Daniel C.
asked • 08/26/15have no idea where to start cryptography
Assume you are a spy. You need to send an encrypted message to MI6, the fictional headquarters for James Bond. Your task is to use a one-to-one function to encode your message using the table below.
A
B
C
D
E
F
G
H
I
J
K
L
M
1
2
3
4
5
6
7
8
9
10
11
12
13
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
14
15
16
17
18
19
20
21
22
23
24
25
26
You decide to use a one-to-one function, 8_6.png to encode the message. Agents at MI6 will use its inverse function to decode the message.
To exchange the message "BE VERY CAREFUL", you will send:
7
16
67
16
55
76
10
4
55
16
19
64
37
because B corresponds to 2 and f(2) = 7. E corresponds to 5 and f(5) = 16. Agents at MI6 will use the inverse function 8_6_1.png to decode your message. For example, 8_6_2.png which corresponds to B.
Your mission, should you choose to accept it, is to:
define your own one-to-one function (initial post), and
send an encoded message back to MI6 (initial post), and
decode your fellow agent's message to you (response post to another student).
A
B
C
D
E
F
G
H
I
J
K
L
M
1
2
3
4
5
6
7
8
9
10
11
12
13
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
14
15
16
17
18
19
20
21
22
23
24
25
26
You decide to use a one-to-one function, 8_6.png to encode the message. Agents at MI6 will use its inverse function to decode the message.
To exchange the message "BE VERY CAREFUL", you will send:
7
16
67
16
55
76
10
4
55
16
19
64
37
because B corresponds to 2 and f(2) = 7. E corresponds to 5 and f(5) = 16. Agents at MI6 will use the inverse function 8_6_1.png to decode your message. For example, 8_6_2.png which corresponds to B.
Your mission, should you choose to accept it, is to:
define your own one-to-one function (initial post), and
send an encoded message back to MI6 (initial post), and
decode your fellow agent's message to you (response post to another student).
More
1 Expert Answer
Shradha S. answered • 08/26/15
Tutor
4
(1)
Experienced Maths Teacher with Master's Degree in Mathematics
the one to one function will be f(x)= 3x+1 :as
B->2: f(2)= 7 = 3*2 + 1
E->5: f(5)= 16 = 3*5 + 1
v->22:f(22)= 67 =3*22 + 1..and so on
inverse if this will be : y= 3x+1
y+1 =3x
(y-1)/3 =x =f(y)
replacing y by x,
so the inverse function will be given by f(x)= (x-1)/3
Daniel C.
so how do i write the message owned?
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08/26/15
Shradha S.
I think using this function you need to write some message .suppose you want to send message "ATTACK".
you will send the encoded message 4 61 61 4 10 34 to your friend and then using inverse function your friend will decode this message. I am not getting how to use 8_6.png format in the message.
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08/26/15
Shradha S.
I think you are supposed to send a message to your friend using this function.suppose you want to send message "ATTACK" then you will send 4 61 61 4 10 34 and your friend will decode your message using inverse function .But I am not getting the point how to use the format 8_6.png in the message.
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08/26/15
Shradha S.
"ATTACK" you will send 4 61 61 4 10 34.
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08/26/15
Shradha S.
suppose you want to send message"ATTACK" then you will send 4 61 61 4 10 34
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08/26/15
David W.
EXECUTIVE SUMMARY: In answer to your question, “How do I write the message owned?” I think the problem asks you to write your own message (but, remember, it won’t stay secret for long) and then to use the position value of each letter as input to the function f(x) to encode the message [and I would recommend that you use the inverse function to decode your message before you send it, just to insure that the function is one-on-one and works for your message].
- - - - - - - - -
Your mission (have you accepted it?) starts with defining a one-to-one function that only you and your fellow agent (and your teacher and anyone else who can read your post and …) knows. O.K., so, maybe it’s not so secret. The important thing about this function is that it is one-on-one. That means that the input value x generates at most one output value y when using the function and that the inverse function also generates at most one output value for any input value given it. [This problem is really about inverse functions, not spy secrets, isn’t it? – I’ll take a few minutes to write about math, but I have other secret projects to work on.]
Before posting your one-on-one function, be sure that is works with input numbers 1-26 (for the entire alphabet, and maybe allows for a space (which the example didn’t), and maybe allows for punctuation, and maybe allows for numbers, and if it allowed for pictures I wouldn’t have to guess what the pictures were in this WyzAnt Answers post. But, let’s get back to the math. Also be sure that the inverse of your function works -- I’d recommend decrypting your own message before you post any function that people might say is not one-on-one.
You might already have thought of a message to send. Keep it simple, but not so easy that someone can decrypt it without doing all the calculations to the very end of the message. The message “BE VERY CA…..” could be guessed early.
Send the encrypted message to you fellow agent (student) at MI6.
Now, as Shakespeare would say, here’s the rub. If you are to decode a different student’s message (other than the one you already agreed with about your secret function and the inverse function), you will have to first agree with them about their secret function so you can use the inverse of that function to decrypt the message they send. Now, if everyone posts their function along with their message, this surely is “spy school,” not MI6. And, I presume that you must post the cleartext after you have decoded the message and the teacher and the other student and anyone else who … Well, it’s not secret at all!
In answer to your question, “How do I write the message owned?” I think the problem asks you to write your own message (but, remember, it won’t stay secret for long) and then use the position value of each letter and the function f(x) to encode it [and I would recommend that you use the inverse function to decode you message before you send it, just to insure that the function is one-on-one and works for your message].
Before posting your one-on-one function, be sure that is works with input numbers 1-26 (for the entire alphabet, and maybe allows for a space (which the example didn’t), and maybe allows for punctuation, and maybe allows for numbers, and if it allowed for pictures I wouldn’t have to guess what the pictures were in this WyzAnt Answers post. But, let’s get back to the math. Also be sure that the inverse of your function works -- I’d recommend decrypting your own message before you post any function that people might say is not one-on-one.
You might already have thought of a message to send. Keep it simple, but not so easy that someone can decrypt it without doing all the calculations to the very end of the message. The message “BE VERY CA…..” could be guessed early.
Send the encrypted message to you fellow agent (student) at MI6.
Now, as Shakespeare would say, here’s the rub. If you are to decode a different student’s message (other than the one you already agreed with about your secret function and the inverse function), you will have to first agree with them about their secret function so you can use the inverse of that function to decrypt the message they send. Now, if everyone posts their function along with their message, this surely is “spy school,” not MI6. And, I presume that you must post the cleartext after you have decoded the message and the teacher and the other student and anyone else who … Well, it’s not secret at all!
In answer to your question, “How do I write the message owned?” I think the problem asks you to write your own message (but, remember, it won’t stay secret for long) and then use the position value of each letter and the function f(x) to encode it [and I would recommend that you use the inverse function to decode you message before you send it, just to insure that the function is one-on-one and works for your message].
Report
08/27/15
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David W.
08/27/15