Homework 7
Math 108, Spring 2015
Due Date: Saturday, April 4
The goal of this assignment is to decode the ciphertext in Homework7Ciphertext.xlsx,
which can be found on the class web page. This ciphertext was encoded with a Vigenère
cipher of unknown keyword length. You might find it helpful to refer to the notebook
VigenereDecoding.xlsx.
1. (a) Use Excel to find the letter frequencies for the ciphertext.
(b) Compute the index of coincidence for the ciphertext, i.e. the probability that
two randomly chosen letters are equal. (See the “Friedman Test” spreadsheet in
VigenereDecoding.xlsx for an example of this computation.)
(c) Use the formula
0.065 − 0.0385
I − 0.0385
to estimate the keyword length. Here I represents the index of coincidence, and
k =
k is the approximate keyword length.
2. Set up a decipherment spreadsheet for the given ciphertext, similar to the “Decipherment” sheet in VigenereDecoding.xlsx. Use your answer to 1(c) as the keyword
length.
3. (a) Set up a spreadsheet that can pick out all the letters in the ciphertext corresponding to a certain position in the keyword and compute the letter frequencies. (See
the “Guessing Letters” sheet in VigenereDecoding.xlsx.)
(b) Use your sheet from part (a) to guess each letter of the keyword. Put your guesses
into the decipherment sheet to decode the ciphertext.