Guess My Word Mr. Nan Wang, C2PRISM Fellow Mr. Gerardo Stricker, Pre-CalculusTeacher Add extra privacy to our communications! – how is it done?

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Presentation transcript:

Guess My Word Mr. Nan Wang, C2PRISM Fellow Mr. Gerardo Stricker, Pre-CalculusTeacher Add extra privacy to our communications! – how is it done?

Motivation Class if I asked you how World War II was won what would you say? (possible responses: strategy, planning, superior armaments, etc.) Well all that is true but I would say that it was won by MATH. What you say? Yes by MATH. You see, there was a secret war going on behind the scenes. A war to intercept enemy communications and figure out the plans of the enemy before they were actually carried out. This saved lives and helped us to carry out successful battlefield strategies. This required many mathematicians and this work eventually led to the invention of the first computer which was kept secret after the war for about 30 years For more on this, rent the video THE ENIGMA MACHINE, a good World War II film Today we will discover how to use MATRICES and MATRIX MATH to encode and decode secret messages.

Code Table A1H8O15V22 B2I9P16W23 C3J10Q17X24 D4K11R18Y25 E5L12S19Z26 F6M13T20space0 G7N14U21 Code Table: Translate between English and numbers. “GOOD”  [7, 15, 15, 4] [13, 1, 20, 8]  “Math”

[-6, 16, -10, 36 ] Use matrix A to solve the word:  “HARD” [8, 1, 18, 4 ]

[-8, 36, -4, 44, ] [?, ?, ?, ? ] Matrix A works like a “key”. [#1, #2, #3, #4 ]  “REVIEW” A1H8O15V22 B2I9P16W23 C3J10Q17X24 D4K11R18Y25 E5L12S19Z26 F6M13T20space0 G7N14U21

How is it done? Math is working behind the scene! If than

1.Pick a 4 to 6 letter word. [ ] 2.Pick a simple 2x2 matrix – call it matrix “S” for secret. (Make sure your matrix “S” is invertible!) A1H8O15V22 B2I9P16W23 C3J10Q17X24 D4K11R18Y25 E5L12S19Z26 F6M13T20space0 G7N14U21

4.Put the result above in sequence into a new 1xN matrix – matrix “E” for Encrypted. My E=[ ] 5.Calculate the inverse matrix of “S” – the inverse of “S” is matrix “K” for Key. 3.Multiply matrix S to your original word, two letters at a time. (Note: If your word has odd number of letters, add a space in the end to make it even.)

Now give the encoded sequence “E” and your key matrix “K” to others and see whether they can figure out what your original word is! A1H8O15V22 B2I9P16W23 C3J10Q17X24 D4K11R18Y25 E5L12S19Z26 F6M13T20space0 G7N14U21