“F13.4f, part 1: two key words added, one from the puzzle and one from the whole dictionary (0115's space), solved from the ciphertext alone: every puzzle word, start and rule subtracted, every dictionary rotation scored per column, the best read by quadgrams and MIX8m; K4 against 100 shuffles, plants at four word lengths”
F13.4f (issue #85), part 1. 0115 closed this space exactly with the 24 known letters, which force the second word letter by letter (a lookup). Here the known letters are not read. For each of 24 rules (Vigenere, Beaufort or variant; plain, cipher and key alphabets standard or KRYPTOS), each puzzle word (0115's 171) and start (1,085 pairs), the puzzle word's stream is subtracted; what is left is a periodic key of the dictionary word's length n (3-24). Every rotation of every dictionary word of that length (2,248,310 rotations in all) is scored exactly by the English letter frequencies of the columns it decrypts (compiled, with early abandon), the 10 best per setting and length read in full by quadgrams, the 10 best per length over all settings rescored by MIX8m (0233). Statistic, copies and plants as 0234: max z over n against K4's 100 climbed shuffles; plants at n = 5, 10, 15, 20, 8 each, each against 10 own shuffles.
Using the sculpture's tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS. twice, first with a word from the puzzle (like KRYPTOS or ABSCISSA) and then with any English word, is the same as using one key made by addingVigenere The three rules of arithmetic a table can use: add the key letter to the message letter, subtract the message letter from the key letter, or subtract the key letter from the message letter. the two words. Earlier we used the known clue words to work out the second word directly. Here we pretend we know no clue word: for every puzzle word we take its effect off, then try every English word, from every starting letter, and keep the ones whose letters come out with English letter frequencies, then read the best in full. K4the carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. is compared with shuffles of its own letters treated the same way, and hidden test messages tell us how long a second word this can still find.
Words in the margin are defined on the glossary page.
1.1
The method at work
The carved letters go in at the top; the reading comes out at the bottom.
the idea
F13.4f: the table used twice, with a puzzle word and then any English word, solved from the carved letters alone.
the check
Each puzzle word's effect taken off; every dictionary word, from every letter, scored by its columns' letter counts; the best read in full. K4 against 100 shuffles.
the bound
K4 p 0.4158. Plants found 8/8 at 5, 8/8 at 10, 8/8 at 15, 8/8 at 20.
2
Experiment lineage
What this experiment was built on, from the lineage page: 12 experiments before it, back to the root of its line. Its number is in bold.
keptreverted, in its family's colour×error or timeoutreverted under today's rulesbuilt on a parent in the same familybuilt on a parent in another family
3
Best candidate against the known letters
Laid out as the copper carries K4: OBKR ends the line that finishes K3, then three lines of 31. Left, as carved, the 24 known places in accent. Right, the candidate: a known place it gets right is an accent cell, one it misses is outlined. This is the candidate with most known letters right; none passed every gate.
in: the copper, always the same
as carved, 97 letters; the 24 known places in accent
ECDMRIPFEIMEHNLSSTTRTVDOHW?OBKR
UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO
TWTQSJQSSEKZZWATJKLUDIAWINFBNYP
VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR
OBKR ends the line that finishes K3, then three lines of 31
out: the candidate
every place read; known places in accent, misses outlined
ECDMRIPFEIMEHNLSSTTRTVDOHW?MEIO
RIRWRPAVDUVYBAMTLMARTTOMOHASDAU
DYVXFCLDKTROZUDRGHFOLTICSPHIARK
GLITOFNNUDAETFERINKIRHAPLMTRRAP
checked: the known letters in place, and the reading turns back into the copper
4
How the score is made
The loss of the best candidate, part by part. Zero is solved.
Known letters missed
20 of 24, ten points each
200.00
English
the 73 free letters score -6.93; English text scores -3.6
3.33
Key
39 bits to write it down (key words are cheap, arbitrary letters 4.7 bits each); each 60 beyond 60 costs a point
0.00
Loss
of 240, the worst possible
203.33 84.7%
5
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Pick a rule (say Vigenere on the KRYPTOS table), a puzzle word (ABSCISSA) and where it starts (its first A at place 1).
