Cryptography
First show this scene from The Da Vinci Code where the Fibonacci numbers are showed
in a mixed up order to introduce the idea of cryptography. The clip can be found here:
https://www.youtube.com/watch?v=GKb9zzNkwzM.
Cryptography is a way to encode and decode information. A simple kind of cryptography
is the Caesar Cipher. This allows for coding and decoding messages by shifting letters a certain
number of places in the alphabet. For example, A shift of 2 will move a to c, b to d, etc. The
Caesar Cipher is named after Julius Caesar because he used it to send secret messages to
soldiers. Print this decoder ring for each group: http://www.thingiverse.com/thing:14891. You
can also print the attachment for it.
1. Use the Caesar Cipher on your ring with a shift of 3 to decode the following message:
pdwk lv ixq.
Math is fun.
2. Why would the Caesar Cipher not be good to use for important information?
It is too easy to crack.
3. A slightly more complicated cipher is called the Vigenè re cipher. This cipher uses a
key. This is a chosen word that is public knowledge. To encrypt a message using the Vigenè re
cipher it would be helpful to have a Vigenè re table as shown here:
A B C
A A B C
B B C D
C C D E
D
D
E
F
E
E
F
G
F
F
G
H
G
G
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I
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I
J
I
I
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J
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L
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K
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L
M
N
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M
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O
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N
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P
O
O
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Q
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To decode a letter look at the column of the letter and the row of the corresponding letter in the
key. For example, if the key is “key” and the word to encode is “math” start with the column
with “m” and the row with “k.” This yields a “w.” Repeat this process for the remaining letters.
When the key is shorter than the word, it gets repeated as many times as necessary. In this case
there is only one extra letter so the key becomes “keyk.” Using this method the decoded word is
“werr.” Decryption works the same way. Since the key is known look at the row with “k” and
find the “w” within it. Tracing that back to the column heading yields the “m.”
Use the Vigenè re cipher with key “love” to decode the word “jcp.”
You.
4. The decoder ring can actually be used in place of the Vigenè re table. Figure out and
explain how this would work.
C
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The key letter tells you what shift to make. In the example from question 3 the first letter in the
key is L, so first use the ring to match A with L. You will see that J and Y are paired up. For the
next letter do another shift, matching A to O, and keep going like this.
5. Make up a key and encode a secret message with your decoder ring. Switch your
message in encoded form and your key with another group. Then decode the new message you
received.
(extension) If your students know modular arithmetic or have done this activity
http://www.thingiverse.com/thing:1693134 they can also answer the following:
6. Explain how these ciphers use modular arithmetic.
The alphabet has 26 letters so to do the matching
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
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Think of the Caesar Cipher with a shift of 3. To see where each letter goes, look at its numerical
value and add 3. For example, m becomes 12+3=15 = p. Once you get to the higher numbers
though you can’t just add 3. If you look at y that becomes 24+3=27, but there is no 27. After 25
you start back at 0. Thus, y becomes 1=b. This is the same as adding in mod 26.
Caesar Cipher Decoder Ring Rounded by
cymon
Published on December 21, 2011
www.thingiverse.com/thing:14891
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