“A1.5: a move, then the table (and the reverse), over every dictionary-keyed columnar, Myszkowski, double columnar, rail fence, AMSCO and type-1 route, with a repeating key of length 1-26 on the sculpture's tables and up to two of the 24 known letters carved wrong; exact, judged against scrambled copies, with planted slipped messages”
A1.5 (Stage 2, step 2, issue #76). 0110-0114 and the type-1 library (0080-0129) required all 24 known letters to agree with one repeating key after or before the move (nothing below key length 21-22). k = 1 was run as 'one carved letter wrong' (0093); slipped columns are F6.21. Here k = 2: the union of 0110's keyword columnar, 0111's Myszkowski, 0112's double columnar, 0113's rail fence and redefence, 0114's AMSCO (all from the whole dictionary) and 0129's type-1 library, deduplicated by where the known letters land, both orders, 8 table classes, key lengths 1-26, compiled with an exact early exit; K4 against 20 scrambled copies; readings that keep 3 or more checks to quadgrams and the blind judge; three planted messages with two slips each.
Sanborn described writing the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. into a grida grid Writing the message into rows of some width and reading it out in another order, column by column for instance, which shuffles the letters without changing them., reading it out in another order, and then using 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. with a key wordthe secret word The word or string a cipher needs besides the method.. Experiments 110-114 tried every such grid keyed by any dictionary word, before and after the table, and found nothing with all 24 known letters right. If he slipped at two of those places, that test would have missed it. Here we allow two wrong, on the carving and on scrambled copiesa shuffled control The same experiment run on the carved letters shuffled into a random order., and hide three messages of our own made that way, 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. included, to check the search finds them.
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
Sanborn's 'matrix codes... then went back to this table': a grid move and a repeating key. Every keyword grid from the dictionary was tried before, and nothing kept all 24 known letters; two hand slips would have hidden it.
the check
Every route of experiments 110-114 and the type-1 library (1,847,590 distinct), both orders, the sculpture's 8 table classes, key lengths 1-26, up to 2 slips; K4 against 20 scrambled copies, the readings judged blind, three planted slipped messages.
the bound
With two slips the shortest key that fits K4 is 18 after the move and 16 before it (copies 16-18 and 16-17); K4 ahead of every copy in 1 cells (copies 0-3); K4's best reading scores 6, the copies' 12; the plants are found.
2
Experiment lineage
What this experiment was built on, from the lineage page: 6 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?UDYW
HEKOVYGWAKEKRAXHSEASTNORTHEASTE
VHWOODNSOMAMALKEYKWHENPUXQKQBER
LINCLOCKZOOZHTIKLPUBVIEQTUATMIQ
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 -6.94; English text scores -3.6
3.34
Key
795 bits to write it down (key words are cheap, arbitrary letters 4.7 bits each); each 60 beyond 60 costs a point
12.25
Loss
of 240, the worst possible
15.58 6.5%
5
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Write the message into a grid under a key word and read the columns out in the word's order.
Choose a key length, say 11, and a table; each known letter now sits at a new carved place, and its key letter is read off the table from the carved letter.
Known letters in the same slot of the key must give the same key letter.
Count how many would have to be slips; keep the setting if 2 or fewer.
Read the message back through the key and the grid, and do the same on scrambled copies of the carving.
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.
keyword columnar PYRAMID (move first), then the KRYPTOS table, key length 11: key letter forced at each known place
slot 0: 26N@45:S
slot 1: 33S@46:U 66R@79:Y 70C@24:S
slot 2: 73C@80:P
slot 3: 22E@59:M 25T@4:X 69N@37:E
slot 4: 29T@60:L 32A@5:O 65E@93:A
slot 5: 72O@94:V
slot 6: 24S@73:X 28R@18:L 68I@51:P
slot 7: 31E@74:P
slot 8: 27O@31:I
slot 9: 23A@87:T 34T@32:W 64B@65:U 67L@10:X
slot 10: 30H@88:H 71L@66:M 74K@11:V
slips needed: 13 (2 allowed)
7
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C1(a) (Sanborn, CNN 2005: 'I used a matrix code... double matrixes and triple matrixes... then went back to this table'), C11 ('the other 91 characters and their proper order'), A1 (knowledge/12-assumptions.md), C27(a). Model: a transposition w (message place i to carved place w(i)) and a periodic key k of length L on the table, plain and cipher alphabets standard or KRYPTOS, added or Beaufort form (8 classes; the key alphabet drops out). Order A, move then table: the key runs along the carved places, slot w(q) mod L; order B, table then move: slot q mod L, carved letter at w(q). Each known letter forces a key value in its slot; the least number of slips is 24 minus the sum over slots of the most common forced value's count, at most 2 here (17.5 bits to name). Cost estimated before the run: about 1.8 million route maps x 2 orders x 8 classes x 26 lengths per text, compiled. Statistic: per order and length, the number of (route, class) cells with 0, 1, 2 slips, K4 against each copy; the shortest length that fits; the judge's best on readings keeping 3 or more checks.
8
Prediction
Written before the run; the result decides it.
With two slips the shortest key length that fits K4 drops from 21-22 to about 17-19, as on the copies; K4 above every copy in no more (order, length) cells than a copy is above the rest; nothing judged above every copy. The three plants are found. Zero candidates pass gate 4.
