“F2.2: nulls placed by any rule, which for a repeating or progressive key act only through the number of nulls between the two known runs (0-29): exact”
F2.2. Rather than list rules (a null after every X, after each known word, before each, doubled letters), note what any rule does to a repeating key: the known runs stay whole (the carved runs are contiguous), nulls before the first run shift both runs alike and nulls after the second shift neither, and a repeating key's consistency depends only on the distance between known places. So every rule acts through one number: how many nulls fall between place 35 and place 63, d = 0-29. The same holds for a progressive key (a constant step per letter). All d are tested: periods 1-26, steps 0-25, 12 table rules; K4 against 20 shuffled copies. The named rules are listed with their d.
Perhaps some letters are fillers placed by a rule, say one after every X. However the rule goes, a repeating secret wordthe secret word The word or string a cipher needs besides the method. only notices how many fillers sit between EASTNORTHEAST and BERLINCLOCK, because only the distance between 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. matters to it. That number is 0 to 29, so we can try them all, and every rule at once.
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
Fillers placed by a rule (one after every X, one after each known word) would shift the known words. To a repeating or stepping key only the distance between the known letters matters, so every rule comes down to how many fillers fall between EASTNORTHEAST and BERLINCLOCK.
the check
Every count of 0 to 29 fillers, every key length 1-26, a repeating key or one that steps by a constant, on 12 table rules; K4 and 20 scrambled copies.
the bound
At no count does K4 fit more settings than the copies; overall it fits the fewest. F2.2 closed for keys of this kind.
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.
Suppose 3 fillers sit somewhere between EASTNORTHEAST and BERLINCLOCK.
In the message, BERLINCLOCK then starts at place 61 instead of 64; EASTNORTHEAST stays at 22.
For a secret word of length 7, places 22 and 64 shared a slot before; now 22 and 61 do not, and other pairs do.
Check every pair that shares a slot, for every length, rule and number of fillers 0-29.
Do the same on 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.
message places of the known letters with d nulls between the runs
d = 0: EASTNORTHEAST at 22-34, BERLINCLOCK at 64-74
d = 1: EASTNORTHEAST at 22-34, BERLINCLOCK at 63-73
d = 3: EASTNORTHEAST at 22-34, BERLINCLOCK at 61-71
d = 10: EASTNORTHEAST at 22-34, BERLINCLOCK at 54-64
5
Hypothesis, for a cryptanalyst
Family, key space, the constraint under test, and the clues it reads.
Scheidt: 'I masked the English language' (C2); nulls placed by a rule are a hand masking device (F2). Model: the plaintext with nulls is enciphered with key value k_j = w[j mod L] + s j at its own place j (s = 0 repeating, s = 1-25 progressive), 12 rules; the carved text is that. The known places after the gap move by -d in the message. Consistency needs every slot of w to agree. Statistic: live (d, rule, s, L) cells with L <= 26, K4 against 20 shuffled copies; the smallest live L per d.
6
Prediction
Written before the run; the result decides it.
Live cells with key length up to 26 at the shuffled copies' rate for every gap; no gap gives K4 a short key the copies lack. Zero candidates.
7
Method
For d = 0-29: the 24 known letters' message places (the second run moved d to the left).
For each text, rule, step s (0-25) and key length L (1-26): forced key values minus s times place; slots agree?
Count live cells per d; smallest live L per d at s = 0.
K4 against 20 shuffled copies; list the named rules with their d.
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
live cells over all gaps: K4 3840 (copies 3840-3970); gaps where K4 is above every copy: []; smallest repeating key on K4 per gap: [None, 26, 26, 25, 25, 24, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 26, 25, 24]
What was searched, as the harness recorded it.
family
nulls by any rule, through the gap d between the runs; repeating (s = 0) and progressive (s = 1-25) keys of length 1-26, 12 table rules, exact