Worksheet 4.0 (page 1 of 1)
Random ciphers: using frequency analysis
A random cipher is one which uses a letter to replace another letter, but does it
by choosing the letters in a ‘random order’. The person encoding and the person
decoding both need a list of matching letters, but anyone intercepting the
message has to be very clever to work out the matching letters. One of the ways
to be clever is to use frequencies of letters in the message to help try to match
them to English.
Activity
1. The most frequent letter in English is E. Here is a sentence without any Es.
‘Drilling for oil is boring.’
Can you invent a sentence without Es?
2. Make a frequency table from this message: When it rains why don’t sheep
shrink?
a
k
u
b
l
v
c
m
w
d
n
x
e
o
y
f
p
z
g
q
h
r
i
s
j
t
Is E the most frequent letter?
In all of English the frequent letters are (in order): e t a o i n s h r. However these
will possibly not be in that order in a short message – very long messages are
needed (or many of them with the same cipher) to be able to match the common
frequencies.
3. Try to decode this message. There are some hints below.
D KRVBRYY HZ D KWL NRX D EDAW HTNDTY
Which letters stand alone as words in English? Choose a match for D.
What are the most common two letter words? Choose a match for H and Z.
The next most common letters (R and Y) should come from the most frequent
four letters: e, t, a and o. Try all the possibilities and eliminate some using
unlikely spellings.
The spreadsheet, Letter frequencies, is designed to calculate and graph the
frequencies of the letters in any message that is typed. Compare the frequencies
with those in the English language.
4. The spreadsheet, Random cipher, automatically generates a random
matching of letters. It then chooses a mystery message and encodes it. Try
to find the correct message. The word spaces are still there, which provides a
clue. The frequency table and graph (showing the frequencies for each letter
in the coded message and in English) will be helpful in trying to find the plain
text message.
CSF Sample Units: Years 8 to 10 Maths – Codes