[04] · D'AGAPEYEFF INVESTIGATION

What has been tried

Every attack run against this cipher, the control that proves each one works, and the raw output.

How the search works

Substitution and transposition cannot be attacked separately — a wrong column order makes every substitution look like noise and a wrong substitution makes every column order look like noise. Simulated annealing over both at once fails at this message length; it was tried and it does not converge.

What works is exploiting the one thing a transposition cannot hide. Symbol frequencies survive it untouched, so ranking the 18 units against English letter frequencies gives a substitution that is roughly right. With that in hand the column order can be solved exactly — Held-Karp dynamic programming over subsets, scoring each candidate pairing of adjacent columns by the bigram statistics of the letters that would sit side by side. The recovered order gives a text; the text refines the substitution; the refined substitution gives a better order. Two or three rounds and it converges.

Scores are mean log₁₀ probability per letter under an interpolated four-gram model built from 147,626 letters of 1939 British prose — the book's own text, which is the right register. Real English scores −0.74; the same text shuffled scores −1.89; uniform random letters score −2.36.

The transposition convention itself was checked against the author. Feeding the code d'Agapeyeff's own worked example from page 118 — keyword MANCHESTR over ENEMY ATTACKS AT DAWN — reproduces his key numbering 5 1 6 2 4 3 8 9 7 and his ciphertext NKMAADYTECESANTATW exactly. His "Chinese manner" route on page 126 reproduces too, letter for letter. Whatever else is wrong, the machinery does transposition the way he did.

The control — proof the attack works, and where it stops working

196 letters of English, a MANCHESTER square, a random columnar key. The solver is given the digits and nothing else, and has to recover both the key and the alphabet.

Width	Seeds	Score	Letters correct	Result
2 – 12	250	−0.7914	196 / 196	solved at every width
13	250	−1.2753	93 / 196	not enough seeds
14	250	−1.4528	10 / 196	not enough seeds
15	250	−1.3834	28 / 196	not enough seeds
13	24,000	−0.7914	196 / 196	solved
14	24,000	−0.7914	196 / 196	solved
15	3,200	−0.7914	196 / 196	solved

That middle block matters, and it is exactly the sort of thing a search is happy to hide from you. Widths with many possible long-column patterns get many effective restarts; width 14 divides 392 exactly, so it has one pattern and got 250 attempts where width 11 got 82,500. The fix is simply more seeds. Widths 13 to 15 were rerun against the real cipher at the deeper settings too, and returned −1.32, −1.34 and −1.32 — nothing.

In a blind sweep across widths 2–14 the true width scored −0.79 and every wrong width scored between −1.42 and −1.55. The gap is not subtle. If the D'Agapeyeff cipher were a columnar transposition of a substitution over English, it would look like the top row of that table.

What came back from the real cipher

Attack	Search space covered	Best score	Verdict
Substitution only	all mappings of 18 units to 26 letters	−1.49	no
Keyed columnar, whole units	widths 2–15, every long-column pattern, column order solved exactly, 250 seeds each and 24,000 at the widths that needed it	−1.32	no
Keyed columnar, single digits	widths 3–13 — all 641,000 keys that leave the alternation intact; even widths are impossible outright	−1.42	no
Unkeyed geometry	614 routes — plain columnar to width 40, boustrophedon columns, the book's own "Chinese manner" from page 126, right-to-left, rail fence 2–30, four spirals and both diagonals on every exact rectangle, each also reversed	−1.42	no
Repaired text	digit 195 set to 6, 7, 8 and 9 in turn, and the whole stream reversed, each through the full width sweep	−1.33	no
Double transposition, one key twice	every column order at widths 2–11, applied twice — 43.9 million keys	−1.35	no
Double transposition, all four directions	priority 2 — every pair of column orders with both widths from 2 to 7, in all four combinations of apply and undo. UU is the ordinary reading; UA, AU and AA had never been searched, and the 2017 finding says direction is exactly what he got wrong. 139,806,976 key pairs across 144 width-and-direction combinations	−1.34	no
Crib dragging	a structural test rather than a statistical one — a crib's letter-repetition pattern must be reproduced exactly by the units it lands on, which is checkable without knowing the substitution and cannot be overfitted. Every crib of nine letters or more against widths 2–12, every consistent column order enumerated. Proved on a control first: handed one crib that genuinely occurs, it returns the true plaintext ranked first at −0.7914, runner-up −1.31. On the real cipher: 1,495,884 placements, 143,948 pattern-consistent, best −1.41 — and the top fifteen span a band just 0.021 wide, against the control's 0.52 gap between the answer and the runner-up. When the answer is present it separates; here nothing does	−1.41	no
Wide keys that divide 392	priority 8 — widths 28, 49 and 56, where the rectangle is complete and only one long-column pattern exists, solved by beam search	−1.19*	no
Irregular columnar	the same widths again with the short cells allowed in the wrong columns — the commonest hand slip	−1.34	no
Scoring only the opening	priority 1 — the four-gram score taken over the first 24, 32, 40, 50, 64, 80, 100, 130 and 196 letters, at every width 2–15. A genuine partial solution would hold near the English reference and then fall off a cliff	see notes	no
The midpoint split	priority 3 — the anomalous unit sits at unit 98 of 196, so each half swept alone, halves swapped, each half reversed, and the anomaly deleted	−1.15*	no
Other unit counts	priority 4 — 193 to 197 units, in case the tail is not three nulls or a group was lost from the end	−1.35	no
Nulls at fixed intervals	p.111's own suggestion — every 2nd to 9th unit struck out at every offset, and the complement; then every subset of 1–4 cells treated as null cells (4,047 subsets); then both together	−1.24*	no
The transposition run backwards	widths 2–30 read the other way — ciphertext across the rows, columns off in key order. The natural-order column of that sweep needs no key search at all, so it is a clean detector, and it is flat everywhere	−1.32	no
Real words and phrases as keys	6,616 candidates — every word in the book's vocabulary, every date in 1939, the chapter titles, the author's name, and the challenge sentence itself with its fourteen initials — each read four ways	−1.42	no

