“F13.4d: every move of the type-1 library (27,852), before or after a periodic key on the sculpture's 8 table classes, key lengths 1-20, from the ciphertext alone; F6.1's free alphabet after a move blocked by 0236's power”
F13.4d (issue #85). 0234 solved the sculpture's tables with no move from the ciphertext alone; here every move of 0129's type-1 library (K3's rule at every shift, quarter turns, columnar and double turns at every width, the keyword columnars of the vocabulary; forward and inverse) is put before (A: move, then the table) or after (B: the table, then the move) the periodic key, key lengths 1-20, 8 table classes. A climb per setting is about 12 hours per text, so: for A the column statistics do not depend on the move, so each column's shift comes from one letter-frequency screen per class and length and every move is then scored by quadgrams; for B each move is undone first and then screened. The 30 best settings per order and length get 0234's coordinate-ascent climb (the move held) and MIX8m rescoring. Statistic, copies and plants as 0234. F6.1 (one free alphabet after a move) is not run: 0236 found one free alphabet cannot be recovered from the ciphertext alone beyond length 5 with no move at all, and 27,852 moves only add alternatives. Cost stated before the run: 541 texts x about 25 s, about 4 core-hours.
Sanborn said he scrambled with 'matrix codes' and then used the tablethe table The right-hand half of the sculpture, 26 rows of the alphabet each shifted one place further, starting from the word KRYPTOS.. Here the scramble is any of 27,852 grid moves we have listed, done before or after the table with a repeating secret wordthe secret word The word or string a cipher needs besides the method., and the whole thing is solved from the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. alone. For each guess of the scramble and the word length, the quick letter-count test picks each column's shift; the most English-looking guesses are then improved and compared with shuffles of K4.
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
F13.4d: Sanborn's 'matrix codes, then the table', solved from the carved letters alone over 27,852 grid moves.
the check
Every move in both orders, lengths 1-20, the 8 table classes; K4 against 100 shuffles; plants found to length 12.
the bound
K4 scored above every shuffle at table-then-move, key length 2 (p 0.0099), with a reading that is junk and has 3 of 24 known letters: the queue stopped for a replication (0238).
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?LDFC
TSBAMCWZEIEDAYSHEEATINQLLVRDJEW
INKWORNYDFCHUTVISMNBULOOBLNVCON
TRYCFXPAIXHIWCJIPZADKJVBPREJIHG
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 -6.99; English text scores -3.6
3.39
Key
669 bits to write it down (key words are cheap, arbitrary letters 4.7 bits each); each 60 beyond 60 costs a point
10.15
Loss
of 240, the worst possible
213.54 89.0%
5
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Pick a grid move from the list, for instance K3's rule or a keyword columnar.
Either undo the move on the carved letters first (table last) or keep it for the end (table first).
Write the letters in as many columns as the key is long and choose each column's shift by letter counts.
Read the result in the message's order and score it as English.
Keep the best guesses, improve their shifts, 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.
Order A on a planted message: K3's rule with step 7 (letter i goes to place 7i mod 97), then the KRYPTOS table with SHADOW:
message THEHOTAIRESCAPINGFROMTHECHAMBERCAUSEDTHEFLAMETOFLICKERBUTPRESENTLYDETAILSOFTHEROOMWITHINEMERGEDTH
carved DPILCFDYKUWKWYMWSBAQVXLSDZFPDXGNGVJRECNUCIGSGRXELPEUQRLIBXISWIQUJRSJFUESQZLIISQZBUWRGUNMCQQLZRKTU
undone THEHOTAIRESCAPINGFROMTHECHAMBERCAUSEDTHEFLAMETOFLICKERBUTPRESENTLYDETAILSOFTHEROOMWITHINEMERGEDTH
The search tries all 27,852 moves in both orders, every length 1-20 and the 8 ways of using the table.
7
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
F6 (Sanborn's 'matrix codes... then went back to this table', C1(a); K3's rule, C2(a)) read without the known letters: the hedge for A2 (the known letters defined on an intermediate text) and A1 on the family ranked second. F13.1 puts a move and a fixed-table key decidable by quadgrams (log2 27,852 = 14.8 bits for the move, 3 for the class and order, 4.7 per key letter: 112 bits at 20, under MIX8m's 189). Pre-registered: S = max over (order, length) of the z-score of the best MIX8m log-probability against K4's 100 climbed shuffles; K4 flags at p < 0.05; plants at lengths 3, 5, 8, 12, 20 (half each order, random move and class), each against 10 own shuffles; a length is decided at 6 of 8. The item closes for the decided lengths and is blocked above.
