Implementing-cryptography-using-python

Chapter 4 ■ Cryptographic Math and Frequency Analysis 119
Because we started with a 3 × 3 encoding matrix, we will break the enumerated
message into a sequence of 3 x 1 vectors:
16
18
05
16
01
18
05
27
20
15
27
14
05
07
15
20
09
01
20
05
27
There are only 20 characters in the message; since we have a matrix with 21
positions, we need to populate the last position with a space (27) to complete
the last vector. We may now encode the message by multiplying each of the
preceding vectors by the original encoding matrix:
– 3– 3–
4
0 1 1
4 3 4
16 16 05 15 05 20 20
18 01 27 27 07 09 05
05 18 20 14 15 01 27
This will produce the following encoded message that can be transmitted
in a linear form:
−122, 23, 138, −123, 19, 139, −176, 47, 181, −182, 41, 197, −96, 22, 101, −91, 10, 111,
−183, 32, 203
To decrypt the message, the recipient writes the message as a sequence of a
3 × 3 matrices and uses the inverse of the encoding matrix:
1 0 1
4 4 3
– 4– 3–
3
With the inverse, you can perform matrix multiplication on the received
message:
1 0 1
4 4 3
– 4– 3–
3
– 122 – 123 – 176 – 182 – 96 – 91 183
23 19 47 41 22 10 32
138 139 181 197 101 111 203
The matrix multiplication should produce the following:
16 16 05 15 05 20 20
18 01 27 27 07 09 05
05 18 20 14 15 01 27
Once you have the matrix calculated, you should be able to expand the message
and map the numbers back to their original letters:
P R E P A R E T O N E G O T I A T E
16 18 05 16 01 18 05 27 20 15 27 14 05 07 15 20 09 01 20 05