“F1.7: ciphertext and plaintext autokey on one unknown alphabet (both sides, any of 26! orders), every lag, three forms, decided exactly”
F1.7, no move. Autokey was tested on the standard, KRYPTOS and 1,092 keyword tables (0002, 0025, 0064, 0071, 0072) but never on a free alphabet: the NSA's 1992 guess (C11a) on K1 and K2's system. With one unknown alphabet x on both sides, each known letter past the primer gives an equation in alphabet places only: ciphertext autokey x(c_i) = x(p_i) + x(c_{i-L}) (and the Beaufort and variant forms); plaintext autokey the same with the message letter L back, usable where both letters are known (lags 1-12 and 30-52). Decided exactly by a propagation search over the 26 places (one-to-one), every lag 1-96, ten scrambled coppers. The move-first version is left for a later run (27,852 moves x 96 lags x 3 forms x 11 texts, about 90 million searches).
revertedstatus
a new rootparents
2 mintime, all phases
0candidates
0/24known letters
unclocked
1
The experiment method
What the method does with the 24 known letters.
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 messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. (or the scrambled textthe carved letters The 97 letters cut into the copper at the CIA, shown at the top of every experiment page.) becomes its own key, a fixed number of letters back. We had only tried it with the sculpture's alphabets and alphabets built from words. Here the alphabet can be in any order at all. 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. then give equations about the alphabet alone, and a search decides exactly, for every distance back, whether any alphabet satisfies them, on the carved text and on scrambled copies.
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
The NSA in 1992 guessed plaintext autokey on K1 and K2's system. Autokey had only been tried with the sculpture's alphabets and word alphabets; here the alphabet may be in any order.
the check
Each known letter past the primer gives an equation in the alphabet's places alone; a search over the 26 places decides every lag exactly, for K4 and ten scrambled copies.
the bound
K4 fits as many lags as the copies in every kind and form, and has 4 rare fits against up to 27 for a copy. Dead lags closed; fitting ones would need the English decider, about an hour each.
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.
Ciphertext autokey at lag 8: the key for place i is the carved letter at place i - 8.
At known place 30 (H under N), the key is the carved letter at 22, F: place(N) = place(H) + place(F) in the unknown alphabet.
Each known place past the primer gives one such equation; 24 equations in 26 unknown places.
Search for one alphabet order that satisfies all of them, filling places one at a time and following each equation that has a single unknown left.
Repeat for every lag, the three ways of using the table, plaintext autokey, and scrambled copies.
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 autokey, lag 8, added form, one unknown alphabet: one equation per known place past the primer
place 22: place(F) = place(E) + place(S) (key: carved letter at 14)
place 23: place(L) = place(A) + place(O) (key: carved letter at 15)
place 24: place(R) = place(S) + place(L) (key: carved letter at 16)
place 25: place(V) = place(T) + place(I) (key: carved letter at 17)
place 26: place(Q) = place(N) + place(F) (key: carved letter at 18)
place 27: place(Q) = place(O) + place(B) (key: carved letter at 19)
place 28: place(P) = place(R) + place(B) (key: carved letter at 20)
place 29: place(R) = place(T) + place(W) (key: carved letter at 21)
place 30: place(N) = place(H) + place(F) (key: carved letter at 22)
place 31: place(G) = place(E) + place(L) (key: carved letter at 23)
...
24 equations in the unknown places; solved exactly
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
C11a (NSA 1992, knowledge/sources/nsa-foia-1992-2014-blackvault-compilation.txt: 'plain-text auto-key... if a high-frequency letter is assigned 0'; NSA 2007 summary, nsa-2014-summary-of-previous-work.txt: plaintext and ciphertext autokey tested), C27(c) (a 'slightly different' tableau: any alphabet), C1(b). Model: x a bijection letters -> Z26; forms V: x(c) = x(p) + x(k), B: x(c) = x(k) - x(p), R: x(c) = x(p) - x(k); key letter k_i = c_{i-L} (ciphertext autokey, primer free for i <= L) or p_{i-L} (plaintext autokey). Solver: depth-first over places with propagation of every equation left with one open variable, translation fixed where the equations allow, node limit 200,000 (undecided counted); checked on planted autokey texts under random alphabets before K4. Statistic fixed before the run: per (kind, form, lag) fit or not; a K4 fit counts as rare where at most 1 of 10 coppers fit; K4's rare fits against each copper's rare fits against the rest.
6
Prediction
Written before the run; the result decides it.
Short lags die (many equations), long lags fit (few), K4 like the coppers: rare fits on K4 no more than the most a copper has against the rest. Fitting cells are left for an English decider (F1.5's design 2), which this run does not apply. Zero candidates.
7
Method
Check the solver: 6 planted autokey texts (random alphabet, random lag and form, both kinds) must fit.
For K4 and 10 coppers, each kind, form and lag: build the equations, decide.
Count fits per cell; mark rare fits; compare K4 with the coppers.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.