A well-known concept from classical cryptanalysis is the Kasiski test. You have

Question

A well-known concept from classical cryptanalysis is the Kasiski test. You have found an

old ciphertext, where you know that the plaintext discusses cryptographic methods. You suspect

that a Vigenere cipher has been used and therefore look for repeated strings in the ciphertext.

You find that the string TICRMQUIRTJR occurs twice in the ciphertext. The first occurrence

starts at character position 10 in the text and the second at character position 241 (we start

counting from 1). You make the inspired guess that this ciphertext sequence is the encryption of

the plaintext word cryptography. If this guess is correct, what is the key?

Explanation / Answer

To estimate the period we use the Kasiski test. The distance between the two occurrences given is 241 10 = 231 = 3 · 7 · 11 positions.

Possible periods are thus 3, 7 and 11. If the guess is correct, we can immediately find the corresponding shifts: at position 10 the shift is

T c = 19 2 = 17 = r .

Similar computations for the other positions gives the shift keys rrectcorrect

We now see that this is not periodic with periods 3 or 11, while period 7 is possible. The keyword of length 7 starts at position 15; hence the keyword is correct.

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