cryptology stem workshop 60-90 mins - uccs · pdf filecryptology stem workshop 60-90 mins ......

1 © University of Colorado Colorado Springs, Center for STEM Education. Creative Commons License (by-nc-sa), 2011. Curriculum creation funded by Air Force Office of Scientific Research (AFOSR). Curriculum format design adapted from CDIO developed by Massachusetts Institute of Technology (MIT).

Cryptology STEM workshop 60-90 mins

LEARNING GOALS: After the completion of this workshop, students will understand:

1. Cryptology is the practice of making codes to protect information.

2. Cryptology has been in use almost as long as written language.

3. Modern cryptology uses complex mathematics to develop codes.

CONCEIVE – What do I wish to accomplish through this project?

This stage involves guiding students in defining the goals of the project, then helping them develop conceptual,

technical, and action plans to meet those goals while considering the technology, knowledge, and skills that apply. This

guidance is provided in the form of Essential Questions that use student’s preconceptions, and misperceptions then

move them toward a deeper and more realistic understanding of the process and skills needed to complete the

project.

ESSENTIAL QUESTIONS:

1. How is math used to create codes to protect information?

2. What makes codes harder to break? What tradeoffs are there between ease of use and

security?

3. How do we use math based codes in our everyday lives?

DESIGN - How will I accomplish the project?

This stage focuses on creating the plans, drawings and algorithms that describe the product, process

or system that will be implemented.

NOTES: for this project, the transfer of information will be split up into two parts: part 1 will be a

short presentation on cryptology, the history and practices of it. Part 2 will be a hands on coding and

decoding exercise for the kids to practice cryptology themselves.

Following is an outline of the class activities.

Part 1: A short power point presentation on the history and practice of cryptology. This will be a multi-media

presentation, with pictures and details and perhaps animations. It will cover a brief history of

cryptology from ancient times to the present, from the Ceasar cipher through modern day math

based encryption, including stories of the differences that cryptology has made in wars/the course of

history. This will include a brief discussion of how cryptology has evolved into math based in our


modern computer era and how we use it everyday in protecting our privacy of emails, messages, and

copyrighted material.

Part 2: Here the kids will play a game involving cryptology. Divide the group into two teams, each team split

into two smaller groups (these should be 3-5 kids, if there are too many, make additional teams). Try

to keep messages around 8-10 words long. Give the kids movie quotes if they cannot think of

messages to send.

Round 1: Each group will get a message to encode to their team mates as they choose. The first team

to code and decode both messages wins this round.

Round 2: Each team will be given two coded messages, one that their “General” is sending them, for

which they know the decryption key, and one that is meant for the other team, but was intercepted,

for which they do not know the decryption key. The fist team to decode both their own message and

the intercepted message wins.

If time remains: Play a round three in which the teams have 1 minute to discuss a key with their entire

team, then the teams split back to opposite sides of the room, encode their own messages, and

communicate the key and the message to their team mates best, without the opposing team

decrypting it first. Both teams will be given the codetext, but only team mates will have the keys. See

if the codes can be broken.

Prizes: Perhaps award candy as prizes or rewards for all code breakers!

IMPLEMENT - From an idea to a product!

This stage refers to the transformation of the design into a product. It includes hardware, manufacturing,

software coding, testing and validation.

OPERATE – Does it work the way I planned?

This stage uses the built product, process or system to satisfy the intended goal.

RESOURCES NEEDED – What equipment and supplies do I need?

This presentation needs only a projector, computer to run power point, paper and pens for

the kids to work with, and candy for rewards. If you are planning on having students make

their own scytale – you will need pencils, rulers, tape, scissors and rods (markers).

There are also two worksheets (Polybius Square and PlayFair Cipher) that can be

implemented into the curriculum if there is extra time allotted.


NOTE: If you have the budget, providing the students with a small chocolate bar (with bar

code) at the end of class and encouraging them to verify the bar code is a fun way to end

the workshop.

SET-UP

1. Print out worksheets for students for Atbash, Pigpen, Playfair, Polybius Square

2. Need computer and projector for power point

3. Pencils, paper, rulers, tape and scissors, sticks, markers or some type of rod to make a

scytale.

Colorado State Math Standards

Standard Grade Level Expectations

HIGH SCHOOL

2. Patterns, Functions, and Algebraic Structure

1. Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables 2. Quantitative relationships in the real world can be modeled and solved using functions 3. Expressions can be represented in multiple, equivalent forms 4. Solutions to equations, inequalities and systems of equations are found using a variety of tool

3. Data Analysis, Statistics, and Probability

1. Visual displays and summary statistics condense the information in data sets into usable knowledge

8th Grade

3. Data 1. Visual displays and summary statistics of two-


Analysis, Statistics, and Probability

variable data condense the information in data sets into usable knowledge

7th Grade

2. Patterns, Functions, and Algebraic Structure

1. Properties of arithmetic can be used to generate equivalent expressions

6th Grade

NOT APPLICABLE AT THIS GRADE LEVEL

Supply Price Pencils, tape, markers ,paper $10.00

Rulers, scissors $35.00

Stick for scytale $10.00

Total $55.00

Cost/student=$2.75 (based on 20 students) 1- 2 staff recommended


Atbash Cipher

The Atbash cipher is a very specific case of a substitution cipher where the letters of the alphabet are reversed. In other words, all As are replaced with

Zs, all Bs are replaced with Ys, and so on.

