**Mathematics of Information Security**

Computer Lab 2. M360. Friday 9/17/2004

** Opening the program:**

1) Open (My computer -> Math on Pop G: -> m360).

2) Open (My computer -> local disk c -> temp).

3) Move the file "crypto.mws" from 1) to 2) (Zube wants it done this way).

4a) Either double click on "crypto.mws" or do 4b).

4b) Open Maple 9.5 and open the file "crypto.mws" from c:temp.

5) Press "return" somewhere in the midst of the file and ignore the warning signs.

** Goals for today:**
(These problems are all part of the homework set due Friday 9/24, so you can try whichever you like).

1) Decryption problems: 2.14 #8,9.

2) Number theory problem:

Pick a large prime p (2 digits).
For each number a between 1 and p-1, compute powers a, a^2, a^3, ... mod p.

Find the smallest positive number e so that a^e = 1 mod p.
The number e is called the order of a mod p.
Make a list of all these orders.

A. What is the largest number on the list?

B. What is the smallest positive number E so that every e divides E?

C. If you know the order of a mod p and the order of b mod p, can you find the order of ab mod p?

3) Encryption problem:

Pick two numbers m and n.

What is the period if you encrypt a message first with a Vigenere cipher of period m and
then encrypt the ciphertext with a Vigenere cipher of period n?

Experiment with this a bit, choosing a message and two keys, and compare your data with your neighbor.

The answer depends on m and n but it can be a bit subtle depending on your choice.

** Printing:**

Do not print your whole document. It is too long. Open a new file and copy the good stuff.