Theresa C. McGoldrick (mcgoldri@dimacs.rutgers.edu)

**Category**

Basic Crypto Systems, Modular 26

**The Problem**

Julius Caesar used codes to get messages across without people knowing what the messages said. The students will explore the advantages and disadvantages of this system of encryption and the structure of the cryptosystem.

**Materials**

Modular 26 Sheet and CaesarCipher Sheet

**Prerequisites**

None

**Activity Description**

**Guided Exploration**

1) Put on the board an encrypted message and ask the students to decrypt it.

EX: WKLV LV D VHFUHW FRGH.

*(This is a secret code)*

2) As the students are trying to decipher the code the teacher should pose the following questions:

a) Do the size of the words help you?

b) Do you see any word patterns that could help you?

c) Which letters appear most and how can this help you?

3) After approximately 10 minutes, assist students decipher the code by handing out a sheet with the alphabet and asking the following question:

How are the letters in the code related to the letters you have deciphered?

4) Once students have deciphered the message, explain to students the origins of the Caesar cipher and then have the students make an observation on the code.

a) Each letter of the code always corresponds to the same letter of the message, so letter frequencies and patterns can be exploited.

b) There is a uniform rule for decyrption. Once it is known, deciphering is easy.

**A Mathematical Approach**

Introduce students to definitions and parts of a cryptosystem.
1) Plain text- Words that you want to be encrypted.

2) Cipher Text- The words that we encrypted.

3) Key- addition taken place for the cipher.

4) Encoding rule- what we add the letter by to get the new letter

5) Decoding rule- what we subtract by to get the original letter

Elicit from the students which parts of the Caesar cipher are which:

1) WKLV LV D VHFUHW FRGH

2) k-3

3) This is a secret code.

4) k+3

5) k=3

Ask: Which part of the cryptosystem must be kept secret?

Ask the students the following questions:

How many keys are there? (There are only 25 keys)

Is 7 a key?

Is zero a key?

Is 27 a key?

Hand out Mod 26 worksheet and have students begin filling it in.

Elicit from the students the patterns they see.

What will T be coded if k=5?

k=9?

k=20?

Ask: Do you need to use a chart? (No! Subtract 26 from the letter.)

**Activity**

Ask students to write two advantages and two disadvantages to the Caesar cipher.

**Concluding the Exploration**

By now the students have had time to explore and discuss the structure of the cyrptosystem.

Working in groups the students will create a shift cipher and exchange it with a partner to decode.

**Further Activities**

For homework students will complete the attached worksheet. This will allow them to fully comprehend shift ciphers.