> ## Documentation Index
> Fetch the complete documentation index at: https://docs.cipherinspector.com/llms.txt
> Use this file to discover all available pages before exploring further.
# Kasiski Examination
> Find repeated sequences in ciphertext to determine the likely key length of polyalphabetic ciphers.
## How it works
The Kasiski examination is a cryptanalysis technique used to attack polyalphabetic substitution ciphers (like the Vigenère cipher) by
finding repeated sequences and analyzing the distances between them.
The tool scans the ciphertext for repeated character sequences (n-grams) within a configurable length range. Only sequences
appearing two or more times are considered.
For each repeated sequence, the distances between consecutive occurrences are calculated. These distances are measured in
character positions.
The key insight: if a sequence repeats, the distance between occurrences is likely a multiple of the key length. The tool
calculates all factors of each distance and counts their frequencies across all repeated sequences.
Factors that appear most frequently across all distances are the most likely key lengths. The tool ranks potential key lengths by
their frequency of occurrence.
## Display Modes
### Factor Frequency
A bar chart showing potential key lengths ranked by how often they appear as factors of the distances between repeated sequences.
**How to interpret:**
* The x-axis shows potential key lengths (factors)
* The y-axis shows how many times each factor appeared across all distance calculations
* **Tallest bars = most likely key lengths**
* Look for a clear winner or a small group of related values (e.g., 5, 10, 15 all being multiples of 5)
* If multiple bars are similar in height, the key length may be their greatest common divisor
* The chips at the top highlight the top 3 most likely candidates
### Sequence Table
A detailed table listing each repeated sequence found in the ciphertext.
**How to interpret:**
* **Sequence**: The exact characters that repeat. Longer sequences are more reliable indicators
* **Count**: Number of times this sequence appears. Higher counts provide stronger evidence
* **Positions**: Where in the ciphertext (0-indexed) each occurrence starts
* **Distances**: The gaps between consecutive occurrences. These are the key values for analysis
* **Factors**: Common divisors of the distances. Factors appearing across multiple sequences are strong key length candidates
* Look for sequences where all distances share a common factor—this strongly suggests that factor is the key length
### Text Highlighting
The original ciphertext with repeated sequences color-coded for visual pattern recognition.
**How to interpret:**
* Each color represents a different repeated sequence
* The legend shows which sequence each color represents and its occurrence count
* Hover over highlighted sections to see position details
* **Evenly spaced highlights** of the same color suggest a consistent key length
* Clusters of different colors in the same region may indicate a portion of the key that produces common letter combinations
* Sequences that appear at regular intervals (e.g., every 5th position) strongly indicate that interval as the key length
### Arc Diagram
A visualization where arcs connect positions in the ciphertext where the same sequence appears.
**How to interpret:**
* The x-axis represents character positions in the ciphertext (0 to text length)
* Colored dots mark where each repeated sequence occurs
* Arcs connect consecutive occurrences of the same sequence
* **Arc height corresponds to distance**—taller arcs mean larger gaps between occurrences
* Look for arcs of similar heights across different sequences; this suggests those distances share a common factor (the key length)
* Hover over arcs to see the exact sequence, positions, and distance
* Multiple short, similar-height arcs often indicate a short key length
### Key Length Analysis
A horizontal bar chart showing relative confidence scores for the top potential key lengths.
**How to interpret:**
* Each bar represents a potential key length
* Bar length shows relative confidence as a percentage (longest bar = 100%)
* **Higher percentages = stronger candidates**
* This view normalizes the factor frequencies, making it easier to compare relative strengths
* A key length with 100% confidence that's far ahead of others (e.g., next is 40%) is a strong indicator
* If multiple key lengths show similar confidence, they may be multiples of each other—the smallest is likely the actual key length
Note: since 2 is an extremely common factor, the tool does have a bias towards a key
length of 2. So keep this in mind.
### Distance Heatmap
A matrix showing the Greatest Common Divisor (GCD) relationships between pairs of distances.
**How to interpret:**
* Both axes list the unique distances found between repeated sequences
* Each cell shows the GCD of the two distances (row and column)
* **Brighter/lighter cells = higher GCD values = stronger common factors**
* The diagonal always shows each distance's GCD with itself (the distance value)
* Look for rows or columns with consistently bright cells—those distances share factors with many others
* A GCD value that appears frequently throughout the matrix is a strong key length candidate
* Hover over cells to see the exact calculation: GCD(distance₁, distance₂) = value
## Kasiski Settings
### Sequence Length Range
* **Minimum Length**: The shortest sequence to search for (default: 3 characters)
* **Maximum Length**: The longest sequence to search for (default: 20 characters)
Shorter sequences occur more frequently but may be coincidental. Longer sequences are more reliable indicators but occur less often.
### Max Results
Limits the number of sequences displayed. The tool prioritizes sequences by frequency (most common first) and length (longer sequences
preferred when counts are equal).
## Practical Application
The Kasiski examination is most effective when:
* The ciphertext is long enough to contain repeated sequences
* The cipher uses a repeating key (polyalphabetic substitution)
* The key length is relatively short compared to the message length
Once a likely key length is determined, the ciphertext can be divided into groups (every Nth character) and each group analyzed
separately using single-alphabet techniques like frequency analysis.
## Caveats
* Very short ciphertexts may not contain enough repeated sequences for reliable analysis
* Random coincidental matches can produce false positives, especially with short sequences
* Modern ciphers and properly implemented encryption are not vulnerable to this technique
* The analysis assumes the original text has natural language patterns; random or compressed data will not produce meaningful results