Kasiski Examination

The Kasiski Examination, developed by Friedrich Kasiski in 1863, represents a groundbreaking method in cryptanalysis that fundamentally changed the approach to breaking polyalphabetic substitution ciphers, particularly the Vigenère cipher.

Historical Context

Before Kasiski's discovery, polyalphabetic ciphers were considered virtually unbreakable, earning the Vigenère cipher the nickname "le chiffre indéchiffrable" (the indecipherable cipher). The technique was independently discovered by Charles Babbage several years earlier, though his work remained unpublished.

Methodology

The examination works through several key steps:

1. Pattern Identification

   • Locate repeated sequences of characters in the ciphertext
   • Record the distances between these repetitions

2. Distance Analysis

   • Calculate the factors of the distances between repeated sequences
   • Common factors likely indicate the key length or its multiples

3. Key Length Determination

   • The greatest common divisor of the distances often reveals the key length
   • This reduces the problem to multiple simple substitution ciphers

Mathematical Foundation

The technique works because in polyalphabetic substitution:

• Identical plaintext sequences encrypted with the same key portion produce identical ciphertext
• The distance between repetitions is typically a multiple of the key length

Applications and Significance

The Kasiski Examination:

• Provided the first systematic method to attack polyalphabetic ciphers
• Led to the development of more sophisticated statistical analysis techniques
• Influenced modern cryptographic algorithms design principles

Limitations

The method has several constraints:

• Requires sufficient ciphertext length
• Depends on the presence of repeated plaintext sequences
• May produce false positives in highly repetitive text

Modern Relevance

While modern encryption has moved far beyond classical ciphers, the Kasiski Examination remains:

• A fundamental teaching tool in cryptography courses
• An important historical milestone in cryptographic theory
• Relevant for analyzing certain types of stream ciphers

Related Techniques

The method is often used in conjunction with:

• frequency analysis
• Index of Coincidence
• Friedman test

The Kasiski Examination marked a crucial turning point in cryptanalysis, demonstrating that even sophisticated polyalphabetic ciphers could be systematically attacked. Its principles continue to influence modern approaches to cryptographic security and analysis.