TOP SECRET – DO NOT BEND
NAME: ___________________
Federal Bureau of Investigations
3020 Rucker Avenue
Everett, WA 98201
To Whom It May Concern:
You have been selected for a special task, which may prove vital
to protecting the future of the United States of America. Your
mission, if you choose to accept it, is to create a new
encryption code that will permit vital communications to travel
untapped along insecure lines.
You must use matrices to create your secret code. You will
encode a message using your cipher and pass it along to a fellow
agent so they may decode it.
To create your encrypted message, you must have 3 components:
 A key for converting the letters and symbols you wish to
represent into numbers,
 An encryption matrix,
 A decryption matrix, which will be the inverse of your
encryption matrix.
The key that the FBI has selected to use for converting
alphanumeric symbols into numbers is presented to you in the
following tables:
Input
a
b
c
d
e
f
g
h
i
j
k
l
m
Output
10
11
12
13
14
15
16
17
18
19
20
21
22
Input
n
o
p
q
r
s
t
u
v
w
x
y
z
Output
23
24
25
26
27
28
29
30
31
32
33
34
35
Input
!
?
*
Output
62
63
64
Input
.
,
/
Output
68
69
70
Input
A
B
C
D
E
F
G
H
I
J
K
L
M
Output
36
37
38
39
40
41
42
43
44
45
46
47
48
Input
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Output
49
50
51
52
53
54
55
56
57
58
59
60
61
$
#
@
65
66
67

(
)
Space
71
72
73
The numbers 0-9 are represented by 0-9 (no change).
For example:
“Sally went to the store.” would convert to:
54 10 21 21 34 73 32 14 23 29 73 29 24 73 29 17 14 73 28 29 24
27 14 68
Now that we have a message represented as numbers, we must fit
it into a matrix. The example message is 24 characters long and
can therefore fit easily into a matrix, but for messages with
prime numbers of characters, you may pad the end with
whitespace. Try to keep the number of rows low, as these will be
multiplied by our encryption matrix later on. Our example,
formatted as a 6x4 matrix, is below:
54
34
23
𝑀=
24
14
[24
10
73
29
73
73
27
21
32
73
29
28
14
21
14
29
17
29
68]
It is now time to create an encryption matrix. You will multiply
your message matrix by the encryption matrix to cipher the
message it contains. Then the recipient will multiply it by the
inverse of the encryption matrix – the decryption matrix – to
turn it back into the original, clear text message. Therefore,
it is vital that your encryption matrix be invertible. If not,
there will be no way to decrypt your message! Equally important
is that your encryption matrix must remain secret; otherwise the
security of your code will be compromised.
The encryption matrix can contain whatever numbers you want, as
long as it is invertible. It must be a square, and contain the
same number of rows as the message matrix has columns. For
example:
7
1 5
4
3 9
𝐸=[
−1 −9 2
0
1 8
8
4
]
6
4
Then multiply your message matrix by your encryption matrix to
get your encrypted message:
397
498
204
𝑀𝐸 =
431
362
[262
−84
−21
−518
−1
10
47
570
1003
754
971
1015
935
682
812
854
726
688
656]
Once your partner has your encryption key, they can decode the
original message by multiplying it by the inverse of the key:
𝑀 = 𝑀𝐸𝐸 −1
This will give them back the original message (with text still
represented by numbers). Then simply use the provided table to
convert the numbers back to the original text.
Now you must create an encoded message using your own encryption
matrix. Follow the steps below to do so.
1. Write your original message text.
2. Write the series of numbers which represent it, using the
table provided.
3. In the space below, determine a matrix which your message
will fit into. Remember, the more rows you have, the larger
your encryption matrix will have to be.
4. Write a square encryption matrix with the same number of
columns as your message matrix has rows. Ideally, use a
cryptographically secure pseudorandom number generator to
determine the numbers within it. Remember, this matrix must
be invertible or your message will not be decodable!
5. Multiply your message matrix by the encryption matrix and
write down the result below.
6. Cut this paper on the dotted line, and pass it to your
neighbor so they can test your encryption.