“Sanborn's matrix with a key letter per row: write the message in rows of width w, encipher each row with one letter of the key”
Not a transposition this time but a grid-shaped key: every letter in a row shares one key letter, and the rows take the key word's letters in turn. A column-shaped key is an ordinary periodic key and is dead; the row-shaped one was never swept.
Imagine writing the messagethe message The 97 letters of English that Jim Sanborn wrote and enciphered. in 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., say seven letters per line, and putting one letter of a secret word beside each line: every letter on that line is shifted by that one letter. The 13 known letters of EASTNORTHEAST fill a whole line or two, and every letter on a line must agree on the shift. We try every line width and every secret-word length, with every table the puzzle's words can builda reordered alphabet An alphabet that starts with a word, dropping repeated letters, followed by the rest of A to Z., and see whether 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. ever agree.
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 grid
Write the message in rows of a fixed width and give each row a single key letter, the rows cycling through a key word. Every letter in a row is shifted the same way.
the test
So all known letters in one row must force the same key letter. On the sculpture's table at width 7, every row that holds two known letters forces two or more.
the bound
Widths 2 to 48 under 63 alphabets and three ways of adding: 559,629 cases, and no width survives.
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.
Width 7: the rows are positions 1-7, 8-14, 15-21, 22-28, 29-35, and so on.
Row 22-28 holds E A S T N O R against the carved F L R V Q Q P.
On the plain alphabet with Vigenere, E to F is a shift of 1, A to L a shift of 11: the row cannot have one key letter, so width 7 is dead for this alphabet.
Width 20: rows 21-40 and 61-80; the first holds 13 cribs, the second 11; each row must agree internally.
Try every alphabet the puzzle's words build; a surviving width then gets every key length tried, which ties rows together.
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.
width 7, plain alphabet for both message and carved letters, Vigenere: shifts within row 22-28
pos plain carved shift
22 E F 1
23 A L 11
24 S R 25
25 T V 2
26 N Q 3
27 O Q 2
28 R P 24
one row, seven different shifts: width 7 cannot have one key letter per row under this alphabet.
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Sanborn's 'matrix code' is text written in rows and read another way (C1). A natural hand variant keeps the reading order and keys by row: position i takes key letter key[(i div w) mod L], so all w letters of a row share one key letter and rows cycle through the word. EASTNORTHEAST occupies 13 consecutive positions, so for w up to 13 at least one row holds several cribs that must force the same key letter, with chance 26 to the minus (k - 1) for k cribs in a row; the row-length L then adds collisions between rows. Swept: w = 2 to 48, L = 1 to 48, plain and cipher alphabets from the standard, KRYPTOS and keyword-mixed vocabulary alphabets (63), three modes; the key alphabet drops out of the consistency test. Survivors with a short L have their forced key read in the standard and KRYPTOS alphabets and matched against the vocabulary and K1-K3 windows. Bounds: complete for these widths, lengths and alphabets.
6
Prediction
Written before the run; the result decides it.
No width up to 13 survives under any alphabet pair, because a row full of cribs disagrees. Widths above 13 survive only where no row holds two cribs with different shifts, and then only for key lengths that avoid pairing the two crib runs; no forced key matches a word. Zero candidates pass.
7
Method
Build the alphabet pool.
For each plain alphabet, cipher alphabet and mode, compute the forced key index at each crib.
For each width w, group cribs by row and reject on disagreement within a row.
For surviving widths, for each key length L, group rows by L and reject on disagreement.
Read surviving forced keys in the standard and KRYPTOS alphabets; match against the vocabulary.
8
Result and bounds
The harness's record: candidates, gates, loss, and the negative result this experiment leaves behind.