The head-scored sweep deserves its own note, because it is the one that mattered most and its failure is instructive. At N=24 the best fits reach −0.61 — better than real English's −0.74 over the same span. That is not a solution, it is proof that 24 letters and 18 free symbols can be forced to look like anything. What a real partial solve looks like is a score that holds near the reference as N grows and then drops off a cliff at the point where the hand slipped. Instead every width decays smoothly from N=24 onward, identically. There is no cliff because there is no plateau.

*The wide-key, midpoint and null rows score higher only because they leave the solver more freedom, not because they read. At width 49 each column holds four units, so ordering 49 near-arbitrary fragments will fit almost anything; the midpoint and null rows leave shorter texts standing — 97 units, or 78 — and short texts overfit. None of them read. The null row's −1.24 comes from a reduction that leaves only 78 letters standing; short texts overfit, and it reads as nothing. Otherwise nothing rises above −1.32. The control's wrong widths sat at −1.42 to −1.55, so every number in that column is what this machinery returns when there is nothing there. About 222 million distinct keys have now been tried, plus roughly 1.8 million runs of the exact column-ordering solver, each of which searches every column order at its width.

Raw output — every run, unedited

These are the actual console transcripts. Scores are mean log₁₀ probability per letter under the four-gram model: real English −0.74, the same text shuffled −1.89, uniform random −2.36. Anything in the −1.3 to −1.5 band is what this machinery returns from noise.

CONTROL: the attack solving a cipher it is allowed to know exists

the same pipeline, on English put through a keyword square and a real columnar key. 196/196 letters at every width up to 12, and past that only because 250 seeds is not enough — at 24,000 it solves 13 and 14 too.

$ solver dpcontrol 2 15 250

DP CONTROL  -- English through a keyword square, then a columnar transposition
 true w  tried w  per letter   correct   plaintext
      2        2     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
      3        3     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
      4        4     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
      5        5     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
      6        6     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
      7        7     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
      8        8     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
      9        9     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
     10       10     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
     11       11     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
     12       12     -0.7914   196/196   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATE
     13       13     -1.2753    93/196   OPTENGLONDSOUNGSTHIGPURMIANDEFPACENGPURHOLLOVWAMPETI
     14       14     -1.4528    10/196   ODLIYLUSINBTILGDRUNBLSETHADAEONDLYINGPUROMCHSONSEVVI
     15       15     -1.3834    28/196   ONMODSUGMONRTINSIFNGADERLYTHEMROWUUORHMDLACINKYOHITE

CONTROL: crib dragging, proved on a known cipher

a crib asks a structural question, not a statistical one. THREE has a letter-repetition pattern the ciphertext must reproduce exactly, and that is checkable without knowing the substitution at all. Handed one crib that genuinely occurs, the attack returns the true plaintext ranked first, with the runner-up half a point behind.

$ solver crib 11 11 12 control

CRIB CONTROL - a known cipher, width 11.
  plaintext begins: ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWVIBRATESWITHABO
  control cribs (all verified present): BEINGAFRICAN
  true position of BEINGAFRICAN in the plaintext: 23
1 cribs of 12+ letters, widths 11-11
A hit is a placement whose letter-repetition pattern the ciphertext reproduces exactly.
reference: real English -0.74 (p05 -0.85), shuffled English -1.89

placements tested : 10,175
pattern-consistent: 1,847   (18.1523% survive)

   score crib             w  pos   plaintext
 -0.7914 BEINGAFRICAN    11   23   ORTANDLONGSOUNDSTHEDRUMBEINGAFRICANDRUMHOLLOWV  <== EXACT
 -1.3073 BEINGAFRICAN    11   23   OFTANDLNOGSOUNDSTHDEFUMBEINGAFRICANDFUMHLOLOWV
 -1.3264 BEINGAFRICAN    11   23   ORTANOLDNFSOUNDSEHTDRUMBEINGAFRICANDRUOHMLLOWV
 -1.4118 BEINGAFRICAN    11   23   OGTANNPODRSOUNDSDHETGULBEINGAFRICANDGUPHOLPOWV
 -1.4467 BEINGAFRICAN    11   23   ORSANCYONGNOWWCSTHUCRUMBEINGAFRICANORWMHOYYILV
 -1.4748 BEINGAFRICAN    11   24   CCFTANDWNSGECONDSTHDOFUPBEINGAFRICANDFOPHWCWEM

CONTROL RESULT: 196/196 letters correct  SOLVED

Crib dragging on the real cipher

every crib of nine letters or more against widths 2 to 12, all consistent column orders enumerated, the substitution completed by restarts with the crib's own letters held fixed.

