See:
- Part 1/3
- Part 2/3
Last part of my series about Vigenere cipher. (3 post in a row? I am proud of myself :-P)
In my previous posts I already showed how to use Vigenere square to encrypt/decrypt text, so this time I'll follow the algebraic method described in the Wikipedia:
{% img center https://bynario.com/img/vigenere.jpg 'vigenere' %}
I'll use the same input, same key, and same alphabets as in previous exercises:
mykey: "WHITE"
input_text: "en un lugar dela mancha de cuyo nombre no quiero acordarme"
Position: 00 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
Ref alphabet(M): 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
Key alphabet(K): 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 A
(In the reference alphabet,we have shifted the letters one position, as the author did in the book, so K alphabet starts in "B" not in "A"
Encryption:
Now we are going to use numbers instead of the square approach.
If you remember the first post, the foundation of this cipher is the tuple (letter,key):
INPUT: EN UN LUGAR DE LA MANCHA
KEY: WH IT EWHIT EW HI TEWHIT
TUPLE: ('E', 'W'),('N', 'H'),('U', 'I'),('N', 'T'), ('L', 'E'),('U', 'W'),[...]
Let's get the positions of each element in the tuple in M[] and K[]:
1st tuple: 'E' is in position 4 in our reference alphabet(M). 'W' is in position 21 in the Key alphabet(K)
2nd tuple: 'N' is in position 13 in M[], 'H' is in position 6 in K[]
3rd tuple: 'U' is in position 20 in M[], 'I' is in position 7 in K[]
('4','21'),('13','6'),('20','7'),('13','18'),[...]
So putting this in the mathematical notation:
C[i] = (M[i]+K[i]) mod len(M)
C[0] = (4 + 21) % 26 = 25
C[1] = (13 + 6) % 26 = 19
C[2] = (20 + 7) % 26 = 1
[...]
So the letter "E" in position 4 in M[] will be replaced by the letter in position 25 in K[], which is "A". The same way, the letter "N" in position 13 in M[] will be replaced by the letter in position 19 in K[], which is "U", and so on...
E -> K[25] ->A
N -> K[19] ->U
U -> K[1] ->C
N -> K[5] ->G
L -> K[14] ->P
U -> K[15] ->Q
G -> K[12] ->N
[...]
Decryption:
Decryption works pretty much the same way... The message is calculated this way:
M[i] = (C[i]-K[i]) mod len(M)
Let's check step by step.. This is our input data:
INPUT: AU CG PQNIK HA SI FEJJPT
KEY: WH IT EWHIT EW HI TEWHIT
TUPLE: ('A', 'W'),('U', 'H'),('C', 'I'),('G', 'T'), ('P', 'E'),('Q', 'W'),('N', 'H'),('I', 'I'),('K', 'T'),('H', 'E'),[...]
We have to look for the positon of the each letter (of each tuple) in alphabet K[]:
1st tuple: Position of letter "A" and "W" in K[], 25 and 21.
2nd tuple: Position of letter "U" and "H" in K[], 19 and 6.
3rd tuple: C,I -> 1, 7
Now, coming back to the formula:
M[0] = (C[0]-K[0]) mod len(M) = (25 - 21) % 26 = 4
M[1] = (C[1]-K[1]) mod len(M) = (19 - 6) % 26 = 13
M[2] = (C[2]-K[2]) mod len(M) = (1 - 7) % 26 = 20
M[3] = (C[3]-K[3]) mod len(M) = (5 - 18) % 26 = 13
And looking for those positions in our reference alphabet M[]:
A -> M[4] -> E
U -> M[13] -> N
C -> M[20] -> U
G -> M[13] -> N
P -> M[11] -> L
Q -> M[20] -> U
N -> M[6] -> G
I -> M[0] -> A
K -> M[17] -> R
[...]
Let put this into python code:
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70 | #!/usr/bin/env python
import string
mykey="WHITE"
input_text="en un lugar de la mancha de cuyo nombre no quiero acordarme"
code_text="AU CG PQNIK HA SI FEJJPT HA JCRS JVUUVA UW JYELZH EYVZWENTM"
# Alphabet used as reference (M)
# ABCDEFGHIJKLMNOPQRSTUVWXYZ
source = string.ascii_uppercase
# Key alphabet (K) shifted 1 position to the left
# BCDEFGHIJKLMNOPQRSTUVWXYZA
shift = 1
matrix = [ source[(i + shift) % 26] for i in range(len(source)) ]
def coder(thistext):
ciphertext = []
control = 0
for x,i in enumerate(input_text.upper()):
if i not in source:
#If the symbol is not in our reference alphabet, we simply print it
ciphertext.append(i)
continue
else:
#Wrap around the mykey string
control = 0 if control % len(mykey) == 0 else control
#Calculate the position C[i] = (M[i]+K[i]) mod len(M)
result = (source.find(i) + matrix.index(mykey[control])) % 26
#Add the symbol in position "result" to be printed later
ciphertext.append(matrix[result])
control += 1
return ciphertext
def decoder(thistext):
control = 0
plaintext = []
for x,i in enumerate(code_text.upper()):
if i not in source:
#If the symbol is not in our reference alphabet, we simply print it
plaintext.append(i)
continue
else:
#Wrap around the mykey string
control = 0 if control % len(mykey) == 0 else control
#Calculate the position M[i] = (C[i]-K[i]) mod len(M)
result = (matrix.index(i) - matrix.index(mykey[control])) % 26
#Add the symbol in position "result" to be printed later
plaintext.append(source[result])
control += 1
return plaintext
# Print results
print("Key: {0}".format(mykey))
print("\nDecode text:")
print("-> Input text: {0}".format(input_text))
print("-> Coded text: {0}".format(''.join(coder(input_text))))
# Print results
print("\nDecode text:")
print("-> Input text: {0}".format(code_text))
print("-> Decoded text: {0}".format(''.join(decoder(code_text)).lower()))
|
Code stored in GitHub
The script is pretty basic and simple to understand. There are two functions, and the key part is the calculation of result using the math formula shown above.
And see the result:
$ python Vigenere_cipher_mod.py
Key: WHITE
Decode text:
-> Input text: en un lugar de la mancha de cuyo nombre no quiero acordarme
-> Coded text: AU CG PQNIK HA SI FEJJPT HA JCRS JVUUVA UW JYELZH EYVZWENTM
Decode text:
-> Input text: AU CG PQNIK HA SI FEJJPT HA JCRS JVUUVA UW JYELZH EYVZWENTM
-> Decoded text: en un lugar de la mancha de cuyo nombre no quiero acordarme
There are tons of references about how to break this code on the internet. I found these two very interesting:
Later
PS: I hate markdown. Just a little bit...
