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 :
  1. Take a String convert to corresponding number shown below
  2. convert to 2D matrix(array). Now we have 2x2 matrix!
  3. When we multiply this matrix with encoding matrix we get encoded 2x2 matrix.
  4. now convert to vector(1D array) and Display to user
Decoding 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.
  • Code : Encode.py

    Python3
    # 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)
    
    Time Complexity : O(n)(where n is length of message) Space Complexity : O(n)   Output:
    Encoding matrix =  [[3, 4], [3, 6]]
    Encrypted form =  [63, 46, 12, 81, 48, 12]
    

    Code : Decode.py

    Python3
    # 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)
    
    Time Complexity : O(n)(where n is number of elements) Space Complexity : O(n) Output:
    Decoded message = india 

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