“A1.4, part 2: plaintext autokey on the sculpture's and the vocabulary's tables, lags 1-52, with up to two carved slips breaking the chain, or one lost step that runs on through it; exact, the readings judged against scrambled copies, with planted slipped messages”
A1.4 (Stage 2, step 2, issue #76), second part. 0003, 0012 and 0025 chained plaintext autokey from the known letters with no slip: lags 1-25 and 30-52 dead, 26-29 noise by quadgrams. In plaintext autokey a wrong carved letter does not change the message but breaks our derivation through it, so (a) every lag 1-52 is rerun allowing up to 2 breaks (slips anywhere in the chain, the known places included); (b) one lost step (from some place on, the key is the message letter L + 1 or L - 1 back), at every place, as its own setting: everything after it shifts; (c) at lags 26-29, where the known letters give 0-1 checks, every table's reading is scored and the best go to the blind judge, which reads past a slip that garbles the rest of a chain (bench class 'half'). 35,721 table setups (0025's), compiled; K4 against 20 scrambled copies; three planted messages.
revertedstatus
a new rootparents
10 mintime, all phases
10candidates
24/24known letters
1
The experiment method
What the method does with the 24 known letters.
In a plaintextthe message The 97 letters of English that Jim Sanborn wrote and enciphered.autokeyan autokey cipher A cipher that uses the message itself, or the scrambled text itself, as the secret word, each letter enciphered with the letter a fixed distance before it. the message is its own key: each letter is enciphered with the message letter L places before it. The known words then let us work out letters further along the message, one step at a time, like a chain. One wrongly carved letter breaks the chainthe chain In an autokey cipher each known letter reveals the letter one lag later and the letter one lag earlier; those reveal more, and so on. there, and a hand slip that loses one step shifts everything after it. Earlier experiments allowed neither. Here we allow two broken links, or one lost step anywhere, on the carving and on scrambled copiesa shuffled control The same experiment run on the carved letters shuffled into a random order., and a language model readsthe judge A language model that scores how much of a reading is English, from 0 to 100, allowing misspellings and X between sentences. what comes out, blind to which is which.
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
In a plaintext autokey the message keys itself, so the known words reach along chains of letters L apart. A wrongly carved letter breaks a chain; losing one's place shifts every letter after it.
the check
Every lag 1-52 on 35,343 tables, allowing 2 broken links anywhere or one lost step at any place; at lags 26-29 every table's reading scored; the best read blind by the judge with 20 scrambled copies', and three planted slipped messages.
the bound
Nothing fits K4 below lag 24 (copies from 17); K4's best reading scores 4, the copies' 12; the plants, one with a slip running on through its chain, are found.
2
Experiment lineage
What this experiment was built on, from the lineage page: 4 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?IIDP
VLMAAAAAAAAAAAAAAEASTNORTHEASTA
FURGVTAAAAAAAAAAAAAECAITMOFDBER
LINCLOCKAAAAAAAAAAAAAETAKTHIOXD
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
0 of 24, ten points each
0.00
English
the 73 free letters score -6.32; English text scores -3.6
2.72
Key
847 bits to write it down (key words are cheap, arbitrary letters 4.7 bits each); each 60 beyond 60 costs a point
13.12
Loss
of 240, the worst possible
15.84 6.6%
5
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Choose a lag, say 12, and a table.
Known place 22 (E) and place 34 (T) are 12 apart: the carved letter at 34 and E as its key must give T on the table.
Work along each chain of places 12 apart, from one known letter to the next, and mark the pairs that disagree.
Each disagreeing pair needs one carved slip somewhere between them; allow up to two.
For a lost step, from some place on use the letter 13 (or 11) back as the key instead, and require every pair to agree.
Read every letter a known letter reaches through its chain, and compare with scrambled copies.
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.
plaintext autokey, lag 12, KRYPTOS table, Vigenere: chains of places 12 apart, walked from one known letter to the next
22 E -> 34: the chain gives U, known T break needed
23 A -> 71: the chain gives P, known L break needed
24 S -> 72: the chain gives X, known O break needed
25 T -> 73: the chain gives H, known C break needed
26 N -> 74: the chain gives D, known K break needed
28 R -> 64: the chain gives B, known B
29 T -> 65: the chain gives H, known E break needed
30 H -> 66: the chain gives M, known R break needed
breaks needed at lag 12: 11 (2 allowed)
7
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
A1 (knowledge/12-assumptions.md); C11a (NSA 1992: 'plain-text auto-key (if a high-frequency letter is assigned 0)'; NSA 2007 tested it without cribs), C27(a), Sanborn 2005 'Saying I was sloppy'. Model: c_i = C[E(P(p_i), K(p_{i-L}))] after a primer of L letters; P, C from 0025's 63 alphabets (standard, KRYPTOS, vocabulary keyword), K standard, KRYPTOS or the plain alphabet; Vigenere, Beaufort, variant. Each equation links p_i and p_{i-L} by a bijection, so the message splits into L chains; two known letters in one chain must agree through every carved letter between them. A slip at place j cuts the chain at j: the least number of cuts is the number of disagreeing neighbouring known pairs, at most 2 here (17.5 bits to name). A lost step at j: p_i keyed by p_{i-L-1} or p_{i-L+1} from j on, which joins the chains differently (a forest; known letters in one tree must agree), j = 2-74, about 7 bits. Readings: every letter whose chain holds a known letter. Counted per lag, K4 against each copy; readings keeping 3 or more checks, and at 26-29 the best by quadgrams of every text, go to the judge in one call.
8
Prediction
Written before the run; the result decides it.
No lag below 26 fits K4 with 2 breaks or one lost step where it keeps 3 or more checks beyond the copies' rate; at 26-29 K4's best reading is judged inside the copies'. All three plants found. Zero candidates pass gate 4.