$ solver crib 2 12 9

CRIB DRAGGING  196 units, 18 distinct
9 cribs of 9+ letters, widths 2-12
A hit is a placement whose letter-repetition pattern the ciphertext reproduces exactly.
reference: real English -0.74 (p05 -0.85), shuffled English -1.89

placements tested : 1,495,884
pattern-consistent: 143,948   (9.6229% survive)

   score crib             w  pos   plaintext
 -1.4062 THEREADER       12   85   OFNERDSITWAARBISTAHRISFOSTOATEFBHARDBSTHECORRB
 -1.4069 THEREADER       12  161   ALOSSAMAGNINGNENDONMODESAUSTTOGGMATDGRALNUGNIU
 -1.4080 THISISTHE       12   27   DDEAICHBSTOSDOTIENLJNRTDNDCTHISISTHELCRECLITSA
 -1.4106 THEREFORE       12  109   LDHIRAMCAMNDSIDSCHADEAINHIMRHORETNMDIENDACCDIN
 -1.4118 THEREFORE       12  128   ITROLOMILDITMAITREASIERLTTNOMROCANMASAHONTLOAO
 -1.4198 THEREFORE       11  154   RUSEANPTRPDALLEOFPEONAONNFYOMLIILEAROEENANFAMT
 -1.4201 THISISTHE       12   42   DETPPRITHTOOETCOISDPIESOHANDPAPPCHECABORDOTHIS
 -1.4213 THEREADER       12  169   UIEOILDRUENEONADUORTDULTULHDEANDIURCITDASOOKSL
 -1.4219 THISISTHE       12    5   NTGRATHISISTHEAECTASDSGIGNIGADDNOCURSACTCEAHTC
 -1.4222 THEREADER       12    5   TYRSLTHEREADERAAIUAISRLUTASNTSOELIENTILHREMINA
 -1.4227 THISISTHE       12   27   DCTIFSHOSFOEURREECLERCINOLOTHISISTHEERLNRROHSS
 -1.4235 THISISTHE       12   15   TNNEAOENUSAHOMSTHISISTHEADSTITURNUOMETHMNGSHCC
 -1.4253 THEREADER       12    1   MTHEREADERRDSNDTOISAHEENHARDTLOACONDARNIHADITT
 -1.4269 SUBSTITUTION    11  104   IRRRIESELAMOIOWNMEDSADVOTSIMAGDGTAADDSUSOROGLU
 -1.4272 THISISTHE       12   25   UPTHAESITISMAOASCPEACAPORTHISISTHEPHYSUERMECAE
CRIBDONE2

The main attack on the real cipher

keyed columnar over whole units, every long-column pattern, column order solved exactly.

$ solver dpattack 2 15 250

DP ATTACK on 196 units, 18 distinct: 04 62 63 64 65 71 72 74 75 81 82 83 84 85 91 92 93 94
reference: real English -0.74 (p05 -0.85), shuffled English -1.89, random -2.36
  w  per letter   plaintext
  2     -1.4697   DTIAURUESUMAEUSONIOOEUNDAEBSAOADEDURESULDIUMPITIODNDTRYANOLT
  3     -1.4906   OOSMITEMIATEEIRAATERREOALBOIHADTRTANUMETMMORAOUNDENONIARMLOU
  4     -1.4614   NDDUSUNAIONODAROOTSHSMICOULDREDHAEUTRDCROIIDUENTDRUSHSEQRMAS
  5     -1.4319   DNEIDASHIPNOBBRTADICHBOOCAACRIHCDDROAGNIISCIDODSOTHYASDEBORD
  6     -1.4187   XNUTEDTOOEFNELSLITDINFAUDDPOISFORLANCDCAINIALDINFELECGUARGLC
  7     -1.4391   SDBERCODCCLOCDITSOTETTENTTHANHNDRESHCHLRHIDHIIILOLSEATHTBALB
  8     -1.3750   NFLUDASABLLRULTSSEURROUSVOTITEANBONUIBOTICSATRTUTDICELOWNAUS
  9     -1.3800   LAMIESPONEIOVEMRPMTORINTSIMERPINORORAHARORSSORIOHIERHMAHERST
 10     -1.3844   SRNEBENEURONTMEEDBBINUREDLMBLARISECECONTEEBUTACMALICTUAMESCT
 11     -1.3722   IOGSNROASGRANTGLTABITRSAONNEESANCESOFGITDLMTICONNELINDSINUNT
 12     -1.3503   DEESANOLEASIOLADRDINSTORONSSUTLIAMEOTRSENDDLFOFPIANSITSTULRU
 13     -1.3628   UOCNTTETHTODDBBINNSUPSCHCHAREBOBEHODRANEIGREATUSTSDOUTDODIAB
 14     -1.3652   LRONLATEMDADAMDIOOUNTRONEMRTSCESOTEDASEMROSCCESSSSUIDISALUEC
 15     -1.3699   GSSTODOUGGASSINGESGOINNUNGANTTDUBACDSSISMTUSTENBURBALIEUROGB