Because reversing the alphabet twice will get you actual alphabet, you can encipher and decipher a message using the exact same algorithm.

Example

Plaintext: This is a secret message

Ciphertext: Gsrh rh z hvxivg nvhhztv

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

Z Y X W V U T S R Q P O N M L K J I H G F E D C B A


PIGPEN Cipher

The pigpen cipher (sometimes called the masonic cipher or Freemason's cipher) is a simple substitution cipher exchanging letters for symbols based on a

grid. The scheme was developed and used by the Freemasons in the early 1700s for record-keeping and correspondence. The example key shows one way the

letters can be assigned to the grid.


You may also change the positions of the letters to create your own key. Make sure you write down your grid if you choose to do so.


Playfair Cipher

Memorization of the keyword and 4 simple rules is all that is required to create the 5 by 5 table and use the cipher.

The Playfair cipher uses a 5 by 5 table containing a key word or phrase. To generate the table, one would first fill in the spaces of the table with the

letters of the keyword (dropping any duplicate letters), then fill the remaining spaces with the rest of the letters of the alphabet in order (to reduce the

alphabet to fit you can either omit "Q" or replace "J" with "I"). In the example to the right, the keyword is "keyword".

To encrypt a message, one would break the message into groups of 2 letters. If there is a dangling letter at the end, we add an X. For example: "Secret

Message" becomes "SE CR ET ME SS AG EX". We now take each group and find them out on the table. Noticing the location of the two letters in the

table, we apply the following rules, in order.

1. If both letters are the same, add an X between them. Encrypt the new pair, re-pair the remining letters and continue.

2. If the letters appear on the same row of your table, replace them with the letters to their immediate right respectively, wrapping around to the left

side of the row if necessary. For example, using the table above, the letter pair GJ would be encoded as HF.

3. If the letters appear on the same column of your table, replace them with the letters immediately below, wrapping around to the top if necessary.

For example, using the table above, the letter pair MD would be encoded as UG.

4. If the letters are on different rows and columns, replace them with the letters on the same row respectively but at the other pair of corners of the

rectangle defined by the original pair. The order is important - the first letter of the pair should be replaced first. For example, using the table

above, the letter pair EB would be encoded as WD.

To decipher, ignore rule 1. In rules 2 and 3 shift up and left instead of down and right. Rule 4 remains the same. Once you are done, drop any extra Xs

that don't make sense in the final message and locate any missing Qs or any Is that should be Js.

K E Y W O

R D A B C

F G H I J


L M N P S

T U V X Z

Polybius Square

A Polybius Square is a table that allows someone to translate letters into numbers. To give a small level of encryption, this table can be randomized and

shared with the recipient. In order to fit the 26 letters of the alphabet into the 25 spots created by the table, the letters i and j are usually combined.

To encipher a message you replace each letter with the row and column in which it appears. For example, D would be replaced

with 14.

To decipher a message you find the letter that intersects the specified row and column.

Example: Plaintext: This is a secret message

Ciphertext: 44232443 2443 11 431513421544 32154343112215

1 2 3 4 5

1 A B C D E

2 F G H I K

3 L M N O P

4 Q R S T U

5 V W X Y Z


Make a scytale Investigation - Decoding and analysing information

Purpose To build a scytale and demonstrate the concepts of coding and code keys in a physical way.

Age range (years) Subjects

7 8 9 10 11 12 13 14 15 16 Art and Design, History

Background

Spies need to keep their messages secret. This activity demonstrates a simple low-tech way of encrypting data.

Steps

You will need:

pencils, A4 paper, rulers

tape and scissors for sharing

some kind of rod (thick pens such as markers are ideal).

1. This coding method may have been used by ancient Greeks in military campaigns. It is often called the ‘Spartan cipher’. Can students imagine what sort of messages were passed on in this way?

2. Ask students to cut their sheets of A4 paper into strips about a centimetre wide. It is important the paper strips are straight. (The marked up cutting sheet on page three may be useful).

3. Give students the activity sheet on page two and ask them to follow the instructions for making a scytale.

Discussion

What would happen if you were caught carrying your message and the rod?

How could you make it more difficult for others to find out the message?

How could you let another agent know the size of the rod they need to use to decode messages (essentially the ‘key’ to the code)?


Make a scytale – Activity Sheet

1. Attach a paper strip to the rod with a small piece of tape.

2. Wrap the paper strip tightly around rod making sure edges meet but don’t overlap.

3. Fix the strip in place.

4. Write your message on the paper along the length of the rod.

5. Carefully unravel the paper strip. See how the words have been broken up.

6. Swap your unravelled strip with a classmate. Can you read the message on the strip you have been passed?


7. Re-wind the strip around a rod to clearly reveal the words. What happens if you use different sizes of rods

cryptology stem workshop 60-90 mins - uccs · pdf filecryptology stem workshop 60-90 mins ......

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