Math 1314.P02 Spring 2018 Lab 4 Due 4/9 Information: Cryptology is the science o
ID: 3734722 • Letter: M
Question
Math 1314.P02 Spring 2018 Lab 4 Due 4/9 Information: Cryptology is the science of making and breaking codes. This lab explores how the idea of functions and their inverses can be used to encode and decode messages. To encode and decode a message, first replace each letter of the alphabet with a positive integer using the following code, thus rewriting the original message as a series of numbers: K-11 L-12 M-13 N-14 P-16 Q-17 R- 18 S-19 U-21 V- 22 W-23 X- 24 Z- 26 G-7 H-8 27 Period-28 D-4 ENCODING: A one-to-one function can be used to encode a numerical message. Suppose you want to send the message MATH to a friend, and you have decided that the function fx)-3x+4 will be the encoding function. This function simply describes the procedure used to create the encoded message-in this case multiply by 3 and add 4 First change the letters to corresponding numbers as shown above: 13 1 20 8. Then use these as the input values in f(x). f(13) 3(13)+4 43 f(1) 7 f(20) 64 f(8) 28 So the encoded message that you send to your friend is: 43 7 64 28 NOTE: A graphing calculator can be used to evaluate a function as above: i. Press [Y-Lon the calculator. Type 3x+ 4. i. Choose [2ndTWINDOW] (TBLSET). Set the independent variable to Indpnt: Ask ii. Then choose [2nIGRAPHI (TABLE). Input each x value (13 1 20 8). The calculator will return the function values 64 28) which is the encoded DECODING an encoded message: Now it is up to your friend to decode the message. Decoding is the process that "undoes" the encoding process. If f(x) encodes the message, what will decode it? The inverse of f(x) or f'(xSo(x) will be the decoding function. x-4 In the example, the inverse of fx) 3x+ 4 can be shown to be f'Take the encoded message (43 7 64 28) and use these values as input values in f(x). That's the original numerical message! The last step is to convert back to letters using the table Now your friend knows the that you sent: MATHExplanation / Answer
2 a.
Collin Cougars
3 15 12 12 9 14 29 3 15 21 7 1 18 19
16 88 70 70 52 82 172 16 88 124 40 4 106 112
b Inverse of x:
f-1(x) = (x + 2)/6
c
94 88 10 88 22 148 160 112 172 82 28 106 34 28 16 118
16 15 2 15 4 25 27 19 29 14 5 18 6 5 3 20
d) If encoding function is not one to one , then it won't be possible to code
because there is more than one possibility for the encoded character and
even if we chose one option, decoding will be a problem beacuse which option
we have chosen should also get refelected in decoding and we neet to keep
that information also in the encrypted text.