period 220: 31, 32
Period 221: 32, 34
Period 222: 31, 31
Period 223: 31, 35
Period 224: 31, 32
Period 225: 30, 34
Period 226: 34, 30
Period 227: 31, 31
Period 228: 32, 31
Period 229: 31, 32
Period 230: 32, 32
Period 231: 31, 33
Period 232: 29, 35
Period 233: 32, 33
Period 234: 30, 33
Period 235: 31, 32
Period 236: 30, 35
Period 237: 30, 34
Period 238: 30, 35
Period 239: 30, 34
Period 240: 34, 35
Period 241: 33, 35
Period 242: 33, 35
Period 243: 30, 34
Period 244: 30, 34
Period 245: 31, 34
Period 246: 31, 32
Period 247: 34, 35
Period 248: 32, 35
Period 249: 29, 32
Period 250: 34, 32
Period 251: 34, 33
Period 252: 33, 33
Period 253: 35, 35
Period 254: 32, 33
Period 255: 36, 33
Period 256: 36, 34
Period 257: 39, 30
Period 258: 34, 31
Period 259: 34, 31
Period 260: 34, 33
Period 261: 33, 30
Period 262: 32, 31
Period 263: 32, 32
Period 264: 34, 32
Period 265: 38, 32
Period 266: 32, 31
Period 267: 32, 33
Period 268: 31, 33
Period 269: 32, 37
Period 270: 34, 32
Period 271: 32, 32
Period 272: 33, 32
Period 273: 36, 31
Period 274: 35, 33
Period 275: 33, 32
Period 276: 34, 35
Period 277: 34, 31
Period 278: 36, 33
Period 279: 34, 31
Period 280: 36, 31
Period 281: 33, 34
Period 282: 33, 32
Period 283: 32, 33
Period 284: 35, 34
Period 285: 35, 31
Period 286: 37, 39
Period 287: 36, 34
Period 288: 40, 36
Period 289: 38, 31
Period 290: 40, 38
Period 291: 36, 40
Period 292: 35, 34
Period 293: 38, 36
Period 294: 34, 36
Period 295: 35, 35
Period 296: 33, 31
Period 297: 35, 32
Period 298: 33, 33
Period 299: 36, 37
Period 300: 33, 33
Period 301: 36, 37
Period 302: 33, 39
Period 303: 34, 34
Period 304: 35, 34
Period 305: 38, 35
Period 306: 36, 38
Period 307: 39, 35
Period 308: 39, 37
Period 309: 39, 36
Period 310: 39, 36
Period 311: 40, 34
Period 312: 39, 35
Period 313: 42, 36 <---
Period 314: 38, 33
Period 315: 36, 37
Period 316: 38, 32
Period 317: 37, 37
Period 318: 38, 34
Period 319: 40, 36
Period 320: 39, 32
Period 321: 36, 33
Period 322: 36, 34
Period 323: 35, 34
Period 324: 35, 34
Period 325: 36, 36
Period 326: 37, 35
Period 327: 39, 36
Period 328: 37, 36
Period 329: 37, 33
Period 330: 36, 34
Period 331: 38, 34
Period 332: 35, 37
Period 333: 36, 38
Period 334: 36, 38
Period 335: 36, 37
Period 336: 38, 40
Period 337: 39, 39
Period 338: 37, 38
Period 339: 38, 40
Period 340: 37, 37
--------------------------------------------------
Transposition average: 33.21
Untransposition average: 33.50


Fractional periods do have my interest at the moment and I'm going to run a very big AZdecrypt test with stacked periods (transposed + untransposed) * (transposed + untransposed) for the normal, mirrored, flipped and reversed base directions. It's going to take a while (459684 combinations per base direction) and I'll get back with the stats and plots once it is finished.

Jarlve wrote:I'm thinking about scoring this way, a 2-gram repeat scores 1, a 3-gram repeat scores 2, a 4-gram repeat scores 4, a 5-gram repeat scores 8, etc. My reasoning here is that two 2-gram repeats can potentially form a 3-gram repeat, so the score of two 2-gram repeats should be equal to the score of one 3-gram repeats. The score of two 3-gram repeats equals the score of one 4-gram repeat and so forth. What do you think?

It seems to work well this way. So well that I'm going to include it with AZdecrypt under stats and also with the solver. Here's an example, a 340 character part of the 408 scores 1077 while the 340 can only muster a score of 330. That way people have an additional measure to gauge the solutions they are getting and/or wether these solutions have long repeating fragments or not. I've set the ngram range equal to the cipher length minus 1.

Code: Select all

Score: 23928.77 Ioc: 0.06533 Ngrams: 1077

ILIKEKILLINGPEOPL
EBECAUSEITISSOMUC
HFUNITIAMOREFUNTH
ANKILLINGWILDGAME
INTHEFORRESTBECAU
SEMANISTHEMOATDAN
GERTUEANAMALOFALL
TOKILLSOMETHINGGI
VESMETHEMOATTHRIL
LINGEXPERENCEITIS
EVENBETTERTHANGET
TINGYOURROCKSOFFW
ITHAGIRLTHEBESTPA
RTOFITIATHAEWHENI
DIEIWILLBEREBORNI
NPARADICEANDALLTH
EIHAVEKILLEDWILLB
ECOMEMYSLAVESIWIL
LNOTGIVEYOUMYNAME
BECAUSEYOUWILLTRY


Code: Select all

Score: 20350.26 Ioc: 0.07520 Ngrams: 330

GSHISCENTOPERNATM
ESTELSILARLDEIAVO
EDVANTOCARLORSEGI
NSSPECTINGSITTHAT
SUNTERIMPORTTHEOF
STHERCISIMPORITAL
SOTABLYTOACANDERP
LATIVISITSELETORU
MENTATCHTREADYSEA
SECONTEITISPEREDS
OTHFORSPALESANNAI
TEACHIPIONENDTHER
ESUNDSTEPOREALYTH
CAREEVOTEADANERTT
DECEIVEUPSINOCOST
PADGEEALISEDVNBAT
HANTRESPETRCREPOR
TTORPERATINGNFLOS
PROMREPRESLIEISPA
INAGESONECITYPAYT


As a measure of plaintext direction it finds (Period 101: 24, 44) as highest, that is untransposed period 101. doranchak, I know this is one you found before with the 5-gram.

I got a solution for message 2, but not perfect. It had at least two misalignments I think, unless I was untransposing with the wrong column count. I sort of fixed the misalignments for the time being. This is two 10 x 17 inscription rectangles. I want to report, however, that even with untransposing at 9 x 17 and even to some extent 8 x 17, I got some of the words below. Telling me that if Zodiac used multiple inscription rectangles with either 15 or 19 rows, the 340 should be pretty easy to solve.

EDIT: Some weird stuff in red.

OUSOMUCHIC
HOSEHERFOR
SEVERALREA
SONSACTUAL
LYFIRSTOFF
ILOVEHERSH
EHASBEENTH
ROUGHSOMUC
HANDISONEO
FTHESTRONG
ESTFEMALEH
EROINESILO
VETHEFACTT
HATSHEHASD
ABBLEDONBO
THSIDESOFI
TWELLTHANY
EALWAYSGOE
SFORWHATSH
EINOWSISRI
GHTSHEWILL
ALWAYSBEAN
AVENGERIAL
SOCHOSEHER
BECAUSEIWA
NTEDACOSTU
MECHALLENG
EHERCOSTUM
EHASNEVERB
EENWELLUPD
ATEDTOTHEE
XTENTSHEDU
HTHELINEBS
SINTHEENDH