8
Prediction
Written before the run; the result decides it.
Plants found at 3 and 5 (8/8), most at 8, few at 12, none at 20: decided to about 8. K4 inside its shuffles (p above 0.05), its readings at most 4-5 known letters. F13.4d closes for the short lengths, blocked above; F6.1 blocked by 0236.
9
Method
Moves: 0129's route_library (forward and inverse, distinct), rebuilt here from the vocabulary.
Order A: per class and length, each column's shift by English letter frequency on the carved text; the decryption read through each move (letter i of the message is carved at where[i]) and scored by quadgrams. Order B: each move undone on the carved text, then each column's shift by letter frequency, and the reading scored by quadgrams. The 30 best (move, class) per order and length kept (C).
Those climbed by coordinate ascent on the shifts, the move held (screen's shifts and 5 random starts); rescored by MIX8m (0233); per order and length the best.
S = max z over the 40 cells against K4's 100 shuffles; K4 ranked; each plant against 10 own shuffles.
K4's best reading per cell submitted (key: move, order, class, shifts).
10
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
40candidates returned
0passed every gate
4/24known letters, best
88.5%lowest loss
nonechampion before
All 40 candidates, lowest loss first.
1failed at cribs4/24 known lettersloss 88.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?GFAT
FROLDDAISOORDMEASLAKEAPRSURGLCS
UNDADJOBERIANDRICEEPATITTIESSMR
SUNRYLAPTOYEARMSEOFSRSTELHITWIN
2failed at cribs4/24 known lettersloss 88.7%
ECDMRIPFEIMEHNLSSTTRTVDOHW?IFTD
ONSTGCDLISBITDRMBIULASHOEAINSEE
FLIVIUCTHAIDMACOCARIKSGLUMNOMER
IUNRARVSMBINGFAPPADTYIFHARPYBEC
3failed at cribs4/24 known lettersloss 89.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ICAR
MUNSSILHAYWWGAGESHINFANPAULSSHI
RDAVZVISMONKSDXEMFUGDIEJINNSWIT
HDTKLOCDHFELIECCSXPXURGTFEWMRHC
4failed at cribs4/24 known lettersloss 89.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?LDFC
TSBAMCWZEIEDAYSHEEATINQLLVRDJEW
INKWORNYDFCHUTVISMNBULOOBLNVCON
TRYCFXPAIXHIWCJIPZADKJVBPREJIHG
5failed at cribs4/24 known lettersloss 89.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?LDFC
TSBAMCWZEIEDAYSHEEATINQLLVRDJEW
INKWORNYDFCHUTVISMNBULOOBLNVCON
TRYCFXPAIXHIWCJIPZADKJVBPREJIHG
6failed at cribs3/24 known lettersloss 92.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?YILI
AMJUSTNSTDIRDARENCEITREETRCEMER
GEPITOVEORELTSETHCARSTHOUFFEREA
SYKRIMRERBYANYZETESTHATCHCATENQ
7failed at cribs3/24 known lettersloss 92.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?CCMS
ANFIAASBPCOSMOYAMESCEFMUSTIONOB
ROOTYNETOREDSFITOFILLHORWTCFARN
LITYSTERRDGIRATERNCEGORSTSERNEC
8failed at cribs3/24 known lettersloss 93.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?NBEN
DJZERANDBCKNFILLBAADWRONNWIIHLG
ARTNRHHKORCULLHCNCSIDEPXMEDFCKR
HALORKYXQTRGROWDOJOWSMSHDVNLYAT
9failed at cribs2/24 known lettersloss 97.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?KATC
HMTOREURESTICSTTHESESIGHTRICEAN
UMWLERLEACALHEGPICSINHOSKMLSROM