Write ABSCISSA repeated under the carved letters and take it off each letter on the table: the text that remains has a single repeating key word left in it.
Guess that word's length, say 9, and write the remaining text in 9 columns.
For each column and each of the 26 shifts, note how English the column's letters look by their frequencies.
For every 9-letter English word, read from every starting letter, add up its letters' column scores; keep the 10 best.
Read those in full and keep the most English; do this for every puzzle word, start, rule and length, and compare K4's best with what shuffles of K4 reach.
the worksheet: the first steps by hand, on squared paper
6
Worked example, generated
The same steps run by the code on the real letters.
Rule var on plain std, cipher std, key letters numbered on std; first word ORDINATE from 7, second HUP from 1
carved OBKRUOXOGHULBSOLIFBBWFLRVQQPRNGKSSOTWTQSJQSSEKZZ
first word EORDINATEORDINATEORDINATEORDINATEORDINATEORDINAT
first word off SPBUCBXHKVLOJFOEMTSEESLKZEHSZAGDWGFWEGQLNEJVMXZS
second word UPHUPHUPHUPHUPHUPHUPHUPHUPHUPHUPHUPHUPHUPHUPHUPH
reading MEIORIRWRPAVDUVYBAMTLMARTTOMOHASDAUDYVXFCLDKTROZ
The search never reads the known letters: the second word is chosen by how English its columns look.
7
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
F3 (two-part key with a combiner; Scheidt's 'key word/s', C5; his key-splitting habit, 03-scheidt-said.md) and C20(a) 'layer two' as a second pass with a second word: the table applied twice with words of lengths m and n is one key k_i = a[(i + o1) mod m] + b[(i + o2) mod n]. 0115 killed it exactly for every puzzle word and every dictionary word of 3-24 letters, but only if the known letters sit where stated, letter for letter, with no slip (A1, A2); F13 is the hedge that never reads them. F13.1 (reports/f13-solvability-map.md): the space is about 24 x 1,085 x 2.2 million, 35 bits, far under the 173 that 97 letters carry by quadgrams, so it is decidable in principle; the question is whether a search can reach it. Subtracting the puzzle word leaves a periodic key, and a dictionary word scored per column by letter counts is the Friedman hand method with the key restricted to words. Pre-registered: S = max over n of (best MIX8m at n minus the shuffles' mean at n) / their sd; K4 flags at p < 0.05 against 100 shuffles (one test). A plant is found when its S is above all 10 own shuffles' S (null 1/11); a length is decided when at least 6 of its 8 plants are found.
8
Prediction
Written before the run; the result decides it.
Plants found 8 of 8 at n = 5 and 10, most at 15, fewer at 20 (columns of about 5 letters, where the per-column screen loses the true word among 2 million): decided to about n = 15. K4 inside its shuffles (p above 0.05), its readings English-like junk with at most 3-4 of 24 known letters in place (harness gate 2). F13.4f part 1 closes for the decided lengths and is blocked above them.
9
Method
Texts: K4; 100 shuffles of K4; 32 plants (n = 5, 10, 15, 20; 8 each, half with X stops; random rule, puzzle word, start, dictionary word and rotation; Carter's held-out last 20%, no known word) and 10 shuffles of each: 453 texts.
Per text, rule (24) and puzzle word and start (1,085): x_i = the carved letter with the puzzle word's stream taken off. Per n = 3-24: a 26 x n table of column scores (sum of English log letter frequencies of the letters each shift gives); every dictionary rotation of length n scored as the sum of its letters' column scores, with early abandon against the 10th best; the 10 best read in full and scored by the harness's quadgram table.
Per n, the 10 best readings over all settings rescored by MIX8m; the best kept.
z per n against K4's shuffles; S = the largest z; K4 ranked among its shuffles; each plant among its own copies.
