Cryptography: Problems and Solutions

1. 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 ?
Hint : Analyze the possible periods.

Solution:
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.