FMBVPSEDFRANENBRANDTHOSHLEYJELT
10failed at cribs2/24 known lettersloss 97.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?HAHG
ECYRUARDBOTOWIGAYCREHUHTIUMORSH
ATASHARBYROLFAITHZAZMSFTHINEHEV
EPUTSSIKADOURCLTIHCIPEVEATHINTA
11failed at cribs2/24 known lettersloss 97.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?PSDR
IVILEWORTODESLEYBIGUHBZURNTYSSU
AETOQISBGOFIEYCDSSOCPSAYTYRALDE
LSYMPINCYVIMEILLFAMEIFYRFBMEIIM
12failed at cribs2/24 known lettersloss 97.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?EUFI
GSJMUMDRAPNUIWFMHIPWRIDNAWWFWSC
MOSOUTLEHTAHADLOSTNOGLEALLVEMTC
HRYALOXDAISIOFAORVAASHRAICEFJEC
13failed at cribs2/24 known lettersloss 97.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?EFIN
TSBDIVILEIOFCANAWAITHSDEEEJAMEI
RFIATHEMOTINUTPETSTHEIRCNAIRMPW
HOWNPOOACRAMUAWLBANYONDENTERREM
14failed at cribs2/24 known lettersloss 97.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?BYFI
EDARATSEASZUYDTCNGCEWPTRSGIXPHM
QAISLVSCUMFHAUTIVOISASPDAJONAND
YOJNMNIKOAMNEDRUPBYCOYRWSFIFMIL
15failed at cribs2/24 known lettersloss 97.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ENTY
OTFSUMJNLBALDHAMSRIORULMISTDEON
ELSACKEWCAMNITVSOKTPYKIRRTASFER
ALEIDEITUPWHENKBRAUNKISNTMCVLED
16failed at cribs2/24 known lettersloss 97.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?HASC
IPLYNELEDMLOPNEPPDEKWSIXOROHWFM
JWSDAFREYTJORNTCUEJDUFNRMLZIPER
UKIYUZPHXWILSHKESTLYQBVUSHOWGYF
17failed at cribs1/24 known lettersloss 101.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?PAND
ANGIVEPASHYOOSTTROUDAILQUBSDETT
RAROTAKEDACITYREDBERRUPORTSAIRO
NEATICUOSEDRSHALKSANOTNATTEROSU
18failed at cribs1/24 known lettersloss 101.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?HVEB
OINGMISEBIGFELYENGJEFITIONINOOC
OSFIXPFFTHESHOKSUMPHTRANDOFIMID
HDDCJTTGOAFDAYASBEETIMDOHTOGOHS
19failed at cribs1/24 known lettersloss 101.1%
ECDMRIPFEIMEHNLSSTTRTVDOHW?UHTI
ERNOFININLLWLEDFCTANNETCENSMKCA
GENTLISTGOLOGTICMOONHUTORYRERIO
KSUHIABATTHENSULOVETAHGORUHASUC
20failed at cribs1/24 known lettersloss 101.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?SUME
ONVANENDARTTOISNTYRENWONNESOXAY
ATYHISMICARLIVKATEGOLUSIASAPTOK
EEGUEBATNKDAPERNHARDTHEHOFVELLK
21failed at cribs1/24 known lettersloss 101.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?OKPA
RRENSEGUSHHALFILEDEIWEDDELSSTAD
ODBPOLLEDHOUTROCUNNERESBRIRTEAL
LEGOVFAULLOYERESECCITRLIBLISDEI
22failed at cribs1/24 known lettersloss 101.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?NGIN
ANISTCOURYDAWEEKSPLHALIVATHADST
EETIFERSINCECCLYGOIIONYMSLOSMJE
EBUSTASIATAEIFCARILSHABLEMOOTIM
23failed at cribs1/24 known lettersloss 101.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ODDS
OELBABOYLTDJONGRANTSIXCESGINAUT
HDCAPANTALFBNCWHKDSTINTIESFUMMS
INVEHFSHROGEAUTHEIWOUISUNIVEAEV
24failed at cribs1/24 known lettersloss 101.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?PVWI
NGTENTTHISTLETHEDIMPANEWANIDORE
DITINHOCYOUBAGALLDARDISBUYDRAIN
ODILFSMMODEKJTLEYFTLUCEASKTIFYR
25failed at cribs1/24 known lettersloss 101.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?FTHL
