Begin the lesson by posing the question, "What methods have you seen
for encoding secret messages?" Student responses may include Morse
code, decoder rings from cereal boxes, or taking the letters of the
alphabet and assigning a number (A = 1, B = 2, ...) or a symbol (A = ♣,
B = ♠, ...) to each of them. Students may indicate that the ciphertext
(the result after a message has been encoded) is sent to someone else,
and the recipient can decode the message only if they know the system
that was used. Some students may add that they used similar systems,
except that they assigned numbers to each letter of the alphabet in a
random way. Students should be encouraged to share their ideas with the
class.
Next, have students work with a partner to break a simple coded
message, one that uses A = 1, B = 2, C = 3, ..., Z = 26. On the board
or overhead projector, display the following ciphertext:
20-15-4-1-25 25-15-21 23-9-12-12 12-5-1-18-14 1-2-15-21-20 3-15-4-5-19In all likelihood, students will quickly decode this message because
of the simplicity of the coding system. However, should some students
have difficulty decoding the message, prompt them by asking, "What
numbers occur most frequently in the ciphertext?" Ask them to consider
what letters occur most frequently. This hint should put them on the
path to a correct solution.
After students have decoded the message (or at least part of
it), display the decoded message: "Today you will learn about codes."
If students did not realize what coding system was used, reveal that
A = 1, B = 2, etc.
Point out that this coding system, as well as the ones that
students likely suggested at the beginning of the lesson, are fairly
easy to break; even without knowing the coding system, expert code
breakers are able to decipher them in minutes or even seconds. In all
likelihood, code breakers would use letter frequency analysis to break
this code.
Frequency analysis is the process by which the frequency of a
letter in an encoded messages is compared with the frequency of letters
in English words. For instance, the letter E occurs most often in
English words, so if the letter W occurs most often in ciphertext, then
it is likely that E has been replaced by W.
To show students how to use letter analysis to break a code, give them the following coded message:
TFNRIUJ UZV DREP KZDVJ SVWFIV KYVZI UVRKYJ;
KYV MRCZREK EVMVI KRJKV FW UVRKY SLK FETV.
The decoded message, taken from William Shakespeare’s play Julius Caesar, is "Cowards die many times before their deaths; the valiant never taste of death but once."
Display the Letter Frequency Overhead, which shows which letters are used most often in English
words. Let your students suggest how this information could be used to
crack the code. [The letters that occur most frequently in the
ciphertext will likely correspond to the letters that occur most
frequently in English words.]
By analyzing the ciphertext, students should notice the following:
- The letter V occurs the most times (13) in the ciphertext.
- The letter K occurs the second most times (9) in the ciphertext.
- The letter R occurs the third most times (7) in the ciphertext.
- The first five letters of word just before the semicolon are the same as the letters of the third word from the end: UVRKY.
The most frequently occurring letters in English words are E (13.0%)
and T (9.3%). By comparing these percents to the most frequent
occurrences in the encoded message, it seems reasonable that E and T
might have been replaced by V, K, or R. If the frequencies hold, then E
was probably replaced by V, and T was likely replaced by K.
Substituting these into the ciphertext reveals that the word just after
the semicolon is T_E; this suggests that the middle letter is
probably H, giving THE, so H was probably replaced by Y when the
message was encoded.
Continuing the same type of reasoning, the next five most common letters on the Letter Frequency
Overhead chart are A, I, N, O, and R, all of which are just over 7%. These
letters were probably replaced by the letters E, F, I, J, U, Y, and Z,
all of which occur four times in the ciphertext. Students can use this
information with some logic to begin putting letters in place.
Eventually, some words will become obvious, and students can make
guesses at the missing letters without using the frequency table. You
may wish to guide students as they crack this code and decipher the
message.
While cracking this code, students may realize that the
ciphertext was created by replacing each letter of plaintext with a
letter 17 places ahead in the alphabet. In particular, A was replaced
by R, B was replaced by S, C was replaced by T, and so forth. That is, a shift of 17 units was used. If students did not notice this, point it out to them.
A Caesar cipher is a coding system in which letters are
replaced by letters a certain distance ahead in the alphabet. Julius
Caesar is thought to have used this method to communicate with officers
in the Roman army. When sending a message, Caesar would inform his
generals what the shift was, so they would be the only ones who could
read the encrypted message.
Armed with this information, the students are ready to proceed
to code a message using the Caesar cipher. Pretend that you are Julius
Caesar, and your students are your generals. You are conducting a
meeting about sending encrypted communications. You have decided to us
a shift of 7 units, which allows for the following replacement of
letters:
| Plaintext: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
| Ciphertext: | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | A | B | C | D | E | F | G |
Distribute the Caesar Shifter
handout. Students can cut out the circles to make a Caesar Shifter,
which can be used for encoding and decoding methods with the Caesar
substitution cipher.
For the shift of 7 described above, students would use the
Caesar shifter by rotating the letter A on the smaller circle so that
it appears under the H on the larger circle. The number 7 above the H
on the larger circle indicates that this is a shift of 7 units.
On the chalkboard or overhead projector, write the following message:
ROME IS THE GREATEST EMPIRE.
Allow students to encrypt this message using the Caesar shifter. When encoded, the message will read:
YVTL PZ AOL NYLHALZA LTWPYL.
Next, provide the ciphertext message below ("Rome was not built in a day.") for the generals to decode.
YVTL DHZ UVA IBPSA PU H KHF.
Have students decode this message using either the Caesar Shifter or
frequency analysis. (You might even want to divide the class into
two groups, with each group using one of these methods, to see which
method is faster.) Although this is a small amount of text, the
following online tools can be used to tally letter frequencies:
Students may also use logic when decoding the message. Some students may notice the one-letter word h that appears near the end of the message. Since this letter must represent either a or I
(these are the only two single-letter English words), students can
determine the possible shifts and see which one works for the remainder
of the message.
Have students use the Codes Tool
to verify their results. To replicate a Caesar shift of 7, students
will need to enter a Shift Value of 7 and a Stretch Value of 1. (Note
that the Codes Tool only works with lowercase letters; if uppercase
letters are used, they are not changed when encoded or decoded. For
instance, if "rome" is entered into the tool, it will be encoded
correctly as "yvtl." However, if "Rome" is entered, it will be encoded
incorrectly as "Rvtl," because the uppercase R will remain. This
apparent flaw in the tool is actually by design. When encoding a
message, it is best to remove all uppercase letters; because they
indicate the start of a proper noun or the word I, they offer clues to code breakers. Therefore, it is better to use only lowercase letters when encoding a message.)
Now that students are familiar with the Caesar cipher, distribute the Caesar Cipher activity sheet.
In pairs, allow students to answer Questions 1-5. For
Question 1, allow students to research Julius Caesar; the following
site may be helpful:
Allow sufficient time for students to complete Questions 1-5, then bring the students back together and review the answers.
[Julius Caesar was the Emperor of Rome. He lived from
100-44 B.C. The Caesar cipher has 25 possible shifts. A shift of 26 or
more will simply repeat one of the shifts of 1-25. This was probably
sufficient during Caesar’s time, but it is insufficient today because
of advanced code breaking methods. Because there are only 25 possible
shifts, a person could test each possible shift to determine if an
encoded message uses the Caesar cipher.]