w=12  -1.3503  columns [3,1,6,7,11,4,0,8,9,5,2,10]  long blocks [1,3,6,7]
  DEESANOLEASIOLADRDINSTORONSSUTLIAMEOTRSENDDLFOFPIANSITSTULRULMMULDISEAOMPADORDSARTOLDANTOMTYRROLEEFFALAFDMYUMETOTUTILLMULLDHOISTRDFROIFFERENTAFLETIRDIDNIMADROVIAANSUMMNARITIATRIMAOFLIEPUEDFGOLANDA
w=13  -1.3628  columns [6,2,9,1,4,0,3,11,5,8,12,7,10]  long blocks [6]
  UOCNTTETHTODDBBINNSUPSCHCHAREBOBEHODRANEIGREATUSTSDOUTDODIABEWBSOUNSEESTBEDOFAUDCURITHHOTSBYOREACCHESESONTRECESOCCCACETINACBBUNTISITONCIPATENAHIGABANARBBAISRUNSAANTERENDUDICURUBCSSISADETBCBEOBPHOR
w=14  -1.3652  columns [12,7,8,0,13,2,11,4,10,6,5,3,1,9]  long blocks []
  LRONLATEMDADAMDIOOUNTRONEMRTSCESOTEDASEMROSCCESSSSUIDISALUECTUTNUASDURLDCONCARCTLITITERCINOTTDONISSUCAARLIESTEDUEMLINMOMREONIOUANARTMICIINISNEACENOUIDIARASMMRINTEMDLORCIONEONNALDISSITHFUGBGERWAGOB

Priority 1 — scoring only the opening

if the encipherer slipped part-way, the right key still reads the first letters. It does not. Every width decays smoothly from N=24 onward, and at small N the fits beat real English, which is the signature of overfitting rather than of a partial solution.

$ solver head 2 15 250

HEAD-SCORED SWEEP
HEAD-SCORED SWEEP  196 units, 18 distinct
Only the first N letters are scored. A genuine partial solution shows as a high
score at small N that decays as N grows past the point where the hand slipped.

Reference, real English scored over its own first N letters:
  N= 24:  -0.738  N= 32:  -0.741  N= 40:  -0.752  N= 50:  -0.735  N= 64:  -0.741  N= 80:  -0.743  N=100:  -0.737  N=130:  -0.741  N=196:  -0.745

  w      N=24      N=32      N=40      N=50      N=64      N=80     N=100     N=130     N=196   best opening at N=40
  2    -0.782    -0.971    -1.032    -1.074    -1.201    -1.265    -1.326    -1.390    -1.505   CASEDONOOWSVONIWERIIONARNSWHISASANDOWNTO
  3    -0.859    -0.917    -1.015    -1.113    -1.195    -1.213    -1.334    -1.411    -1.502   CIVISETOTSHOEORTHEHORROHIBINTHAGREECHPOS
  4    -0.788    -0.917    -1.058    -1.104    -1.140    -1.254    -1.285    -1.372    -1.453   ASABBRSTBEENDERATHMENLITWASEAHODSMORLDAD
  5    -0.688    -0.895    -0.965    -1.017    -1.122    -1.204    -1.257    -1.273    -1.414   AEOFASEUMCONINTHESARMINIRSTSREMARATIOSBE
  6    -0.657    -0.827    -0.946    -0.970    -1.106    -1.186    -1.262    -1.350    -1.419   CUPICTICAERALENTIRSETUALLIMPRESYONSALLYT
  7    -0.788    -0.917    -1.011    -1.089    -1.192    -1.246    -1.283    -1.340    -1.430   KSONTWHONOTOFTHEWEENDLEARWEELSWHATLASADO
  8    -0.681    -0.807    -0.896    -0.970    -1.064    -1.184    -1.225    -1.294    -1.401   RAUTHTHEENTINFREINTRAMISSYOUMSORIGINEITU
  9    -0.674    -0.806    -0.901    -0.954    -1.026    -1.132    -1.200    -1.304    -1.421   AWASHADASIOAREGREATHOFTHEINGHORINTRATTER
 10    -0.655    -0.737    -0.851    -0.921    -1.027    -1.130    -1.182    -1.281    -1.378   SYAPOSITYTORYOLETTERSEVEADATLAZERSTHEDEC
 11    -0.657    -0.726    -0.843    -0.912    -1.021    -1.113    -1.187    -1.241    -1.388   EWWOFTHOUNDSWHENTASTHEBLISHASINONTHATEST
 12    -0.605    -0.739    -0.836    -0.911    -0.975    -1.103    -1.149    -1.252    -1.360   NNDPAPERANTARTISHANTSPIONTHEUROPERSWROTH
 13    -0.711    -0.774    -0.873    -0.981    -1.062    -1.101    -1.183    -1.232    -1.404   EARTRATIONTOUSFOURUPONDIFWEREANDFICENCET
 14    -0.763    -0.842    -0.902    -0.985    -1.130    -1.216    -1.258    -1.347    -1.384   PATHENTHEPERSOFARANSHORTSOLOONDONTHEADSD
 15    -0.615    -0.787    -0.800    -0.929    -0.982    -1.083    -1.180    -1.280    -1.366   DICTICENTINGITATICALENTEDISESEWHOGAINDIN

