StŠr­frŠ­imynstur Ý t÷lvunarfrŠ­i

Weekly note 7

This week we finish covering number theory by looking at the RSA cryptosystem on pages 191-194 in section 2.6. Then we will revisit proofs and look at sections 3.1 and 3.3

Next week we will cover counting in Chapter 4.

Below are 5 excercises that you are to solve and turn in to your section teacher before noon monday october 17th. Remember to mark your solutions with the number of your section and the name of the section teacher. Also below are few extra excercises that you can use to practice on and make sure that you have understood the material. Some of them will be solved in the sections if there is time.

Homework 7

  1. The string "QSJUVCHA" has been encrypted with Caesar cipher (see page 165). You must decode the string even though you do not know the encryption key. The key is a number from 1 to 25, which represents how far the letters of the alphabet are shifted. You will know the decoded string when you see it.

  2. In this exercise you will use the RSA cryptosystem to encrypt and decrypt Following the textbook we use the key n = 43*59 and e = 13. We only use english upper case letters and they are coded with the values 0 to 25 (i.e. A is 0, B is 1, etc.) It will be necessary for you to use some kind of software that can handle large integers to do this exercise, e.g. ARIBAS.
    1. Encrypt the word "BAUGUR" using the RSA method. Group two and two letters together and return three integers.
    2. Decrypt the message 2299 0468 over to letters with the RSA method. This will be a four letter word that you should know.

  3. Exercise 2 in section 3.1 on page 223 in the textbook.

  4. Exercise 20 in section 3.1 on page 224 in the textbook.

  5. Exercise 8 in section 3.3 on page 253 in the textbook.

Hand these exercices in before noon monday october 17th.

Also take a look at the following excercices:
From section 2.6:
45, 47.
From section 3.1:
3, 7, 23, 27, 49.
From section 3.3:
7, 13, 17, 21, 25, 39, 73.

Remember that the above exercises are for you to practice on, and that you get the most out of them by trying to solve them yourselves (not by looking at someone else solving them!). The exercises in bold are more "interesting" than the others and it is more likely that they will be covered in the sections.

hh (hja), October 10th, 2005.