“The self-feeding autokey again, allowing one carved letter to be wrong, missing or extra”
Experiment 2 tested the self-feeding autokey on the copper exactly as carved, and experiment 62 found it is the only recipe that makes the width-21 repeats. K2 has a known carving error. Here one carved letter may be wrong (any place, any other letter), missing, or extra, at every lag, with or without a constant shift.
The 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. that feeds on earlier carved letters is the only recipe we have found that leaves the width-21 mark, yet experiment 2 showed it cannot produce the known lettersthe known letters Sanborn has confirmed that positions 22 to 34 of the message read EASTNORTHEAST and positions 64 to 74 read BERLINCLOCK. from the copper as carved. The second message on the sculpture has a carving mistake, so we allow one mistake here too: one letter wrong, one missing or one extra, anywhere, at every distance back. Scrambled coppers given the same allowance show how many fits luck gives.
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
If Sanborn miscarved one letter, a cipher could look dead when it is not. A ciphertext autokey with a constant shift is the simplest cipher that makes the width-21 repeats.
the residuals
At distance 21 the residuals at the 24 known places should all be equal; the commonest value, L, turns up only 2 times, so more than two would have to change.
the bound
Every distance, all 32 ways of using the table, every carved letter changed, deleted or doubled: nothing passes three checks, and distance 21 has no survivor at all.
2
Best candidate against the known letters
This experiment produced no candidate: the search ruled everything out before a full text was built. Its product is the bounded negative in section 7.
3
Walkthrough, by hand
Redo the method on a few letters with pencil and paper.
Take lag 21, the sculpture's alphabet KRYPTOSABCDEFGHIJLMNQUVWXZ counted from K = 0, Vigenere.
Place 22: carved F (12) minus known E (11) is 1; the carved letter 21 back is O (5); the residual is 1 - 5 = -4, which is 22.
Place 23: L (17) minus A (7) is 10; 21 back is B (8); residual 2.
Place 24: R (1) minus S (6) is 21; 21 back is K (0); residual 21.
The plain autokey needs every residual to be the same constant; already three differ.
One wrong carved letter can change at most two residuals, its own and the one 21 places later, so if more than two residuals disagree with the rest, no single mistake rescues this lag.
the worksheet: the first steps by hand, on squared paper
4
Worked example, generated
The same steps run by the code on the real letters.
lag 21, sculpture's alphabet throughout, Vigenere
place known carved 21 back residual
22 E F O 22
23 A L B 2
24 S R K 21
25 T V R 17
26 N Q U 6
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Family 1 re-entered with a stated reason: ciphertext autokey is the only generator in 0062 that reproduces the width-21 repeats (lag 21, 5.4% of samples against 0.2%), and 0002, 0063 and 0064 tested it only on the exact copper. Sanborn's K2 has a confirmed carving omission (C14 in 02-sanborn-said.md; Kryptos Group 2006, sources/kryptos-group-2006-corrected-k2.txt), and C17/C18 allow a working text of 98. Construction: T[i] = s*A(c[i-L]) + k0, L = 1..96, k0 any constant (k0 = 0 is the plain autokey), plain, cipher and key alphabets standard or KRYPTOS, Vigenere or Beaufort, s = +1 or -1 (32 classes). Variants of the copper: one letter replaced by any other (97 x 25), one deleted (97), one unknown inserted (98). A substitution at place j can only touch the equation of the crib at j and of the crib at j + L, so substitutions are decided exactly by asking whether all other residuals agree and the touched ones can be met by one letter; deletions and insertions are recomputed in full. Survivors tallied by redundant checks against ten shuffled coppers. Clue entries: C11a ('auto-key'), C17(b), C18(b).
6
Prediction
Written before the run; the result decides it.
No lag survives with three or more redundant checks under any one-letter variant and class, including lag 21. Survivor counts at one and two checks match the ten shuffled coppers. Zero candidates pass.
7
Method
For each lag and class, compute the residual at each known place past the lag: the total key minus the value of the carved letter that far back.
Exact copper: all residuals must agree.
One wrong letter at place j: all residuals not touching j must agree, and the one or two touched must be met by a single replacement letter.
One letter missing or extra: shift the copper and recompute.
Tally survivors by redundant checks and compare with ten shuffled coppers.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.