K4's best reading at each n submitted (key: rule, the two words and starts); gate 4's controls are the shuffles' best readings, scored as the harness scores.
10
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
22candidates returned
0passed every gate
4/24known letters, best
84.7%lowest loss
nonechampion before
All 22 candidates, lowest loss first.
1failed at cribs4/24 known lettersloss 84.7%
ECDMRIPFEIMEHNLSSTTRTVDOHW?MEIO
RIRWRPAVDUVYBAMTLMARTTOMOHASDAU
DYVXFCLDKTROZUDRGHFOLTICSPHIARK
GLITOFNNUDAETFERINKIRHAPLMTRRAP
2failed at cribs3/24 known lettersloss 88.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?CDLO
ADPTATOPDAVHBROWELIJCVWWGMLXWSW
EBMACHNHFTHEALASYKEVCFVBSESOKTH
LENBGACINTBISSVOURGGSSRRANALWUH
3failed at cribs3/24 known lettersloss 88.6%
ECDMRIPFEIMEHNLSSTTRTVDOHW?FKWE
AKDYTOMRKOIGUDEMBEDUBELDRUTCOFR
OCAHJASLOOFFTSLOICIAXCUSJETHAER
BALDWUHWWBJICHOIRAUREILYXNLTIFT
4failed at cribs3/24 known lettersloss 88.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?HBSW
UPEOLCDENNBOOOFITRAFZLWOAVWHETP
FUERFTISAHUTAABKCCLOTAXCOSYWIUL
UTTLFORFROMRCCUTNHGXUMWAYVSEGYU
5failed at cribs2/24 known lettersloss 92.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?OHXD
MVPOSJUMRARTEAPLEISSFIMFITZODOA
TALYRJEDJTGOSIUVFDEASEDIXSXFHIZ
TENDVQAOGLEREPTPPPANCUTWAVUSFIN
6failed at cribs2/24 known lettersloss 92.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?SQMU
JIBDFMWCPSHEPBRAVOASBESSDUMIMUM
PAUSPOTTCHASUARIFEWEYDTUEEMECCK
DEOISHUYPIUNAKOKIJILMAQSSNHAIMW
7failed at cribs2/24 known lettersloss 92.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?DMAH
UVEUVGFRHUXITISASOLYMAGFOHPZCOV
ESWITSAUCEADALNWSPJHPTNDTWOUGGR
EELIDNFUDVFADBEERYANCEUZTNEATSH
8failed at cribs2/24 known lettersloss 92.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?NNIS
ESTKOFWHJGETXLCKAMDBVSCRXSWBNPL
LUUDKIJPTEESYUIJSAFCLLSCEOFLIEF
FRSESIFTIGHIMBSSTNYUNPHOLYUSGNF
9failed at cribs2/24 known lettersloss 92.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?OTHE
NTPAGHGLEWINNJJGMBRATHAKRIRDTOD
SWTFSNEJBITATMPHVBEBAIPEZLEGUYP
HTACCHATOMOVCTFDVAICHOFQFWEKRAT
10failed at cribs2/24 known lettersloss 93.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?YROH
YUNASJRCOSULMEAERSISDOMEXSVEUNI
WDCGLURNOFTULLLGZVIOOBADEZHIMLR
CHTHURYWITWPTVWIFEVERCINIRKINVI
11failed at cribs1/24 known lettersloss 96.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ARNF
RODSSRARYAKDETYEXIUNMPOHOGINZLE
TCOGNYTKASNULLDONTCLNKMRCUORTBP
BOWOEVWRMSSMNRONGYEVESMICHTEIAG
12failed at cribs1/24 known lettersloss 97.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?SUKS
POTRRNPNUCDPILFYAANVOYTOMTDOOAL
ESJURPOSEEOMYTITLOANYESCKRLIVIT
KUTSHOPJPDBFDHELTLUMCTPHENELXAN
13failed at cribs1/24 known lettersloss 97.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?HAMA
