Kasiski examination
Introduction
The Kasiski examination is a cryptanalytic method used to break the Vigenère cipher, a type of polyalphabetic substitution cipher. This technique was developed by the Prussian cryptanalyst Friedrich Wilhelm Kasiski in the 19th century and represents a significant advancement in the field of cryptanalysis. The method allows for the determination of the length of the keyword used in the cipher, which is a crucial step in deciphering the encrypted message.
Historical Context
The Vigenère cipher, once considered unbreakable, was widely used for secure communication. It employs a series of Caesar ciphers based on the letters of a keyword. The Kasiski examination emerged as a breakthrough in the mid-1800s, challenging the perceived invulnerability of the Vigenère cipher. Friedrich Kasiski's work laid the groundwork for modern cryptanalysis by introducing systematic approaches to deciphering encrypted texts.
Methodology of Kasiski Examination
The Kasiski examination involves several steps to determine the length of the keyword used in a Vigenère cipher. The process begins with identifying repeated sequences of letters in the ciphertext. These repetitions often occur because the same segment of the plaintext is encrypted using the same segment of the keyword. By analyzing the distances between these repeated sequences, one can infer the length of the keyword.
Identifying Repeated Sequences
The first step in the Kasiski examination is to scan the ciphertext for repeated sequences. These sequences are typically three or more characters long. The rationale is that longer sequences are less likely to occur by chance, thus providing more reliable data for analysis.
Calculating Distances
Once repeated sequences are identified, the next step is to calculate the distances between their occurrences. These distances are measured in terms of the number of characters between the start of one sequence and the start of the next. The distances are then analyzed to find common factors, which are likely candidates for the keyword length.
Determining Keyword Length
The common factors of the distances between repeated sequences suggest possible lengths for the keyword. The most frequently occurring factor is often the correct keyword length. This step is crucial because knowing the keyword length transforms the problem into a series of simple Caesar ciphers, each of which can be solved individually.
Limitations and Challenges
While the Kasiski examination is a powerful tool, it is not without limitations. The method relies on the presence of repeated sequences, which may not always be present in short ciphertexts or those with highly varied content. Additionally, the presence of noise or errors in the ciphertext can complicate the analysis, leading to incorrect conclusions about the keyword length.
Modern Applications
Despite its age, the Kasiski examination remains relevant in the study of classical cryptography. It is often used in educational settings to teach the principles of cryptanalysis and the historical development of cryptographic techniques. Furthermore, understanding the Kasiski examination provides insight into the evolution of cryptographic methods and the ongoing battle between encryption and decryption technologies.