“A1.4, part 1: ciphertext autokey on every keyword table tried so far, every lag, with up to two of the 24 known letters carved wrong or one skipped step in the chain; and the progressive key on the sculpture's tables with up to two slips; exact, judged against scrambled copies, with planted slipped messages”
A1.4 (Stage 2, step 2, issue #76), first part. 0002, 0025, 0064, 0071 and 0072 required every known letter past the primer to agree with ciphertext autokey (0064's fewest was 3 mismatches on K4, 2-3 on copies); 0011 required all 24 for the progressive key. Here: (a) ciphertext autokey on the union of their tables (about 550,000 table setups), every lag 1-96, with up to 2 failed checks (a slip at a known place stays put: the next key letter is the letter he carved); (b) one skipped or repeated step in the autokey chain (from some known place on the lag is one more or one less), at every place, as its own setting; (c) the progressive key (0011) on the 8 table classes, periods 1-52, steps 1-25, both forms, up to 2 slips. Compiled for (a) and (b). Readings of settings that keep at least 3 checks go to quadgrams and the blind judge with the copies'. Plants for each part in the same run.
In an autokey cipheran 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 keythe secret word The word or string a cipher needs besides the method. keeps growing out of the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. itself: after a few starting letters, each new key letter is a letter already enciphered. Done by hand, one slip is easy: a wrong letter at one place, or losing your place in 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. and carrying on one letter off. Earlier experiments threw away any setting that missed even one known letter. Here we allow two wrong letters, or one lost place, on the carving and on scrambled copiesa shuffled control The same experiment run on the carved letters shuffled into a random order., and we hide messages of our own made with such slipsa slip A mistake made while enciphering by hand: a wrong row or column of the table at one letter, so the carved letter is not the one the method gives there. to check they are found. The same for the progressive key, whose key word shifts one step further along 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. after every letter or every round.
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
An autokey grows its key from the text itself, so a hand slip is easy: a wrong letter, or losing one's place in the chain. Earlier tests threw away any setting that missed one known letter.
the check
Ciphertext autokey on every table tried so far (487,734 setups), every lag, up to 2 slips or one lost step; the progressive key on the sculpture's tables with up to 2 slips; K4 against 20 scrambled copies, readings judged blind, five planted slipped messages.
the bound
Nothing fits K4 below lag 68 (copies 67-69), where 6 or fewer checks are left; the progressive key nowhere below period 25. K4's best reading scores 4, the copies' 12; all five plants are found.
2
Experiment lineage
What this experiment was built on, from the lineage page: 5 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?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKHROPCPRIVOTNOUGOBBVCTOC
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 -6.01; English text scores -3.6
2.41
Key
1496 bits to write it down (key words are cheap, arbitrary letters 4.7 bits each); each 60 beyond 60 costs a point
23.94
Loss
of 240, the worst possible
26.35 11.0%
5
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Write K4 and, under each letter, the carved letter L places before it: that is the autokey's key.
At each of the 24 known places, look up on the table what the known letter and that key letter give.
Count the places where it is not the carved letter: up to 2 are allowed as slips.
For a lost place: from one known letter on, take the key from L + 1 (or L - 1) places back instead, and require every place to agree.
Read the message wherever the key is known, and do the same on scrambled copies of the carving.
For the progressive key, write the key word under the text, add d to every key letter's place on the table for every letter (or every round), and count the slips the same way.
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.
ciphertext autokey, lag 9, KRYPTOS table, Vigenere: the key for each known place is the carved letter 9 before it
place known key(carved L back) gives carved
22 E B N F x
23 A S G L x
24 S O E R x
25 T L U V x
64 B U P N x
65 E D U Y x
66 R I J P x
failed checks: 24 of 24 (2 allowed as slips)
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'; the NSA analyst 2007 tested both autokeys), C5(a) (a key word and a hand schedule), C27(a) (Sanborn's PALIMPCEST slip), Sanborn 2005 'Saying I was sloppy is a good way of saying it'. Ciphertext autokey: c_i = C[E(P(p_i), K(c_{i-L}))], P, C, K alphabets from 0025's 63 (standard, KRYPTOS, vocabulary keyword), 0064's K1-K3 and C13/C14 words, 0072's compass words (pairs of any two; key alphabet standard, KRYPTOS, plain or cipher), and 0071's 925 near-KRYPTOS alphabets (with themselves or the standard alphabet); Vigenere, Beaufort, variant. Every known place q > L is a check; a slip at a known place fails only its own check, because the following key letters are the carved ones. A skipped step: the key for every known place from the e-th on is the carved letter L + 1 (or L - 1) back. Progressive key: key value at place i = w[i mod P] + d i (per letter) or + d floor(i / P) (per repeat), 8 table classes (the key alphabet drops out; variant Beaufort is a negated step). Counted: settings with 0, 1, 2 failed checks per lag (per period and step), K4 against 20 copies. Slip cost: 9.3 bits for 1, 17.5 for 2; a skipped step about log2(24 x 2) = 5.6 bits. Where 2 or fewer checks would remain the known letters decide nothing and the cell is counted only.
