“The text as its own key: the ciphertext under every index rule, and the message keyed by itself backwards”
Autokey generalised. The key letter for position i is the ciphertext letter at a i + b mod 97 for every a and b, which includes every lag and every mirror of the ciphertext; or the plaintext letter at o - i mod 97, the message read backwards from any point.
An 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. uses the text itself as the secret wordthe secret word The word or string a cipher needs besides the method., a fixed distance backthe lag In an autokey cipher, how far back the key letter sits from the letter being enciphered.. We widen that: the key for each letter may be the carved letter at any fixed stride and start, forwards or backwardsa mirror Reading or writing the text from the end to the start., or the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. letter the same distance from the other end. Because the carved lettersthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page. are all known, the first kind is checked at every known letter at once. The second kind pairs the two known words with each other in the mirror, which gives a direct check too.
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 rule
The key for place i is the carved letter at place a times i plus b, wrapping round 97. That covers every lag (the letter before, the one 10 back) and every mirror of the copper.
the check
Each known letter, with its key, predicts its carved letter. Over 223,488 rules and 24 ways of using the table, the best still misses 6 of 24.
the mirror
The message read backwards from a centre was tried as its own key too: the chain of forced letters breaks under every way of using the table.
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.
Rule: stride 3, start 5. The key for position 1 is the carved letter at 5, for position 2 at 8, and so on, wrapping past 97.
Position 22 (E) gets the carved letter at 5 + 3 x 21 = 68, T.
On the sculpture's table with Vigenere, E under T gives some letter; compare with the carved F at 22.
Do this for all 24 known letters; count the misses; any miss kills the rule.
Mirror: with centre 97, position 22 is keyed by position 75, which is not known, but position 24 is keyed by 73, the C of CLOCK, which is known: S under C must give the carved R.
Eleven such pairs decide the mirror at once.
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.
ciphertext self-key, stride 3, start 5, KRYPTOS alphabet throughout, Vigenere
pos plain key pos key E+key carved match
22 E 69 T I F no
23 A 72 F N L no
24 S 75 W P R no
64 B 1 O G N no
65 E 4 R F Y no
mirror key, centre 97 (position i keyed by position 98-i): position 24 (S) is keyed by 74 (K), 25 (T) by 73 (C), ... 34 (T) by 64 (B)
chain under kry/kry/kry Vigenere: breaks after 24 letters
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Sanborn's mirrors and 'spatial systems' (C3) and the NSA's autokey guess (C11a) meet in self-keyed systems. Ciphertext self-key: c[i] = E(p[i], c[(a i + b) mod 97]); since every key letter is a carved letter, all 24 cribs are exact checks for each (a, b) and convention, 9,312 rules x 24 conventions, and a survivor decrypts the whole text at once. Plaintext mirror key: c[i] = E(p[i], p[(o - i) mod 97]) for every o; a crib forces its partner's plaintext letter and the chain closes as in 0012, with up to eleven exact checks where EASTNORTHEAST and BERLINCLOCK mirror onto each other. Survivors with 60 or more forced letters are scored as English against ten shuffled controls; fully forced texts are submitted. Bounds: complete for these rules and 24 conventions.
6
Prediction
Written before the run; the result decides it.
No ciphertext rule passes all 24 checks; the best passes 5 or 6. No mirror centre keeps the chain consistent beyond chance, and the large closures read as noise. Zero candidates pass.
7
Method
For each (a, b) with a in 1-96 and b in 0-96 and each convention, encipher each known letter with the carved letter at a i + b and count mismatches.
Decrypt any zero-mismatch rule and submit.
For each mirror centre o and convention, chain forced plaintext letters from the cribs through the mirror; reject on conflict.
Score closures of 60 or more letters as English; repeat on ten shuffles; submit fully forced texts.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.
0candidates returned
0passed every gate
0/24known letters, best
–lowest loss
nonechampion before
Ciphertext self-key: 223488 rules, best 6 mismatches, 0 survivors. Mirror key: 0 consistent (centre, convention) pairs, 0 fully forced; best closure None vs shuffled [].
What was searched, as the harness recorded it.
family
self-referential keys: ciphertext at a i + b, plaintext at o - i