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Cryptography and Secret Codes. or one reason that linear equations are cool. Basic Cryptography Code. Romans would use this type of code Here “LINEAR” becomes “ OLQHDU ” What would “ HTXDWLRQ ” be?. Numerical Code. We can do more if we change letters into numbers:

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cryptography and secret codes

Cryptography and Secret Codes

or one reason that linear equations are cool.

basic cryptography code
Basic Cryptography Code
  • Romans would use this type of code
  • Here “LINEAR” becomes “OLQHDU”
  • What would “HTXDWLRQ” be?
numerical code
Numerical Code
  • We can do more if we change letters into numbers:
  • So that “FWJH” becomes “6 23 10 8”
  • Can you come up with another example?
numerical codes
Numerical Codes
  • Or we can even modify this code!
  • Here “FWJH” becomes “9 26 13 11”
  • Writing code like a table is hard though.
  • Can you think of a simple rule to describe this code?
linear codes
Linear Codes
  • The rule we came up with “Change it to a number and add 3” is a linear code
  • It is more easily written with the linear equation y=x+3
  • To encode “MUSTANGS” first change each letter to a number, and then apply the linear equation
  • M  1316;U 2124; etc.
linear codes1
Linear codes
  • How would you write “MUSTANG ON” in the linear code y=2x+5?
  • First turn it into numbers: “13 21 19 20 1 14 7 21 14”
  • Then apply the linear code: “31 47 43 45 7 33 19 47 33”
  • Now try with the linear code y=-3x+80
  • How might we undo this?
linear block codes
Linear Block Codes
  • Linear block codes use more than one equation to make a code. How might you do this?
  • First take a message “CRYPTOGRAPHY” and break it up into blocks.
  • Here we will use block size 2, so CR-YP-TO-GR-AP-HY are the blocks.
linear block codes1
Linear Block Codes
  • You then need as many linear equations as your block size.
  • We need 2 equations, so let’s use y=2x+5 and y=-3x+80
  • To make a code for CRYPTOGRAPHY, first take the first block ‘CR’ and encode it.
  • C  3  2*3+5=11; R  18  -3*18+80=26
  • So ‘CR’ becomes ‘11 26’. What is the rest of the code?
a problem
A Problem
  • Now encode “BOOT” using this block system.
  • It becomes ‘9 35 35 20’
  • The problem is that ‘O’ is encoded as ‘35’ for both rules. This is called collision.
  • You can tell there is a double letter.
  • To see this, solve the equation 2x+5=-3x+80 for x.
review
Review
  • Codes: Assign a new symbol to each letter
  • Numerical Codes: Use numbers as the symbol
  • Linear Codes: Use linear equations to change the numbers
  • Linear Block Codes: Use more than one linear equation at a time
  • Collision: When the same letter is changed to the same number in a linear block code