STRONGEST OPENINGS (by score at N=40)
  w=15  -0.800   DICTICENTINGITATICALENTEDISESEWHOGAINDINTHALIAHQGEDHALQECCDXDLWIHSNDCQ
  w=12  -0.836   NNDPAPERANTARTISHANTSPIONTHEUROPERSWROTHERNDIANTPILAIEOHSDRSRSUWSWNTOU
  w=11  -0.843   EWWOFTHOUNDSWHENTASTHEBLISHASINONTHATESTHEOEVTILUDIDMOHAVIEVEAWEXOSLVL
  w=10  -0.851   SYAPOSITYTORYOLETTERSEVEADATLAZERSTHEDECTZZSORYLESVERIYVZHORHVHLEIIHOS
  w=13  -0.873   EARTRATIONTOUSFOURUPONDIFWEREANDFICENCETOATCASEWSDIMDOEVOINETSWNATDCAE

Priority 3, 4 and 8 — the midpoint split, other tail lengths, wide keys

the one anomalous unit sits at the exact midpoint, so the halves were swept separately, swapped, reversed; then unit counts other than 196; then the widths that divide 392 evenly.

$ solver halves 2 13 120

MIDPOINT SPLIT AND TAIL LENGTH
reference: real English -0.74 (p05 -0.85), shuffled English -1.89

A. the message cut at the midpoint, each half swept on its own
  first half, units 1-97             w=10   -1.1537   SOSEAIERTHSTRANDOESNKONESTHESLATTEDLAPOICTID
  second half, units 99-196          w=10   -1.2065   TRGGGMERGAMENDSUPPROPIMATIVEEROMSCOWDEPPMOPA
  first half incl. the 04            w=10   -1.1610   ONMOLERATANATMESPLAJOADSEENTPSNORTUEDNMINLAN

B. halves recombined
  halves swapped                     w=12   -1.3554   ROTESRSOIRSGOTMOROMADEIDESINMMSBETINTARCOMMI
  second half reversed               w=13   -1.3553   ENSTANOCCLEOUOMZTRATSASUSANDSANINNAMEARAOMIN
  first half reversed                w=12   -1.3520   NSLALLGHTEEDONETISREACMCESSCAEREDHEORLSONMRD
  the 04 removed entirely (195)      w=11   -1.3584   OFOMOLLOMNDSTEMERIISTIUSTBEARRASTRIISUSEGULI

C. the tail is not what we assumed - other unit counts
  196 units (drop 0 digits)          w= 8   -1.3549   IONANALSSINDEDURSNADMRSALMROMOVIRELATRUMAUSI
  195 units (drop 2 digits)          w=12   -1.3519   TDVOTETASHEFNUEMADOFMONDDDDONNTATESSHIMMOSTH
  194 units (drop 4 digits)          w=12   -1.3690   FFMIRDENTDALMISTOTRINAFRIONOFCAIMENARARNSTOE
  193 units (drop 6 digits)          w=13   -1.3622   TTBRCBCHBRINSONBONLEOLASTNNANSDAHNDCCBHESHTO
  192 units (drop 8 digits)          w=13   -1.3174   LOBDOINSASRUDCLLONENDUNBELLEIEIDECAROSEISLAA
  197 units (all 395 digits)         w=12   -1.3453   LRECONPLUSONROMEEROMEDALDDUSANENINSARESRSNDB

D. wide keys where 392 divides evenly
  w=28   -1.3096   RDRULTUOILOADHESHIDABDDBCUABOITEATSHOATISTOT
  w=49   -1.1901   INDSONSSTHENSESWEROWARSTHOSEDSTHEWWMMOTSTOMA
  w=56  no arrangement

Priority 2 — double transposition in all four directions

the 2017 finding says direction is exactly what d'Agapeyeff got wrong. UU is the ordinary reading; UA, AU and AA had never been searched.

