1. MAT 1000 Mathematics in Today's World Winter 2015

2. Last Time We looked at the Caesar cipher and modular arithmetic

3. Today We will take a look at the decimation cipher, linear cipher and Vigenère cipher.

4. Decimation cipher For the Caesar cipher we added a set number and worked mod 26. For the decimation cipher we will multiply by a number (called the key) and work mod 26. To encode: Multiply the assigned number by the key and find the mod 26 representative.

5. Decoding with the decimation cipher To decode: Add multiples of 26 to the assigned number until we get to a multiple of the key. Divide by the key to get the decoded number (which can be used to find the decoded letter)

6. Let’s do some examples

7. Linear Cipher The linear cipher is a combination of the Caesar Cipher and decimation cipher We take the numerical representative of each letter (we will denote as x) and replace it with the letter represented by kx+s mod 26 We call k the key and s the shift To decrypt, work backwards

8. Examples

9. Vigenere Cipher For the Vigenere Cipher we pick a key word or phrase We determine the numerical value of each letter to see how much each letter of our encrypted message will be shifted. If necessary, we repeat the key word or phrase.

10. Examples