1.What subjects should you know to play the code cracking game?

Transcription

1 Mathematics: Modeling Our World Unit 2: SECRET CODES HANDOUT VIDEO VIEWING GUIDE 1.What subjects should you know to play the code cracking game? H What is the Zimmermann telegram? 3.How were secret messages coded during World War II? 4.How can machines read zip codes? 5.Why is a check digit used in zip codes? 6. Who are the mathematicians responsible for devising a code for space communications? 7.What are some damages a code cracker might do? 8. On what idea is public-key cryptography based? 145

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3 Mathematics: Modeling Our World Unit 2: SECRET CODES HANDOUT UNIT PROJECT Do you enjoy solving puzzles or figuring out mysteries? Are you good at cracking secret codes? In this unit project, you will use mathematics to design a coding process and create a secret message that can easily be decoded by the person to whom you are sending the message, yet difficult to crack by an unwelcome person who might intercept the message. H2.2 page 1 of 2 1.Decide on an appropriate message to send in a coded form. The message must have at least 25 words. 2.Develop your own coding system or build a coding device. Use mathematical ideas from this unit in the system you design. 3.Use your system or device to encode the message. 4. Describe the process to decode the message. Use diagrams, tables, and graphs when appropriate. 5.Show how mathematics may be used by the code cracker to break your code. Explain how math reveals patterns in the coded message. 147

4 HANDOUT Unit 2: SECRET CODES Mathematics: Modeling Our World H2.2 page 2 of 2 ALTERNATIVE PROJECT IDEAS 1. Prepare a research paper or presentation on public-key cryptography. 2.Read The Gold Bug by Edgar Allan Poe and The Adventure of the Dancing Men by Arthur Conan Doyle. Discuss the use of codes in both stories. 3. Interview a cryptographer. Write a report. Include actual examples of messages that have been encoded and messages that have been deciphered. 4.Give a presentation or write a report about the Gronsfeld system or a Gronsfeld cryptogram. A starting place for this investigation is Solving a Jules Verne Cryptogram by Frederick Gass (see Teacher s Background Reading 2.1). 5. Do a comparative study of letter frequencies in different languages. Identify clues that might indicate the original language of a plaintext message. 6.Investigate the use of codes in children s games and toys. Find a variety of different code toys at a toy store. Report on the mathematics behind each coding system. Discuss ways to crack messages coded with each toy. 7. Research past and present uses of codes to communicate information quickly and efficiently. Examples include Morse code, bar codes, and binary codes. Discuss the mathematics related to each type of code. 148

5 Mathematics: Modeling Our World Unit 2: SECRET CODES HANDOUT USING LIST OPERATIONS ON THE TI-83 CALCULATOR FOR CODING Although the instructions in this handout are for the TI-83 calculator, they also apply to other calculators. Even when the syntax is significantly different, this handout provides you with the kinds of operations needed in general and may still help with your particular calculator. H2.3 page 1 of 2 There are two basic ways of working with lists on the TI-83: using the Home screen and using the STAT Edit screen. This handout shows both methods. The instructions below use L1 for the plaintext values, L2 for the values after the first step of coding, and L3 for the final coded values. Other lists may be used instead, and you may elect to display the coding without showing the intermediate step. HOME SCREEN OPERATIONS Figure 1. Calculator screen after filling list L1 from Home screen. Open a brace, enter your numbers separated by commas, close the brace, and store the result in a list, say L1. Note that the brace keys are the yellow parenthesis keys. The list name, L1, is the yellow 1 key. Your home screen should look like Figure 1 after you press ENTER. The second line on the screen can be scrolled before you touch any other keys, the cursor keys permit you to move to the right to see the rest of the list. Try it. To carry out the c = 4p + 5 coding process, remember that list L1 holds the plaintext values (the ps). To place the 4 * p values in L2, type 4 * L1, then STO, then L2, and ENTER. The screen will look something like Figure 2. Again, the second line can be scrolled. Complete the coding by entering L2+5 STO L3. Although you now know that all this can be done from the Home screen, the real value of calculator lists is that they permit a tabular view of the message. To see that view, press STAT, then select Edit. You should see something like Figure 3. Figure 2. Coding L1 using the 4p process on the Home screen. Figure 3. List table of 4p + 5 coding of the alphabet. 149

6 HANDOUT Unit 2: SECRET CODES Mathematics: Modeling Our World H2.3 page 2 of 2 STAT EDIT OPERATIONS If you have completed the above operations, you will have the plaintext and coded values already in lists L1 and L2. To start over with clear lists, move the cursor to the header of L1 (Figure 4), press CLEAR, then ENTER. Figure 4. List cursor on the L1 header before clearing. Repeat the same process to clear L2 and L3. Be sure your cursor is in the first location in L1, then enter each of the original plaintext position numbers. Note that as you press ENTER after each value, the cursor automatically drops down to the next row of the table. After entering the plaintext position numbers, move the cursor to the header of L2, then type 4*L1, as shown in Figure 5. Note that the formula you type appears at the bottom edge of the table. Figure 5. Coding L1 with the 4p process on the STAT Edit screen. Pressing ENTER completes this step. Move to the header of L3 and enter the formula L2+5 to complete the coding process. You should see the same results as in Figure

7 Mathematics: Modeling Our World Unit 2: SECRET CODES HANDOUT MICROSOFT EXCEL NOTES Label the columns: In the first row of column A, type the letter p and press ENTER, RETURN, or TAB. (Note the behavior of the cursor. Pressing each key has a somewhat different effect; try each one.) Label column B as 4p and column C as 4p+5. Enter the plaintext position numbers: In cell A2, type the number 1 and press return. In cell A3, type the number 2. Repeat until the position numbers 1 26 have been entered into cells A2 through A27. Enter the formulas for the coding process: In cell B2, type the formula =4*A2. The equals mark lets Excel know that a formula is coming (instead of a number or label). After entering the =4*A2 formula in B2, enter the formula =B2+5 in cell C2. Extend the formulas from cells B2 and C2 down to code the other position numbers of column A: Excel provides several ways to extend the formulas. The easiest is the Fill Down command. For all versions of Excel, one way to use this command is first to highlight (using a click and drag ) the entire region to be affected, including both the formulas to be extended and the cells into which the formulas are to go. Here, highlight cells B2 C27. Next, select Fill Down under the Edit menu, and the operation is complete. For later versions of Excel (version 3.0 or later), you can do all this without using the Edit menu. First highlight the two source cells, B2 and C2. Notice that in the lower right corner of the highlight there is a small square. Click and drag on that square, pulling it down to cell C27. When you release the click, the Fill is completed. See Figure 1 for a sample screen. Note the small square in the corner below the value 9. H2.4 Figure 1. Preparing to Fill Down using Excel. 151

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