$ solver dbl4 2 7

DOUBLE TRANSPOSITION, ALL FOUR DIRECTIONS
DOUBLE TRANSPOSITION, ALL FOUR DIRECTIONS  196 units, 18 distinct
d1/d2: U = undo (read columns into rows), A = apply (rows into columns)
reference: real English -0.74 (p05 -0.85), shuffled English -1.89

 dir  w1  w2           keys  best/letter   plaintext
  UU   2   2              4      -1.5654   TIGISTRGOTDDINDRDSFLSOEUDHIGNIFARGLANENIDOIO
  UU   2   3             12      -1.5021   UBODCEEOTUASTDCBIUADELAGDCTSINERIUARDADUATIC
  UU   2   4             48      -1.4434   TINABIRRORMSBAOEBYAOUASYSEVIONNYUMMYISALSBUS
  UU   2   5            240      -1.4838   UONEYARECYARRORSUEENERLANTRLADYDMINORURESRON
  UU   2   6          1,440      -1.4417   LNAAMEINCEEMDIEOISDANTONTIMCAROMSBCMISMTLINE
  UU   2   7         10,080      -1.4134   TMRSLNGGALOSSTREAMANTCANMORLIDIMSOIAOATONLED
  UU   3   2             12      -1.4973   ACROEHTATENINOSCHDIRACTICSMHNDTAUPDICAPICIDA
  UU   3   3             36      -1.4884   LCATEGLRENONUEDETUPTUDORSSGNTDGODEUNNDIAURAD
  UU   3   4            144      -1.4154   LCRCCEIIERAEOADDINBETCOBTAACDSRDUNBRANIDEATD
  UU   3   5            720      -1.4152   DNTIEUITNNANSTERSUSTSISNOTAEDNDURNANHNFUCEEO
  UU   3   6          4,320      -1.4449   NAIOINPAUNCRUIISUMNDTPSOAPIOROEIATPRIEEOPPER
  UU   3   7         30,240      -1.4065   BISHUMBOOUPAAAEETBODASHAEDEDAMTTOETDATITARED
  UU   4   2             48      -1.4898   AODIANNIUTLOUEANUAOOTRTRSIXDSRDEARLTTCOLITSA
  UU   4   3            144      -1.4567   ANUOIUOOABAATERBEAUIRILSOSTORBBITUDYLISBOBAL
  UU   4   4            576      -1.4468   ICOONINTIACOSCASUILTRECCUTPSIIEEUNNTTNUICTCD
  UU   4   5          2,880      -1.4309   SYIOSOTSITDECREAABETNDREORNASROOUPELEEINTERR
  UU   4   6         17,280      -1.4224   AIUSTEUNHOHASAWHEEOMSRAEDMETHYNTHUETRYHIDDLE
  UU   4   7        120,960      -1.4125   OUBUINCDAESUBRCTLRULUTABDALSIEETILISTDIAOADE
  UU   5   2            240      -1.4579   NDANATELEDTLMYAAOEEEIDTABLEDUBSUNTOIEDERMADE
  UU   5   3            720      -1.4498   UDMNSTAMOOCAREDMAMEARRTRONDEMMRICAAATNABCEED
  UU   5   4          2,880      -1.4281   TINITSSSIANDIHADEYDISCHDNDBEHDESTESDEUBRODND
  UU   5   5         14,400      -1.4212   HUELEATSVAOATANLIOSURISETHHHENWEEDOTSNECLTLI
  UU   5   6         86,400      -1.4058   RMCIANFANEDBCCBAEIATBBCBDEBASETEAMCATHERESTC
  UU   5   7        604,800      -1.3523   RISDUTSUCTNSTCRCIICNUEDUSBBBARNEROTENIAUNOSS
  UU   6   2          1,440      -1.4405   OCUNSNEEESANDTEDESLOHLTAAHINDDONUOLASARDDETI
  UU   6   3          4,320      -1.4244   DIAOTLRNISETRRALBIIRULDARAOESNUCSRORSECANSIE
  UU   6   4         17,280      -1.4141   LTLLLYEETIUDSEUNRYORTIBEDELETUOTGNATIONAIDIN
  UU   6   5         86,400      -1.3911   LIRATEPLOOCALLABAROCEDERNETTARYAOPRIIIILAREL
  UU   6   6        518,400      -1.3718   BHDANDERCAHIBCCDOOMASSEONEHERAELICATHESHERIA
  UU   6   7      3,628,800      -1.3392   UEUTTCCCBAODURINRANAPPEDPNSBITRUNUSPEERNEDEC
  UU   7   2         10,080      -1.3937   HNNIAHNPUSROUPPARSRIISHSTODOPAREHEONEALASSTH
  UU   7   3         30,240      -1.4013   MPRIAIDORLOAINDIAOEARLNIROPRTALLISALMSAULEOI
  UU   7   4        120,960      -1.3985   LRTLLDDBBINALBEURSUSCODIAINLRSETOSOEURIATDEE
  UU   7   5        604,800      -1.3810   CCIDCHTTATUSEFICSCHTSALSINOLLECOULDOTODANSND
  UU   7   6      3,628,800      -1.3718   RCCALEDSERRCROOROSCNESSNUNEMAALLTONAOLNDSITM
  UU   7   7     25,401,600      -1.3460   NNRYRHYOTTOORMINEBROEAABOOBEAONALMLEROYANOEB
  UA   2   2              4      -1.4627   UNOIUPRPREAPHOARIASHCEEEAAUINRISPHANSTNNYNTC
  UA   2   3             12      -1.4734   AIUCCUDDUTITHURCIDTWSTCENTACRNEHASACOPISASEP
  UA   2   4             48      -1.5207   TIDIDNNCCTEMTRSAADASMYMEAOTIMRSRCENOTMISEHTA
  UA   2   5            240      -1.4608   SDENCYCSERANDERANIRTINMSEPARMOISATATELLOMASS
  UA   2   6          1,440      -1.4457   ASDSONLLIHHIRTCHARTOAWLIOOSCCECACTLYOCORUDRA
  UA   2   7         10,080      -1.4095   IAWNONGTRNBOUTOISIKEUNUUETKRSOEMOSEDAPPMPPAI
  UA   3   2             12      -1.4658   BATHHIENTECEIGENTSTHHTCSAINACLOBONSAELSONTIE
  UA   3   3             36      -1.5300   EHISMHOHMCTIMCCEDTOONOCCEMSAEDTAHCDLAAAWLNLN
  UA   3   4            144      -1.4824   NRLABLICALICSNROTOAAUINEOFDDRTIRBIRSLCIIELPU
  UA   3   5            720      -1.4733   EROSSRYSSEDANMYUNOUNTRNICLYTACROYYONKLAMAAOO
  UA   3   6          4,320      -1.4359   DDDLECLHOCSAACIEOCISKINARTDEFORCANTTERSDAEAI
  UA   3   7         30,240      -1.3960   EBNDANITHHLTILNONLADEROCIAOCAOLDRABRARLLORDB
  UA   4   2             48      -1.4803   ASEONDDIDCBODICREPRRDIPSIOYCROOSSIDNCIDMESDB
  UA   4   3            144      -1.4691   SRNPOPFINATASPOREURRUNFIITSPIECALNLYRAORLOSE
  UA   4   4            576      -1.4627   UNOIUPRPREAPHOARIASHCEEEAAUINRISPHANSTNNYNTC
  UA   4   5          2,880      -1.4444   INOWNTOHSGAROOMTHEUGSOURTANAUOHDDNEGDEERINGS
  UA   4   6         17,280      -1.4184   BRBETLETOBCHBSHRUNNOACLBBMRSCBSABLISNISHDLCA
  UA   4   7        120,960      -1.3965   ADRESSLRSOISTATUSIONREPLTSATODOTOODINCEDSERA