8
Prediction
Written before the run; the result decides it.
Ciphertext autokey: at lags with 8 or more checks no setting with 2 slips or one skipped step on K4, at the copies' rate elsewhere; nothing judged above every copy. Progressive key: nothing below period 24 with 2 slips (as 0207 for the plain periodic key). All plants found. Zero candidates pass gate 4.
9
Method
Build the tables.
For each table setup and text: the key index each known place needs.
For each lag: compare with the key letter the carved text offers L back, count failures, keep up to 2; for each skipped step (lag L before the e-th known place, L + 1 or L - 1 from it), keep only exact fits.
Progressive key: per class, period, step and form, the forced base values per slot; enumerate settings with up to 2 slips.
Count by lag and slips, K4 against 20 copies.
Readings of settings keeping 3 or more checks: each text's best by quadgrams and every one at or above -5.0 go to the judge, all texts in one call.
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
10.7%lowest loss
nonechampion before
All 10 candidates, lowest loss first.
1failed at baseline24/24 known lettersloss 10.7%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKGJFRWMJVCTURRFLIEVETSAM
ciphertext autokey lag 71, BURIED/keyword|FIFTY/keyword|plain|varbeau, 0 slips at known places, skip (72, 72); free letters filled with A
2failed at baseline24/24 known lettersloss 10.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKHROPCPRIWOTNOUGOCBTCUPC
ciphertext autokey lag 69, LAYER/keyword|MADE/keyword|std|varbeau, 2 slips at known places, skip None; free letters filled with A
3failed at baseline24/24 known lettersloss 11.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKHROPCPRIVOTNOUGOBBVCTOC
ciphertext autokey lag 69, LAYER/keyword|AND/keyword|std|varbeau, 2 slips at known places, skip None; free letters filled with A
4failed at baseline24/24 known lettersloss 11.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKVHAMUDGSSEIEYPNGNXLYCHO
ciphertext autokey lag 70, INTERPRETATION/keyword|TREMBLING/keyword|kry|vig, 0 slips at known places, skip (22, 71); free letters filled with A
5failed at baseline24/24 known lettersloss 11.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKVHAMUDGSSEIEYPNGNXLYCHO
ciphertext autokey lag 70, INTERPRETATION/keyword|TREMBLING/keyword|kry|vig, 0 slips at known places, skip (23, 71); free letters filled with A
6failed at baseline24/24 known lettersloss 11.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKVHAMUDGSSEIEYPNGNXLYCHO
ciphertext autokey lag 70, INTERPRETATION/keyword|TREMBLING/keyword|kry|vig, 0 slips at known places, skip (24, 71); free letters filled with A
7failed at baseline24/24 known lettersloss 11.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKOQISSEYHKSOCKPDESPDPCWD
ciphertext autokey lag 70, ESCAPING/keyword|LIGHT/keyword|cipher|varbeau, 1 slips at known places, skip None; free letters filled with A
8failed at baseline24/24 known lettersloss 11.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKLDTSDUGHOTPPOFUVNTULGDK
ciphertext autokey lag 69, SOUTHBYWEST|OFFSET|kry|vig, 2 slips at known places, skip None; free letters filled with A
9failed at baseline24/24 known lettersloss 11.9%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKLDTSDUGHOTPPOFUVNTULGDK
ciphertext autokey lag 69, SOUTHWESTBYSOUTH|OFFSET|kry|vig, 2 slips at known places, skip None; free letters filled with A
10failed at baseline24/24 known lettersloss 12.0%
ECDMRIPFEIMEHNLSSTTRTVDOHW?AAAA
AAAAAAAAAAAAAAAAAEASTNORTHEASTA
AAAAAAAAAAAAAAAAAAAAAAAAAAAABER
LINCLOCKGABAWKSTAUSIAGTSCWZRTWL
ciphertext autokey lag 71, ABSENCE/keyword|FIVE/keyword|plain|varbeau, 0 slips at known places, skip (72, 72); free letters filled with A
487,734 autokey table setups; K4 shortest fitting lag with <= 2 slips 68, copies [67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 68, 68, 68, 68, 68, 68, 68, 68, 68, 69]; judge sent 56, K4 best 4, copies best 12; plants found [True, True, True, True, True]
What was searched, as the harness recorded it.
family
ciphertext autokey (union of 0025/0064/0071/0072 tables) and progressive key (0011), 0-2 known letters slipped, or one skipped step (A1.4)
ca table setups
487,734
ca lags
1-96
skip
lag L before the e-th known place, L+1 or L-1 from it, e = 2-24, exact fit
prog
8 table classes, periods 1-52, steps 1-25, per letter and per repeat