Python | Encoding Decoding using Matrix
Last Updated :
30 Dec, 2020
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This article is about how we use the matrix to encode and decode a text message and simple strings.
Encoding process :
Take Encoded number convert into 2D matrix(array)
Inverse Encoding matrix!
Multiply Encoded matrix with inverse of encoding matrix.
convert to 1D Matrix(array).then convert to corresponding Alphabets.
Python3
Time Complexity : O(n)(where n is length of message)
Space Complexity : O(n)
Output:
Python3
Time Complexity : O(n)(where n is number of elements)
Space Complexity : O(n)
Output:
- Take a String convert to corresponding number shown below
- convert to 2D matrix(array). Now we have 2x2 matrix!
- When we multiply this matrix with encoding matrix we get encoded 2x2 matrix.
- now convert to vector(1D array) and Display to user
Code : Encode.py
# loading libraries
import numpy as np
a = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
c = [[0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0]]
# encode matrix
ecm = [[3,4], [3,6]]
i = 0
l = 0
# Lists of Alphabets and its values
smallalpha = [" ","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"]
capitalalpha = [" ","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"]
alphavalues = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 26, 27]
# string to convert
b = "India"
listb = list(b)
lenb = len(listb)
# Loop to convert Word to Values that
# are further useful for Encoding
for i in range(lenb):
for j in range(27):
if(listb[i] == smallalpha[j]):
a[i] = alphavalues[j]
if(j == 23):
j = 0
break
if(j == 23):
for k in range(27):
if(listb[i] == capitalalpha[k]):
a[i] = alphavalues[k]
break
if(lenb%2 == 1):
lenb = lenb+1
a = a[0:lenb]
tb = b
# convert this array to 2D array for further
# multiplication with encoding matrix
j = 0
k = 0
# b[m][n] m is always 2
n = int(lenb/2)
for i in range(0,lenb):
if(j<n):
c[k][j] = a[i]
j = j+1
else:
k = k+1
j = 0
c[k][j] = a[i]
j = j+1
# Multiplay matrix by Encoding 2x2 matrix
c = np.matmul(ecm, c)
# Convert to 1D array for displaying
i = 0
j = 0
k = 0
for i in range(2):
for j in range(int(lenb/2)):
a[k] = c[i][j]
k = k+1
a = a[0:lenb]
print("Encoding matrix = ", ecm)
print("encrypted form = ", a)
Encoding matrix = [[3, 4], [3, 6]] Encrypted form = [63, 46, 12, 81, 48, 12]
Code : Decode.py
# importing libraries
import numpy as np
from numpy.linalg import inv
# Initial values
a =[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0]
tdm =[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
# encoding matrix
ecm =[[3, 4],
[3, 6]]
# Lists of Alphabets and its values
smallalpha = [" ","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"]
capitalalpha = [" ","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"]
alphavalues = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 26, 27]
# Take inputs
# elements in Encrypted Matrix
lenb = 6
a = [63, 46, 12, 81, 48, 12]
sobj = slice(lenb)
a = a[sobj]
# convert array to 2d matrix to further
# multiplication with inverse of 2d matrix
j = 0
k = 0
# b[m][n] m is always 2
n = int(lenb / 2)
for i in range(0, lenb):
if(j<n):
tdm[k][j]= a[i]
j = j + 1
else:
k = k + 1
j = 0
tdm[k][j]= a[i]
j = j + 1
# Multiply by inverse matrix
dcm = inv(ecm)
dcm = np.matmul(dcm, tdm)
# Convert to 1d array for extracting word
i = 0
j = 0
k = 0
for i in range(2):
for j in range(int(lenb / 2)):
a[k]= dcm[i][j]
k = k + 1
# Creating a decoded word
text = ""
for i in range(0, lenb):
for j in range(0, 27):
if(a[i]== alphavalues[j]):
text =''.join([text, smallalpha[j]])
print("Decoded message = "+text)
Decoded message = india