... 91 further lines omitted

His own hint about dummy letters, page 111

every subset of one to four cells treated as nulls, 4,047 of them, each struck out and the remainder solved.

$ solver nulls sym 60

SYMBOLIC -- every occurrence of a chosen set of cells struck out
  4,047 subsets of size 1-4
    -1.2912   137 kept   nulls = 74,75,84,85    ENTETSASTSNIAOAANESINTRICORRAOASENGONIAR
    -1.3109   134 kept   nulls = 64,74,83,85    ARTLRLELITIESEETRATILABAAAYSBBESEAAARTMS
    -1.3120   135 kept   nulls = 72,75,81,83    ENASESDDSIATDIINTOIINEDNTSIRFORROADENCAI
    -1.3149   129 kept   nulls = 62,64,74,81    ETALLLAITISNTESTILERSEEEZNRRNEAEETCANTES
    -1.3149   135 kept   nulls = 64,74,81,84    SANEDADDENTINASTNDSHTSSSFIHHISESSANCEINS
    -1.3158   128 kept   nulls = 64,75,81,83    ONRDODDERSEENSIEENONSDEALIAAIRONFREINEAS
    -1.3164   137 kept   nulls = 64,72,75,85    AINANENOTOOITSEREEOOIASITNOLSDRLLEREAICO
    -1.3234   143 kept   nulls = 64,65,74,91    ETIOTRONINSRDRRITESINESEEEZDRDREOEETIMOD
    -1.3237   133 kept   nulls = 65,75,81,83    SAEOSOTTORENTRRANCRRASTANORUCCETSAPERCAR
    -1.3253   135 kept   nulls = 64,65,74,81    DSTEOSOOERTRANTSDATRODADDDBNNDEDDSTMENTD

BEST OVERALL
  -1.2912  137 letters kept  --  nulls = 74,75,84,85
    ENTETSASTSNIAOAANESINTRICORRAOASENGONIARASSONDEIEAADASONASIONAOOOKATTORSREPEETTTDSRFRIESANENSTACRESTITARDIINISEDEREIGDONNDDINNAIDENIASAEG
  -1.3109  134 letters kept  --  nulls = 64,74,83,85
    ARTLRLELITIESEETRATILABAAAYSBBESEAAARTMSTAEBEISTORREEOESATESTESSSWELLISIBBRXRRLLLOABAHBRETIRTLEYBRIILLEBOTRORBRAMOSTTOOTIATEOIRTAEAERM

... 11 further lines omitted

Double transposition, one key applied twice

43.9 million keys.

$ solver dbl same 2 11

DOUBLE TRANSPOSITION (same)  196 units, 18 distinct
reference: real English -0.74 (p05 -0.85), shuffled English -1.89
  w         keys  best/letter   plaintext
 10    3,628,800      -1.3573   ESEEUUCAADEALALLOSUEOSUCCRESPEARELECLATIEFIRAUTIADNO
 11   39,916,800      -1.3451   HSESSDSEWHODONNSLARDARHEIRCALSUTDHTTSORAFUNITEITUTNC

Irregular columnar — the short cells in the wrong columns

the commonest slip when doing this by hand on squared paper.