ZLCGNANAGBOYDKGNTOSABADLARWINWQ
OMBHEAUCGPCVVNVTJAAQPONEOCERVOY
HVNTIMRSANEFJUICVIOEWBCFAFNEWSG
14failed at cribs0/24 known lettersloss 101.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?DFIR
ROGWYWVERCARSBEFEHTYMMFDLLOTDFC
HUCLTVECHTYWEHUEULEHOWEXOKBKANK
MBYUNXITNOTMNIAQPUKAIABITATEBUB
15failed at cribs0/24 known lettersloss 101.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?MOZY
GIRSESSMPSATBRCLEBOOMBAMULUUENM
ERMYZETEETSAIEPGWAPESFTENSSOOPH
AKUKMXISTVMGNEJRNSFDZOKUTFCCHAN
16failed at cribs0/24 known lettersloss 101.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?PLOI
FNARONARFWDLHSCOTHWERPAAFNIWVEH
UNNGSMOAMHZDEJURAMCEINOPEPDIAMO
TPAGFAIGNOLANMGWORAOJAONITXFCDI
17failed at cribs0/24 known lettersloss 101.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?NTWI
EIGIRCJICMETITBMXFVIDCBJEQTHREG
BYPODIIEJOEITHVIGLFKLIOWTOFLEGB
GNGPMCOWOOFGXISBOUSATOSPPRFESIR
18failed at cribs0/24 known lettersloss 101.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?NSOU
SZEMNETVPLEATBLRSSTUHYHOOCHIEME
IXESPVCYLRANNYCHBKEWPYPPGMORYLK
AEIIIAPARIDEDTWCFCIEJWUSMEEEBOC
19failed at cribs0/24 known lettersloss 101.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?TINR
ENSKUDULYNTFSWEPAAHNOASARVABINJ
HHYIKLUCFOWDERBLFVSFGANZEWARCAL
THVIGBROFUDEROFHEMWTFNZHIOPLTOO
20failed at cribs0/24 known lettersloss 101.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?WBFK
LGHZCSTAYECESUEBAORTHAFUPONSOAJ
JPXELCRPTBIHPCENAESRESOTDASMLUI
DLLYASOTISBTEHURSEERYEETEIOIFAE
21failed at cribs0/24 known lettersloss 101.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ZWUT
VPADTOCMHINDYRSCHASAWAREPOLOIZF
TBEWGHIJIGRMHLDAPWLXLSAACENGFIO
CEGROWNURHAGINAPHXTHUNJPWDDOBRT
22failed at cribs0/24 known lettersloss 101.4%
ECDMRIPFEIMEHNLSSTTRTVDOHW?TDBI
LEUBCAKNEFFACTMFLAIPROFEJALNUOQ
FCQUIMNSPEOPDFFISVUMCHFUAZULCQU
YEDSGLEGINZDSPFORUPPZTFWNERBJQJ
K4 statistic 2.26 at n 4, p 0.416 against 100 shuffles; plant power n5 8/8, n10 8/8, n15 8/8, n20 8/8; decided n [5, 10, 15, 20]; 26,040 settings x 2,241,060 rotations per text
What was searched, as the harness recorded it.
item
F13.4f part 1
search reads known letters
no
rules
24
puzzle words
171
puzzle word starts
1,085
settings per text
26,040
second word lengths
3, 24
dictionary rotations
3
3,381
4
18,210
5
48,505
6
103,593
7
165,214
8
238,012
9
290,331
10
308,035
11
285,593
12
245,412
13
194,025
14
136,682
15
88,830
16
54,016
17
30,838
18
15,156
19
8,132
20
3,960
21
1,722
22
902
23
391
24
120
rotations scored per text exhaustive
58,357,202,400
screen
per-column English letter frequencies, exact over every rotation (early abandon only drops rotations that cannot reach the top 10); top 10 per setting and n read by quadgrams; top 10 per n rescored by MIX8m (0233)