Feistel Cipher

Feistel Cipher model is a structure or a design used to develop many block ciphers such as DES. Feistel cipher may have invertible, non-invertible and self invertible components in its design. Same encryption as well as decryption algorithm is used. A separate key is used for each round. However same round keys are used for encryption as well as decryption. 

Feistel cipher algorithm

• Create a list of all the Plain Text characters. 
  
• Convert the Plain Text to Ascii and then 8-bit binary format. 
  
• Divide the binary Plain Text string into two halves: left half (L1)and right half (R1) 
  
• Generate a random binary keys (K1 and K2) of length equal to the half the length of the Plain Text for the two rounds. 
  

First Round of Encryption 

• a. Generate function f1 using R1 and K1 as follows:

f1= xor(R1, K1)

• b. Now the new left half(L2) and right half(R2) after round 1 are as follows:

R2= xor(f1, L1)
L2=R1

Second Round of Encryption 

• a. Generate function f2 using R2 and K2 as follows: 
  

f2= xor(R2, K2)

• b. Now the new left half(L3) and right half(R3) after round 2 are as follows:

R3= xor(f2, L2)
L3=R2

• Concatenation of R3 to L3 is the Cipher Text
• Same algorithm is used for decryption to retrieve the Plain Text from the Cipher Text.

Examples:

Plain Text is: Hello
Cipher Text:  E1!w(
Retrieved Plain Text is:  b'Hello'

Plain Text is: Geeks
Cipher Text: O;Q
Retrieved Plain Text is:  b'Geeks'

Python3

# Python program to demonstrate
# Feistel Cipher Algorithm

import binascii

# Random bits key generation
def rand_key(p):

    import random
    key1 = ""
    p = int(p)

    for i in range(p):

        temp = random.randint(0,1)
        temp = str(temp)
        key1 = key1 + temp

    return(key1)

# Function to implement bit exor
def exor(a,b):

    temp = ""

    for i in range(n):

        if (a[i] == b[i]):
            temp += "0"

        else:
            temp += "1"

    return temp

# Defining BinarytoDecimal() function
def BinaryToDecimal(binary):

    # Using int function to convert to
    # string
    string = int(binary, 2)

    return string

# Feistel Cipher
PT = "Hello"
print("Plain Text is:", PT)

# Converting the plain text to
# ASCII
PT_Ascii = [ord(x) for x in PT]

# Converting the ASCII to
# 8-bit binary format
PT_Bin = [format(y,'08b') for y in PT_Ascii]
PT_Bin = "".join(PT_Bin)

n = int(len(PT_Bin)//2)
L1 = PT_Bin[0:n]
R1 = PT_Bin[n::]
m = len(R1)

# Generate Key K1 for the
# first round
K1= rand_key(m)

# Generate Key K2 for the
# second round
K2= rand_key(m)

# first round of Feistel
f1 = exor(R1,K1)
R2 = exor(f1,L1)
L2 = R1

# Second round of Feistel
f2 = exor(R2,K2)
R3 = exor(f2,L2)
L3 = R2

# Cipher text
bin_data = L3 + R3
str_data =' '

for i in range(0, len(bin_data), 7):

    # slicing the bin_data from index range [0, 6]
    # and storing it in temp_data
    temp_data = bin_data[i:i + 7]

    # passing temp_data in BinarytoDecimal() function
    # to get decimal value of corresponding temp_data
    decimal_data = BinaryToDecimal(temp_data)

    # Decoding the decimal value returned by
    # BinarytoDecimal() function, using chr()
    # function which return the string corresponding
    # character for given ASCII value, and store it
    # in str_data
    str_data = str_data + chr(decimal_data)

print("Cipher Text:", str_data)

# Decryption
L4 = L3
R4 = R3

f3 = exor(L4,K2)
L5 = exor(R4,f3)
R5 = L4

f4 = exor(L5,K1)
L6 = exor(R5,f4)
R6 = L5
PT1 = L6+R6


PT1 = int(PT1, 2)
RPT = binascii.unhexlify( '%x'% PT1)
print("Retrieved Plain Text is: ", RPT)

Output:

Plain Text is: Hello
Cipher Text:  E1!w(
Retrieved Plain Text is:  b'Hello'

Time Complexity: O(n)
Auxiliary Space: O(n)