Chapter 4.6, Problem 17E

Suppose you have intercepted a ciphertext message and when you determine the frequencies of letters in this message, you find the frequencies are similar to the frequency of letters in English text. Which type of cipher do you suspect was used?

The Vigenère cipher is a block cipher, with a key that is a string of letters with numerical equivalents $k_1{k}_2\mathrm{...}{k}_m$ where $k_i\in Z_{26}$ for $i=1,2,\dots$ . Suppose that the numerical equivalents of the letter of a plaintext block are $p_1{p}_2\mathrm{...}{p}_m$ . The Corresponding numerical ciphertext block $(p_1+k_1)mod 26(p_2+k_2) mod \mathrm{26...}(p_m+k_m)mod 26$ . Finally, we translate back to letter. For example, suppose that the key strings is RED, with numerical equivalents 1743. Then, the plaintext ORANGE, with numerical equivalents 14 1700 13 06 04, is encrypted by first splitting it into two blocks 14 1700 and 13 06 04. Then, in each block we shift the first letter by 17, the second by 4, and the third by 3. We obtain 5 21 03 and 041007. The ciphertext is FVDEKH.