1. (4 pts) Fill out the addition and multiplication tables for modulo 2 arithmetic. Keep in mind this means that the only numbers you should be putting in the tables are either 0 or 1! J

2a. (6 pts) Recall that the even integers are {0,2,4,6,8,10,12,…} and the odd integers are {1,3,5,7,9,11,…}.

Have you ever noticed that when you add two even integers together you always obtain an even integer as a result? (For example 2+4=6, 4+4=8, 34+66=100) Also, have you ever noticed that when you multiply two even numbers you also get an even number? (For example: 2×6=12, 4×6=24, 60×22 = 1320)

I’d like you to take cases on adding and multiplying numbers and comment on the results based on whether or not the numbers you experiment with are even or odd. For example, since two even integers always add to an even, I’ve indicated this in the left table below. Since two even integers multiply to an even number, I’ve indicated this in the right table below. Fill out the rest!

2b. (3pts) How do the tables in 2a relate to the tables from problem 1? Explain in detail.

3. (5 pts for each table) Fill out the addition/multiplication tables for modulo 7 arithmetic. Hey look, I already got you started!

[Keep in mind the numbers that go in your table must be 0,1,2,3,4,5,or 6!]

EXTRA CREDIT (+1 points): Color in the tables the way we did in class!

MORE EXTRA CREDIT (+1 points) Describe any strange or cool patterns you see. In detail!

4. (3 pts) Use the website (https://www.dcode.fr/caesar-cipher) to decode the following message:

Wynevkb kbsdrwodsm mkx lo ecopev pyb oxmbizdsxq combod wocckqoc!

a) To do this, copy and paste this into the Caesar Cipher Decoder box.

b) Click on Decrypt (Just make sure the Test All Possible Shifts option is selected)
c) Look at the Results tab on the left-hand side of the page! There you will see all possible ways of shifting the letters around along with the shifting value. (This is just the how far we moved each letter in the original sentence to obtain this encrypted one.)