A Vigenère message with a repeating key uses different Caesar shifts at different positions. If the key period is L, letters L positions apart use the same key position. Separating those positions into columns can expose the count patterns hidden in the mixed ciphertext. This guide concerns repeating-key A–Z Vigenère, not autokey, running-key or an arbitrary unknown cipher.
Split the letter stream into candidate columns
First remove spaces, punctuation and every non-A–Z character. Number the remaining letters from 1. For candidate period 3, column 1 contains positions 1, 4, 7 and so on; column 2 contains 2, 5, 8; column 3 contains 3, 6, 9. The columns are interleaved subsequences, not three consecutive chunks.
A known key to check the grouping
ATTACKATDAWNVigenère key LEMON; A = 0LXFOPVEFRNHR| Candidate period 5 | Ciphertext positions | Column text |
|---|---|---|
| 1 | 1, 6, 11 | LVH |
| 2 | 2, 7, 12 | XER |
| 3 | 3, 8 | FF |
| 4 | 4, 9 | OR |
| 5 | 5, 10 | PN |
Here the key is known and its period is 5. The table is useful for checking indexing, but these tiny columns are much too short to establish the key length statistically. For instance, FF has raw IC 1 solely because its two letters match. That is not strong evidence about English.
Calculate an IC for each column
For a column with N letters, compute Σ n(n − 1) ÷ N(N − 1), using each A–Z count n. The analyzer uses this raw value without a factor of 26. If a column has fewer than two letters, its IC is undefined. To avoid averaging undefined values, the workbench lists only periods up to min(16, floor(total letters ÷ 2)).
The displayed mean is the arithmetic mean of the individual column ICs, giving each column equal weight. A tool that pools all matching pairs or multiplies IC by 26 may display a different number. Read the scale and averaging convention before comparing results. Column sizes are shown alongside the mean so a large value from very little text remains visible.
Run a controlled comparison
- Open the analyzer and select Vigenère · LEMON. This loads an original English practice paragraph encoded with the known key LEMON.
- Expand Vigenère period comparison. Compare period 1 with period 5 and inspect the individual column values and sizes.
- Compare period 10 as well. A multiple of the true period can preserve single-shift columns too; the largest visible number is not automatically the shortest key period.
- Replace the sample with a longer message you encoded yourself using a different repeating key. Keep the key private from a partner until they have recorded their hypothesis.
- After choosing a plausible period, investigate shifts within each column or use the known key in the Vigenère tool to validate the complete message. The analyzer does not recover a key automatically.
Handle multiples, short text and repeated keys
| Observation | Interpretation to test |
|---|---|
| Several related peaks | Try a shorter common period and its multiples; compare more evidence. |
| Very high IC in tiny columns | A few repeated letters can dominate; collect more text if possible. |
| Keyword ABCABC | Its spelling length is 6, but its effective repeating period is 3. |
| No clear peak from 1–16 | The key may be longer, the sample too short or the assumed method wrong. |
| A familiar repeated fragment | It may reflect repeated plaintext aligned with the key, or happen by chance. |
Repeated-fragment distances provide a complementary test, often called Kasiski examination. This workbench counts pairs and triples but does not compute distance factors or perform that examination for you. A full solution must explain the plaintext, key, alphabet and position convention consistently. Statistical patterns are a guide to that work, not a certificate that the message is solved.