9
Method
Build every route map of 0110-0114 and the type-1 library; keep one per distinct landing of the 24 known places.
Compiled: for each route, class, order and key length, add the known places one by one into their slots and count slips (a place whose forced value is not its slot's most common so far); stop at
Count cells by slips, K4 and 20 copies.
For cells keeping 3 or more checks, enumerate the key choices and read; each text's top 5 by quadgrams and every reading at or above -5.0 go to the judge 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
6.5%lowest loss
nonechampion before
All 10 candidates, lowest loss first.
1failed at baseline24/24 known lettersloss 6.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?HRGA
SSTPDNAEAEWADYMOVEASTNORTHEASTB
RBDIUAREDHEBAZKGCARSIUTOHEDXBER
LINCLOCKAFIFROVRXBPEHAVKSBLZDZR
0112 double columnar: IDIOPATHICAL inverse, order B, key length 24, std/kry/vig, slips [22, 72]; open slots filled with A
2failed at baseline24/24 known lettersloss 6.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?UDYW
HEKOVYGWAKEKRAXHSEASTNORTHEASTE
VHWOODNSOMAMALKEYKWHENPUXQKQBER
LINCLOCKZOOZHTIKLPUBVIEQTUATMIQ
0112 double columnar: TOSHNAIL inverse, order B, key length 24, kry/kry/beau, slips [74, 22]; open slots filled with A
3failed at baseline24/24 known lettersloss 6.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?TXAW
UAEZPUGAJTKPUUTREEASTNORTHEASTY
IQAMIRSPZVBRFWITHSITSCDQKEZIBER
LINCLOCKMWNSLOKIRHLYCOHALSHKENZ
0112 double columnar: AVICULTURE, order B, key length 24, std/std/beau, slips [22, 23]; open slots filled with A
4failed at baseline24/24 known lettersloss 6.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?UVYW
HEKOVYGWAKEKRAXHSEASTNORTHEASTE
VHWOODNSOMAMALFEYKWHENPUXQKQBER
LINCLOCKZOOZHTIKLPUBVIEQTUATMIQ
0112 double columnar: TOSHNAIL inverse, order B, key length 24, kry/kry/beau, slips [26, 22]; open slots filled with A
5failed at baseline24/24 known lettersloss 6.5%
ECDMRIPFEIMEHNLSSTTRTVDOHW?DBQI
PWPFOROCENOUTDSSSEASTNORTHEASTC
XIESKAOPCHMYSKESPCCOEXYDYEOBBER
LINCLOCKYDKFFVBSBUESABCYEHTWJDK
0113 rail fence: 19 rails offset 9 order (18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0), order A, key length 25, kry/kry/beau, slips [72, 66]; open slots filled with A
6failed at baseline24/24 known lettersloss 6.7%
ECDMRIPFEIMEHNLSSTTRTVDOHW?MXHU
CVUNYNFITQURESTSPEASTNORTHEASTI
HMBWILNGVBJIRGGFDAUGEFUFMPIDBER
LINCLOCKHOAPMALXCTWENXFBIVXZIIA
0114 AMSCO: UNMETHODIZED first 1, order A, key length 24, std/kry/vig, slips [28, 72]; open slots filled with A
7failed at baseline24/24 known lettersloss 6.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?HQMJ
MUHERSSGUNKSVSZJXEASTNORTHEASTW
PMIUDIOBVWQUXMLWEANDTJITYDYMBER
LINCLOCKLRJUUWINPFAWHBEWFYNBMOH
0112 double columnar: SELFHOOD, order A, key length 25, std/std/beau, slips [29, 67]; open slots filled with A
8failed at baseline24/24 known lettersloss 6.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?YUCZ
OFOTSFGWPJPERLCISEASTNORTHEASTI
GATCREPUAEFQSVCSEAGKNUZLDYKOBER
LINCLOCKKOFDIJRSFJSDSCQTXMHWNYA
0114 AMSCO: OVERIMITATION first 1, order A, key length 25, kry/kry/vig, slips [68, 67]; open slots filled with A
9failed at baseline24/24 known lettersloss 6.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?ZUCZ
OFOTSFGWKJPERLCISEASTNORTHEASTI
GATCREPUAEFQSVCSEAGKNUZLDYKOBER
LINCLOCKKOFDIJRSFJSDSCQTXMHWNYA
0114 AMSCO: OVERIMITATION first 1, order A, key length 25, kry/kry/vig, slips [31, 67]; open slots filled with A
10failed at baseline24/24 known lettersloss 6.8%
ECDMRIPFEIMEHNLSSTTRTVDOHW?JGBA
ARMEWAUQKDNKKALLZEASTNORTHEASTZ
QBWOSCTGARSPDUOPTUASBMCVDOQSBER
LINCLOCKPMOMUFGDZKGHWOPRPLBHAWS
0111 Myszkowski: SATURABILITY, order B, key length 24, kry/std/vig, slips [70, 72]; open slots filled with A
1,847,590 distinct landings; K4 shortest length with <= 2 slips A 18, B 16; K4 above every copy in 1 cells (copies 0-3); judge sent 195, K4 best 6, copies best 12; plants found [True, True, True]
What was searched, as the harness recorded it.
family
a move then the table and the reverse, 0110-0114 and the type-1 library, periodic key 1-26 on 8 table classes, 0-2 known letters slipped (A1.5)