Aim: How can we use Matrices to code and decode a message?

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1 Aim: How can we use Matrices to code and decode a message? Do Now: Explain why A has no inverse A = Afterwards: Create a number system for the English Alphabet A = B = C =... Y = Z =

2 U7L10 CryptoGrams.notebook March 10, 2015 Cryptograms: Encrypted Messages Code making and Code breaking Want to work for NSA or CIA? to join nsa decode the tweet.htm

3 Let's Encode the word MATH Using the simple system above. How would "MATH" be spelled using numbers? What would be some ways to encode our message so its not so easily decipherable (breakable)

4 Rules of the game to code: 1. Express the word or message numerically 2. Form a Square matrix of the word. Use 0's to fill up any remaining empty spaces 3. Create a coding matrix which is the same size as your matrix in step 2. This coding matrix must be invertible 4. [Coding Matrix] x [Word Matrix] = [Cryptogram]

5 [Coding Matrix] x [Word Matrix] = [Cryptogram] Lock x Word = Locked Word x = [Cryptogram] *In these examples, we put the locks and keys on the left. You can put the key and lock on the right, but the text chooses to use the left. We will use BOTH.

[Coding Matrix] x [Word Matrix] = [Cryptogram] Lock x Word = Locked Word [Decoding Matrix] x [Cryptogram] = [Word Matrix] Key x Locked Word = UNLocked Word Given a coding matrix, conjecture

6 [Coding Matrix] x [Word Matrix] = [Cryptogram] Lock x Word = Locked Word [Decoding Matrix] x [Cryptogram] = [Word Matrix] Key x Locked Word = UNLocked Word Given a coding matrix, conjecture what the key could possibly be?! *In these examples, we put the locks and keys on the left. You can put the key and lock on the right, but the text chooses to use the left. We will use BOTH.

7 [Decoding Matrix] x [Cryptogram] = [Word Matrix] Key x Locked Word = UNLocked Word Finding the Key = =

8 [Decoding Matrix] x [Cryptogram] = [Word Matrix] Key x Locked Word = UNLocked Word x = *** Note, for consistency, we will always put the KEY and LOCK matrix on the LEFT when multiplying.

9 *Some of you use the left key/lock method. Others use right key/lock. Part 1) Translate the following Message into numbers: HELP = Use the coding matrix: Part 2) Write your Cryptogram: Part 3) Solve for the Decoding matrix Write your decoding matrix: Part 4) Multiply it with your Cryptogram. What did you get? Did you get the same matrix back in part 1? If not, look for an error. Ask your team!

10 *Switch Left/Right methods from previous problem Part 1) Translate the following Message into numbers: LOVE = Use the coding matrix: Part 2) Write your Cryptogram: Part 3) Solve for the Decoding matrix Write your decoding matrix: Part 4) Multiply it with your Cryptogram. What did you get? Did you get the same matrix back in part 1? If not, look for an error. Ask your team!

11 Riddle time! Below are some famous riddles. Some of them came from a blockbuster movie! You will not know which side (RIGHT or LEFT) the lock/key was created from so it may take you more than one attempt. Try to guess the solutions before unraveling the cryptogram!

12 RIDDLE: I am as light as a feather, yet the strongest man on earth can't hold me for more than 5 minutes. What am I? The Cryptogram of the answer is... The coding matrix used was... Solve the riddle!

13 It cannot be seen, cannot be felt, Cannot be heard, cannot be smelt. It lies behind stars and under hills, and empty holes it fills. It comes out first and follows after, ends life, kills laughter The Cryptogram of the answer is... The coding matrix used was...

14 You'll find her in the mountains, you'll find her in the creek. She has no mouth Yet she speaks in every tongue She has no ears And yet will answer every cry Always having the last word, what am I? The Cryptogram of the answer is... The coding matrix used was... Solve the riddle!

15 Last one: I'm in a rock, but not in stone I'm in a marrow, but not in bone I'm in a bolster, but not in a bed I'm not living, I'm not dead. What am I? The Cryptogram of the answer is... The coding matrix used was...

16 What is given to you, belongs only to you Yet others use it more than you do? The Cryptogram of the answer is... The coding matrix used was... Solve the riddle!

In the book/movie, "The Hobbit" our hero wanders into a cave where he meets a monster named "Gollum". He keeps the monster distracted using riddles to plan his escape.

17 In the book/movie, "The Hobbit" our hero wanders into a cave where he meets a monster named "Gollum". He keeps the monster distracted using riddles to plan his escape. This thing all things devours: Birds, beasts, trees, flowers; Gnaws iron, bites steel Grinds hard stones to meal; Slays kings, ruins town And beats high mountain down The Cryptogram of the answer is... The coding matrix used was...

18 I am your goal :) 12 3 Cryptogram Coding Matrix

19 What if we want to code messages longer than 4 letters long? In the video link, there is an example where someone codes and decode the message: "MATH IS AWESOME" Exceed Standards level of code breaking On next assessment, you will have the option to decode a message that is longer than 4 letters long.

20 Cryptogram HW: Checkpoint 6 and 7 from Chap 8.4 & Riddle! If you still need help getting this: See the examples 6, 7 right before the checkpoints. CREATE a riddle whose answer is a word or message 1) Write the word as a matrix of numbers 2) Choose a coding matrix 3) Create the Cryptogram for your message 4) Solve for the Key 5) Verify and decode your own cryptogram Then on a separate piece of paper, write the following: 1) The riddle 2) The Cryptogram 3) The coding matrix

Riddles in the Dark. By J. R. R. Tolkien

Riddles in the Dark. By J. R. R. Tolkien Riddles in the Dark By J. R. R. Tolkien Adapted for reader s theatre from The Hobbit, Houghton Mifflin, 1966 GENRE: Fantasy CULTURE: THEME: Little guy vs. big; riddles GRADE LEVEL: 5-9 ROLES: 6 TIME: 10