WENTIB ETGONR LOCLAA

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• WENTIB ETGONR LOCLAA
• CUROLT OSYGGW MIPYEO

WELCOME TO USING CRYPTOLOGY IN ALGEBRA TWO
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Using Cryptology in Algebra II

• How to use matrices to show basic cryptology
  techniques

Kevin Giffhorn Liberty High School Eldersburg,
Maryland (Carroll County)
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Todays Objective

• Encode First or Last name (about 8 letters long)
• Have neighbor decode it
• Leave with working project

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Abbreviated History of Cryptology

• Caesar Square
• GOOD AFTERNOON ALL

GARN OFNA OTOL DEOL
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Abbreviated History of Cryptology

• Simple letter replacement
• GOOD MORNING
• BACK 2

EMMB KMPLGLE
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Limitations with previous methods

• Caesar Square
• Possible to see a bit of the code by jumping in
  order
• GARN OFNA OTOL DEOL
• Simple letter replacement
• Each letter has the same meaning
• EMMB KMPLGLE (ex. M O)

Return
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Matrix Project

• Use 1x2 matrices to encode message
• No recognizable pattern between letters and
  numbers
• Virtually unbreakable without computers

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Project Requirements

• School appropriate message
• Maximum number of characters
• Show all work with encoding/ decoding
• Enigma message
• Paper
• Why encoding is important in society
• Suggestions to improve the encoding/ decoding
  process

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Suggestions

• Class against class
• Give them sample 2x2 key matrices with a
  determinant of 1 (no decimals or rounding errors)
• First example in class
• Dry run before switching class papers
• Severe penalties for erroneous encryption

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Matrices 202 (2x2 Matrices)
Determinant Down Diagonal
Up Diagonal 33 24
9 8 1
A
opposite
A-1
A-1
switch
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Matrix Multiplication
1 x 2 2 x 2
1 x 2

Rows Columns

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Encoding- Simple replacement

• G I F F H O R N
• 7 9 6 6 8 16 19 14
• 7 9 6 6 8 16 19 14
• Spaces 0
• Fill in extra character at end with space
• Why dont we leave the
• message like this?

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Encoding with Key Matrix

• Key
• G I F F H O R N
• 7 9 6 6 8 16 19 14
• 7 9

ENCODED!
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Encrypted Message

• GIFFHORN
• Simple Letter-Number Replacement
• 7 9 6 6 8 16 19 14
• Encrypted with Key Matrix
• 39 55 30 42 56 80 85 118
• Each letter is encrypted using two letters

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Decryption
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If encrypted with
Decrypt with
A-1
39 55
7 9
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Decryption

• Message encrypted with Key Matrix
• 39 55 30 42 56 80 85 118
• Message decrypted with inverse key matrix
• 7 9 6 6 8 16 19 14
• Replace numbers with letters
• 1 A, 2 B, , 25 Y, 26 Z, 0 SPACE

G I F F H O R N
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Hands-On

• Encrypt your last name
• Use Key Matrix
• Have someone next to you Decrypt with
• Decryption Matrix

A
A-1
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Final Suggestions

• NSA Field Trip
• Digital Fortress Dan Brown
• Extra Credit (not on tests)
• Paper Spelling, Grammar
• http//teacherweb.com/MD/LibertyHighSchool/MrGiffh
  orn

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In case you were curious
First Slide