$ solver irr 2 13 60

IRREGULAR COLUMNAR (short cells put in the wrong columns)
IRREGULAR COLUMNAR  -- the short cells put in the wrong columns
196 units, 18 distinct.  reference: real English -0.74, shuffled -1.89
  w  per letter   plaintext
  2     -1.4510   ASUNDMRMMIUOMREINTEEMRSTRUIVEUSUSRDMIRLMNSOMNCNASESTDAUBETAL
  3     -1.4762   TOIREBSTERBRSEARSBRAAUOSEHOMLSBBANSDBTROTTOASMNDORDSDEUATION
  4     -1.4927   ATTESEANMEMOMUSTDNLMIOCNTHAMDTRULARSUITUTOOMLERANAUTJRNDNSCU
  5     -1.4653   TEEADRESANCHDCLEIOASLYRLCYYSISEAREYWILDSYAAANNELLESORNULETIC
  6     -1.4247   IULAIDULATENUSELDODBNFANMTUREONLAMONDLUEUNBLOEIMOVIRVENMORBR
  7     -1.4801   COTDFUSTNFFFCTECESOEIAEORBEESTBROURINFBBUBCIBINITEASOBENODAN
  8     -1.3946   NDRLDONSNORDERTUSTABBTONTSOEBALMONLUCTBUFACRIETALONDLEBTDCOA
  9     -1.3951   SABSTUCUSSONOLLESRNEACOPRIANCALELESIOTEOFLRTOLOORLEEEERSAFFF
 10     -1.3663   CNRDOCENOTELEOOUFERSURESOBITSOUBBEFOREACDRENTLLEUNTILBIIDCRE
 11     -1.3823   DAISTIANSAWSECODEBNWIONRILOQDLWERDODEANOEUNLICINATICOURYWORA
 12     -1.3352   ILUNEUAUATIOUSEAPOSEAINENCOURTONPPICEATLACINSINFLYSCOENTOPUT
 13     -1.3790   LOLUSMESCASTSCDDURCOHRNUMATITDDUECLELAMRENTILSORGEISDOSLNLID

w=12  -1.3352  columns [9,10,8,2,5,1,0,6,3,4,7,11]
  ILUNEUAUATIOUSEAPOSEAINENCOURTONPPICEATLACINSINFLYSCOENTOPUTFFOAERSRYINSURPAPENIIIFOCONACEPTURACCOEGRUELROPAIFGROUPPOFLEOFLLIONIASAPCCSLESULUCHAPOPERPISCSLUSITRRATMEECIFTTERCPSLESESANABOUSEFPSCITY
w=10  -1.3663  columns [5,8,4,9,2,6,7,1,0,3]

... 1 further lines omitted

Real words, dates and phrases as keys

6,616 candidates from the book's own vocabulary, every 1939 date, the chapter titles, and the challenge sentence with its fourteen initials — each read four ways.

$ solver words words.txt 40

WORD-KEY SWEEP  6,535 candidate keys x 4 readings = 26,140 trials
reference: real English -0.74 (p05 -0.85), shuffled English -1.89
 per letter  key                    reading        plaintext
    -1.4221  REES                   units, apply   RRTHANSELDWIORSSIONDMEDICLHURLEFTHLRLLSAMDNMHD
    -1.4253  NOLOGIST               units, undo    DMILIMMHNEAISMWHHWIGNNETSWILASLNTROTWOHASDSSSI
    -1.4350  DIVIDED                units, undo    NOUSATROOTONNIEREALETRGEMEDEGRUMMANOGUGGLIGILL
    -1.4364  POWERFUL               units, undo    RDLSFRIIELPOSLRSNPPLYONSNOTIFAEAMTLNTSFODOIOOT
    -1.4381  GOVERN                 units, undo    UCRNEDNETTLICUSLDARUNITISDPULANOBTAINIOUUINDLA
    -1.4381  NOTION                 units, undo    UCRNEDNETTLICUSLDARUNITISDPULANOBTAINIOUUINDLA
    -1.4388  INSTRUCTIVE            units, apply   LTNEEDINBOISALRTCALBOUTARADUCANDRTSEDALUKOSNAR
    -1.4390  SEEMED                 units, undo    CLORRTIULOOINTASUSTRELUABCAILUMNESDIDTAEAUSTAU
    -1.4406  MATHEMATICS            units, undo    POINIDUORAUNIGNSARSTRUASITYREESOLINASNITRNORFL
    -1.4419  ANNOUNCEMENTS          units, apply   ERDELAODINBRITUPNSRATITWOMLNODALANTDIEBCENAMIL
    -1.4430  ARTISTS                units, undo    ANDTRUSSISAARSORTBOONNOLOEOFFALLTUNSIFFBUFFBBA
    -1.4456  DMMZ                   units, apply   ISARBABOUTITIORITOREADORDSRRERCIENOTUBCREECCRA
PHASE2 DONE

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