Cryptography and Secret Codes

1 / 11

# Cryptography and Secret Codes - PowerPoint PPT Presentation

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:

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Cryptography and Secret Codes' - toby

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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:
• So that “FWJH” becomes “6 23 10 8”
• Can you come up with another example?
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
• 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 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 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 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
• 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
• 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