YRATMETIENECROADARRRISSFULTHANI
CINGREADNOSEIKHEPUSICKRTEDSPAWO
MEIMROYSDECOBMOISNINGTERVEHTCHI
26failed at cribs1/24 known lettersloss 101.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?QWHY
ETNREJOURTORHUDOTCODRCBGAMMAASS
ANKVITANYIIILKUTDIUZPDENINTHEFO
REUSTSINTSAWIYOMDEZCOLBFSOBTOHQ
27failed at cribs0/24 known lettersloss 105.2%
ECDMRIPFEIMEHNLSSTTRTVDOHW?LDED
ILLTHAMNTNOTMOCLOUDEESDOMTPIRKH
NGIMELLIEUSEFASHRIHOGCCFWSBYARM
TWVGMRETKNANKAPOREFOFALOPELWOOT
28failed at cribs0/24 known lettersloss 105.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?YAME
PSYFORNDRISRLTCANGLAGIJAMIUMFOU
PHIHPATTYZDANDSCPUPPISIMCSIGANV
EBINSIBNLEPULJRHJDGCUGUREOPENSH
29failed at cribs0/24 known lettersloss 105.3%
ECDMRIPFEIMEHNLSSTTRTVDOHW?EOHR
TOTRESERATICROSOUSEHICFLENTIFUN
YSNEMUSECTDUPPHONINNUSOSMANBATO
OMLROHNCEMOMOEANDNORALSSTACKDRU
30failed at cribs0/24 known lettersloss 105.4%
ECDMRIPFEIMEHNLSSTTRTVDOHW?PUPI
ODOSIROWDELSOASYABCFHABEXONSTER
HIZMVNUNBUTFROMEPHMYBSOIDETEAJI
NJBSOPRSEMOFFEYIMJFCSTHHOUNGCZU
31failed at cribs0/24 known lettersloss 105.4%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ITSB
ULVIORTTELEMPPNEDITAICEHININPHY
RULOVGOWHYDENSEPIXGUGMORELAYNDO
THESXFIEANERSULYOFBEINRESNTEEXB
32failed at cribs0/24 known lettersloss 105.4%
ECDMRIPFEIMEHNLSSTTRTVDOHW?STBL
ENOOOZLASSNBCECATHUCHOFVISBRIKE
LNUWALFTHATMARANLYGAPCONAFTTYDO
EFMPBDPOCPUCWOOLUTTENMHEGHHGHVI
33failed at cribs0/24 known lettersloss 105.4%
ECDMRIPFEIMEHNLSSTTRTVDOHW?GENO
CTIETLISMESEORTOTVBEFOREBEHIREF
INPLAGILLGFSTTOHLRTEZDIKTYIFPHA
NPOWWEFICISANGWEDORHAYANSREDONF
34failed at cribs0/24 known lettersloss 105.4%
ECDMRIPFEIMEHNLSSTTRTVDOHW?BINS
TENTISFITSNOMESOLUMFIDEBOONITUT
EUASENEXPPGRAPMSANDTORESIGHOROG
ERMEERIBBYMARUWERLDDRITWHWOSAYS
35failed at cribs0/24 known lettersloss 105.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ECKR
SWRUTOXWYNLUBPONDLOADTEALITHCLA
SHGIKSRUNOEEXIGNECKRLUSAAVODOMF
RBEWARDFMEILFULISIAITIEWBENZZSW
36failed at cribs0/24 known lettersloss 105.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?NBCD
NBBYGHSAFLCTRAPHGOHRELAMUFMHIPF
IGHREITNEGYJLHEQURRBEFILIRSUAOV
ZYKMSEEDWOVIDEJPVLFOIORSIANGIEA
37failed at cribs0/24 known lettersloss 105.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?CWDI
DTERPAMPDNEREFIBUMSBEMCURIJHFWO
RSLEKWESHISDAMDZIJOCOQFTPUSOGNA
TUFBAVTMESPZGDWOMVEIMRMNMRHKANC
38failed at cribs0/24 known lettersloss 105.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?EPPN
PRCTCORHAKEALIGOMATIKAWUNDMDABU
RGDIAIWYSUSIIBOORFINDHOMPTBAPRO
CGILISTEDASBOTHCOBLEMIUTXTTIUFI
39failed at cribs0/24 known lettersloss 105.6%
ECDMRIPFEIMEHNLSSTTRTVDOHW?VOTI
FTTLETEEFSSEREERINRANOMISLAGEDU
TICBAGONDELAYTOJECNWPLOYZIXSONO
MNAREDSWISTORAYEMPTSTIPPIDLYIGA
40failed at cribs0/24 known lettersloss 105.6%
ECDMRIPFEIMEHNLSSTTRTVDOHW?QQAA
NDFJHMPQSWIXTNVYKGVDEVIHNETBAVS
HRURTHEQUAOREBDXFQASRTEYSCPJSDE
CKFFGIKMRTOVEDRORHINAGRLUFILLME
K4 statistic 5.05 at B2, p 0.010 against 100 shuffles; plant power L3 8/8, L5 7/8, L8 8/8, L12 6/8, L20 1/8; decided lengths [3, 5, 8, 12]