Kasiski Examination

​

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.

​

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

​

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