A one-to-one function and its inverse can be used to make information secure. Th
ID: 3112598 • Letter: A
Question
A one-to-one function and its inverse can be used to make information secure. The function is used to encrypt a message, and its inverse is used to decrypt the encrypted message. The following numerical values are assigned to each letter of the alphabet: Using the function f(x)=3x-1, the message "HELLO" would be encrypted 23 14 35 35 44 since H corresponds to 8 and f(8)=3(8)-1=23, etc This week, each student is to use a one-to-one function to encode a word or phrase that relates to some topic that we have covered in [his class. Post your function and your encrypted message to the discussion forum by selecting "Add a new discussion topic" below. Label the Subject with your name. Then, choose four of your classmate's posts to decrypt. Select a message that has not already been decoded. You will need to first find your classmate's inverse function, explaining carefully how you determined it. Then decrypt the message. Put all of this information in your reply post.Explanation / Answer
lets use a one to one function
f(x) = 8x - 5
the message " VICTORY" would be encrypted as
V corresponds to 22
f(22) = 8(22) - 5 = 171
I corresponds to 9
f(9) = 8(9) - 5 = 67
C corresponds to 3
f(3) = 8(3) - 5 = 19
T corresponds to 20
f(20) = 8(20) - 5 = 155
O corresponds to 15
f(15) = 8(15) - 5 = 115
R corresponds to 18
f(18) = 8(18) - 5 = 139
Y corresponds to 25
f(25) = 8(25) - 5 = 195
encrypted message is 171 67 19 155 115 139 195
to decrypt the message
inverse of the function is
f^-1 (x) = ( x+5) / 8
f^-1 (171) = ( 171 + 5) /8 = 22 ----> V
f^-1 (67) = ( 67 + 5) /8 = 9 ----> I
f^-1( 19) = ( 19+ 5) / 8 = 3 --- > C
f^-1 ( 155 + 5) / 8 = 20 ---> T
f^-1 ( 115 + 5 ) /8 = 15 --- > O
f^-1 ( 139 + 5 ) / 8 = 18 ---> R
f^-1 ( 195 + 5 ) / 8 = 25 --- > Y
hence message is " VICTORY "
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