Question 1192792: MAT 145: Topics In Contemporary Math
QUESTION 12
Convert the message “MAC IS A CAT” using the encryption e = (7m + 3) mod 26. A table showing number values for the letters is below.
A
B
C
D
E
F
G
H
I
J
K
L
M
0
1
2
3
4
5
6
7
8
9
10
11
12
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
13
14
15
16
17
18
19
20
21
22
23
24
25
Find the numerical representation of the message.
Find the encryption for the numbers.
Convert the encrypted numbers back to letters.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
In this message, although the presentation is formatted very poorly, it appears that you are defining A=0, B=1, ..., and Z=25. That would be in line with the fact that you are doing an encryption mod 26, with the results being from 0 to 25 instead of from 1 to 26.
And that would make my responses to the other questions you submitted incorrect -- but that was because you didn't define your questions clearly.
The process here is straightforward; there is no point in our doing the whole problem for you. But there is one part of your question that you might need some help with.
Let's look at just one letter to
(1) find the numerical representation of the letter;
(2) find the encryption (encrypted letter) for that number; and
(3) convert that encrypted number back to a letter
The first letter in the message is M.
(1) the way I read your post, M is 12, not 13.
(2) the encryption of 12 is (7*12+3) mod 26 = (87) mod 26 = 9. That would apparently correspond to the 10th letter in the alphabet, which is J.
Those two parts are straightforward.
For the decryption, we need to find the number n for which 7n+3 is equal to 9 plus some multiple of 26:
n and 3k are integers, so (5k+6)/7 has to be an integer. The elementary (and fastest) way to find k is to list the integers of the form 5k+6 to find the smallest one that is a multiple of 7:
6, 11, 16, 21
So
5k+6=21
5k=15
k=3
26k+9=78+9=87
7n+3=87
7n=84
n=12
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