Comparison of sequence repetition rates
This is a comparison of repeated sequences in both the 408 and 340 ciphers.
Note: I am using the Webtoy's transcription scheme.
These sequences are derived from reading the cipher as normal text (from left to right, top to bottom).
Digrams
| Repeated digrams in the 408 | Total repeated digrams | Repeated digrams in the 340 | Total repeated digrams |
|---|---|---|---|
| #B (6), q_ (4), qE (3), VW (3), OR (3), LM (3), BP (3), A9 (3), 9% (3), 9# (3), r\ (2), r9 (2), qW (2), qG (2), eG (2), cZ (2), c+ (2), _T (2), ^R (2), Xq (2), Wq (2), WV (2), WI (2), VE (2), UI (2), Tt (2), TY (2), S) (2), RU (2), PO (2), P# (2), L( (2), Ik (2), I( (2), HM (2), GY (2), EH (2), DR (2), BV (2), B% (2), AP (2), @X (2), 7L (2), 75 (2), 6q (2), /9 (2), +q (2), (S (2), %% (2) | 112 (49 unique digrams) | M+ (3), G2 (3), FB (3), ++ (3), p7 (2), UZ (2), Op (2), O+ (2), Np (2), I5 (2), Fl (2), By (2), Bc (2), 8R (2), 5F (2), +R (2), +& (2), )L (2), () (2), (# (2), #O (2) | 46 (21 unique digrams) |
Trigrams
| Repeated trigrams in the 408 | Total repeated trigrams | Repeated trigrams in the 340 | Total repeated trigrams |
|---|---|---|---|
| 9#B (3), qEH (2), eGY (2), _TY (2), UIk (2), POR (2), P#B (2), EHM (2), #BV (2), #BP (2) | 21 (10 unique trigrams) | I5F (2), FBc (2) | 7 (2 unique trigrams) |
4-grams
| Repeated 4-grams in the 408 | Total repeated 4-grams | Repeated 4-grams in the 340 | Total repeated 4-grams |
|---|---|---|---|
| qEHM (2), 9#BP (2) | 4 (2 unique 4-grams) | None | 0 (0 unique 4-grams) |
No repeats exist in either cipher for n-grams where n is greater than 4.
N-grams, in multiple rotations and mirrored arrangements
This n-gram analysis was performed upon various rotations. First, the cipher is rotated 0 and 90 degrees clockwise. Each resulting ciphertext's repeated n-grams are tallied. For the second part of the analysis, the cipher is first flipped horizontally, and then rotated 0 and 90 degrees clockwise. The resulting ciphertext's repeated n-grams are again tallied.
Rotations to 180 and 270 degrees are excluded for brevity, because the repeated n-gram counts are identical to the 0 and 90 degree cases, respectively.
Maximum non-zero repeated n-gram counts are in boldface for each combination of cipher and value of N.
| N | Flip/Rotation | Total repeated n-grams in the 408 | Total unique repeated n-grams in the 408 | % of ciphertext covered by repeats | Total repeated n-grams in the 340 | Total unique repeated n-grams in the 340 | % of ciphertext covered by repeats |
|---|---|---|---|---|---|---|---|
| 2 | No/0 | 112 | 49 | 27% | 46 | 21 | 14% |
| 2 | No/90 | 34 | 17 | 8% | 40 | 17 | 12% |
| 2 | Yes/0 | 106 | 47 | 26% | 54 | 25 | 16% |
| 2 | Yes/90 | 42 | 20 | 10% | 41 | 18 | 12% |
| 3 | No/0 | 21 | 10 | 5% | 4 | 2 | 1% |
| 3 | No/90 | 0 | 0 | 0% | 0 | 0 | 0% |
| 3 | Yes/0 | 20 | 10 | 5% | 4 | 2 | 1% |
| 3 | Yes/90 | 0 | 0 | 0% | 2 | 1 | 1% |
| 4 | No/0 | 4 | 2 | 1% | 0 | 0 | 0% |
| 4 | No/90 | 0 | 0 | 0% | 0 | 0 | 0% |
| 4 | Yes/0 | 2 | 1 | 0% | 0 | 0 | 0% |
| 4 | Yes/90 | 0 | 0 | 0% | 0 | 0 | 0% |
Observations:
- The maximum numbers of repeated digrams and trigrams occur for the original 408 cipher, when it is unaltered by flips and rotations.
- However, the maximum number of repeated digrams occurs for the 340 cipher when it is flipped horizontally.
- Also, the 340 cipher's repeated trigram count is unchanged by the horizontal flip.
Remaining questions:
- What is the significance of the increase in the maximum number of repeated digrams when the 340 cipher is flipped horizontally?
- Experiment: Using the known 408 key, generate random encipherments to fill the 408's cipher block with encipherments of random sentences. Then, count the number of times that the encipherment of a random sentence results in ciphertext arrangements that produce maximum repeated digram counts when the ciphertext is rotated and/or flipped.
