Implementing-cryptography-using-python

118 Chapter 4 ■ Cryptographic Math and Frequency Analysis
# find the inverse of A
A_inverse = np.linalg.inv(A)
print (A_inverse)
# solve for X
X = A_inverse * B
print (X)
You can alternatively use the NumPy array method to accomplish the same
task, as shown here:
import numpy as np
# solve the following linear equation
print ('1a + 1b = 35')
print ('2a + 4b = 94')
# create equations
a = np.array([[1, 1],[2,4]])
b = np.array([35, 94])
# print answers
print (np.linalg.solve(a, b))
Now we will examine a practical example to show how matrices can be used
for encryption.
In this example, we will encrypt the message “prepare to negotiate.”
Message = “prepare to negotiate”
The encoding matrix for this example is as follows:
– 3– 3–
4
0 1 1
4 3 4
Assign a number to each letter in the alphabet much like you did for a Caesar
cipher. The letters do not have to map to the same numbers as long as both the
sender and receiver know the assignments. Python uses the ord() function to
assign a letter to a numerical value. You can convert the number back to a letter
using the chr() function.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
This message that we want to encrypt will look like the following:
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