9
Method
For each table setup, lag and text, walk every chain between neighbouring known letters and count the pairs that disagree; keep up to
For each lost step (lag L before place j, L + 1 or L - 1 from it), walk each known letter to the root of its tree and require known letters sharing a root to agree.
At lags 26-29, derive every reading and score it by quadgrams in the same compiled pass.
Readings to quadgrams; each text's 5 best and every reading at or above -5.0 to the judge, all texts in one call.
Counts per lag, K4 against 20 copies; plants and their own copies through the same search.
10
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
10candidates returned
0passed every gate
24/24known letters, best
4.5%lowest loss
nonechampion before
All 10 candidates, lowest loss first.
1failed at baseline24/24 known lettersloss 4.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?PNYP
MCLAAIDGAKLANUMAAEASTNORTHEASTA
AISPRACRATALAEZAHOAYPUAAWCAABER
LINCLOCKAIJJJWIOFQMPSJAAUHIKORY
plaintext autokey lag 27, VIRTUALLYINVISIBLE/keyword|WEBSTER/keyword|plain|beau, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
2failed at baseline24/24 known lettersloss 4.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?BTUM
OPAHOMRAVJABAIAAAEASTNORTHEASTA
NISHDHADEEXAAADFEGOGAVGWBGCABER
LINCLOCKAAARCAMLOIYRJUSVAUIETHE
plaintext autokey lag 28, WALL/keyword|PALIMPSEST/keyword|std|varbeau, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
3failed at baseline24/24 known lettersloss 4.6%
ECDMRIPFEIMEHNLSSTTRTVDOHW?MWVT
ALAKJOVRJERINTAAAEASTNORTHEASTA
TFCKHUVHISAAAAAUEAOFWECTHLDABER
LINCLOCKAAAKSIUZFINHAGUYAWHEOFA
plaintext autokey lag 28, DIGETAL/keyword|WALL/keyword|std|varbeau, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
4failed at baseline24/24 known lettersloss 4.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?MBSR
FWAOWHNWIMIDERAAAEASTNORTHEASTA
VIJWTYVALYAAAAOBCCLTGKBCWOGABER
LINCLOCKAAASUNDLMLARPUNGABYACCV
plaintext autokey lag 28, ILLUSION/keyword|ABSCISSA/keyword|std|beau, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
5failed at baseline24/24 known lettersloss 4.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ROAN
OURMRJAOJOABAAAAAEASTNORTHEASTE
AJAMNYMTNZAAAAAWDESQARTAMWCABER
LINCLOCKAAAAATVJOFFIRIYBRIZHCFR
plaintext autokey lag 29, BERLINCLOCK/keyword|ALEXANDERPLATZ/keyword|std|beau, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
6failed at baseline24/24 known lettersloss 4.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?PSQL
WELANGNIETSTAAAAAEASTNORTHEASTO
FXINVXKIZRAAAAAAKRTUNMCSSGBZBER
LINCLOCKAAAAADBLYGARMYTLEACPUKE
plaintext autokey lag 29, HOWARDCARTER/keyword|LAYERTWO/keyword|plain|beau, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
7failed at baseline24/24 known lettersloss 4.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?STHA
SNALNGEJFADRAAAAAEASTNORTHEASTE
JJABLYDSMRAAAAAFDFIROINMRGOVBER
LINCLOCKAAAAAHGRTFEXWNVERZUVEMP
plaintext autokey lag 29, CARNARVON/keyword|SOMEWHERE/keyword|kry|vig, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
8failed at baseline24/24 known lettersloss 4.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?TPCM
YCIAKPKAWHEEAAAAAEASTNORTHEASTD
HRUPWBYBEKAAAAAPBDYGASOFTEANBER
LINCLOCKAAAAAVVOCZYBETUVLGRODPR
plaintext autokey lag 29, IQLUSION/keyword|WELTZEITUHR/keyword|kry|vig, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
9failed at baseline24/24 known lettersloss 5.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?TAOS
OMDDLOUFEILFAAAAAEASTNORTHEASTA
QGGIROLCAXAAAAAPFLCADCOLOBENBER
LINCLOCKAAAAASMVYONNACZSSAODFIR
plaintext autokey lag 29, WONDERFUL/keyword|SOUTH/keyword|kry|vig, bulk, cuts [], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
10failed at baseline24/24 known lettersloss 6.6%
ECDMRIPFEIMEHNLSSTTRTVDOHW?IIDP
VLMAAAAAAAAAAAAAAEASTNORTHEASTA
FURGVTAAAAAAAAAAAAAECAITMOFDBER
LINCLOCKAAAAAAAAAAAAAETAKTHIOXD
plaintext autokey lag 33, WORLDCLOCK/keyword|UNDERGROUND/keyword|plain|beau, chain, cuts [67], lost step None; unknown letters filled with A, every disagreeing carved letter named as a slip
35,343 tables x lags 1-52; K4 shortest lag with <= 2 breaks 24, lost step 24; copies [17, 17, 17, 17, 18, 18, 18, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24]; judge sent 194, K4 best 4, copies best 12; plants found [True, True, True]
What was searched, as the harness recorded it.
family
plaintext autokey on 0025's tables, lags 1-52, up to 2 chain breaks (slips) or one lost step (A1.4)
table setups
35,343
lags
1-52 (53-96 blocked by 0136's bound)
breaks
0-2 anywhere in a chain between neighbouring known letters (known places included)
lost step
lag L before place j, L+1 or L-1 from j on, j = 2-74; known letters in one tree must agree
bulk
lags 26-29 with no break: every table's reading scored by quadgrams; the top 20 and all at or above -5.0 per text to the judge