Advanced Placement (AP) Computer Science

How can patterns in a Vigenère cipher be analyzed?

1. By using brute force techniques

2. Through frequency analysis methods

3. By identifying the most common letters

4. By counting the gaps between repeated patterns

The correct answer is: By counting the gaps between repeated patterns

In analyzing patterns in a Vigenère cipher, counting the gaps between repeated patterns is the most effective method. This technique, often called the Kasiski examination, involves identifying sequences of letters that are repeated in the ciphertext and noting the distances between them. When these repeated sequences are found, the distances can provide insights into the length of the keyword used in the cipher. In particular, the greatest common divisor of these distances can suggest the keyword length, as periodic repetitions in the encryption process are typically based on the length of the keyword. Identifying the most common letters or using frequency analysis alone may not effectively reveal the underlying structure of the Vigenère cipher, especially since the substitution method it employs shifts letters based on the keyword rather than a direct one-to-one mapping of letters. Brute force techniques might eventually decipher the message but are less efficient than analyzing the ciphertext for patterns.