The Vernam cipher, also known as the one-time pad, is a symmetric key encryption technique that was invented by Gilbert Vernam in 1917. It's known for being theoretically unbreakable when used correctly.
A key is generated that is as long as the message to be encrypted. This key must be completely random
- Convert the message: The message is converted to a binary representation i.e using ASCII code for each character.
- Convert the key: The key is converted into a binary representation i.e using ASCII code for each character.
- Produce the ciphertext: Each bit of the message is XORed with the corresponding bit of the key to produce the ciphertext
Mathematically, this can be represented as: Ci = Pi ⊕ Ki where Ci is the ith bit of ciphertext, Pi is the ith bit of the message (plain text), and Ki is the ith bit of the key
Dec | Char | Dec | Char | Dec | Char | Dec | Char
-----+--------+-------+--------+-------+--------+-------+--------
0 | NUL | 32 | Space | 64 | @ | 96 | `
1 | SOH | 33 | ! | 65 | A | 97 | a
2 | STX | 34 | " | 66 | B | 98 | b
3 | ETX | 35 | # | 67 | C | 99 | c
4 | EOT | 36 | $ | 68 | D | 100 | d
5 | ENQ | 37 | % | 69 | E | 101 | e
6 | ACK | 38 | & | 70 | F | 102 | f
7 | BEL | 39 | ' | 71 | G | 103 | g
8 | BS | 40 | ( | 72 | H | 104 | h
9 | TAB | 41 | ) | 73 | I | 105 | i
10 | LF | 42 | * | 74 | J | 106 | j
11 | VT | 43 | + | 75 | K | 107 | k
12 | FF | 44 | , | 76 | L | 108 | l
13 | CR | 45 | - | 77 | M | 109 | m
14 | SO | 46 | . | 78 | N | 110 | n
15 | SI | 47 | / | 79 | O | 111 | o
16 | DLE | 48 | 0 | 80 | P | 112 | p
17 | DC1 | 49 | 1 | 81 | Q | 113 | q
18 | DC2 | 50 | 2 | 82 | R | 114 | r
19 | DC3 | 51 | 3 | 83 | S | 115 | s
20 | DC4 | 52 | 4 | 84 | T | 116 | t
21 | NAK | 53 | 5 | 85 | U | 117 | u
22 | SYN | 54 | 6 | 86 | V | 118 | v
23 | ETB | 55 | 7 | 87 | W | 119 | w
24 | CAN | 56 | 8 | 88 | X | 120 | x
25 | EM | 57 | 9 | 89 | Y | 121 | y
26 | SUB | 58 | : | 90 | Z | 122 | z
27 | ESC | 59 | ; | 91 | [ | 123 | {
28 | FS | 60 | < | 92 | \ | 124 | |
29 | GS | 61 | = | 93 | ] | 125 | }
30 | RS | 62 | > | 94 | ^ | 126 | ~
31 | US | 63 | ? | 95 | _ | 127 | DEL
- The ciphertext is converted to a binary representation
- The same key is used to decrypt the ciphertext. Each bit of the ciphertext is XORed with the corresponding bit of the key to retrieve the original plaintext.
Mathematically, this can be represented as: Pi = Ci ⊕ Ki where Pi is the ith bit of the message (plain text),Ci is the ith bit of ciphertext, and Ki is the ith bit of the key
- Randomness: The key must be truly random and at least as long as the message. Any predictability in the key compromises security.
- Key Use: The key must be used only once (hence the name "one-time pad"). Reusing the key can allow an attacker to deduce the message
- Key Distribution: The key must be securely distributed to both the sender and the receiver. This is often the most challenging aspect of using the Vernam cipher.
- Gilbert Vernam (wikipedia)
- Bitwise (XOR) - Mozilla web docs
- How to convert binary to hexadecimal
- And a lot of Googling :D
Given the message "LOGIC"
Step 1. Get the ASCII value of each character (Looking at the ASCII table)
ASCII value of L is 76
Step 2. Convert each ASCII value to binary
76 / 2 = 38 r 0
38 / 2 = 19 r 0
19 / 2 = 9 r 1
9 / 2 = 4 r 1
4 / 2 = 2 r 0
2 / 2 = 1 r 0
1 / 2 = 0 r 1
0
Binary representation of L = 01001100
Step 3. Generate a random key in binary format
Assuming the generated random binary key for L is 10101111
Step 4. Generate the ciphertext for each character by calculating the XOR of the in binary and the random key of the character
# Using the rule of XOR which states that:
# - Two same values result to 0
# - Two different values result to 1
Binary representation of L = 01001100
Random key for L = 10101111
-------------------------------------
XOR of L i.e ciphertext = 11100011Character | ASCII value | Binary representation (Pi) | Random key (Ki) (binary) | Ciphertext(Ci) (XOR)
----------+-------------+----------------------------+--------------------------+------------------
L | 76 | 01001100 | 10101111 | 11100011
O | 79 | 01001111 | 01101101 | 00100010
G | 71 | 01000111 | 10010101 | 11010010
I | 73 | 01001001 | 01101011 | 00100010
C | 67 | 01000011 | 11010100 | 10010111
Note: The ciphertext is the XOR of the binary representation and random key of the character
Result:
# The secret key
10101111 01101101 10010101 01101011 11010100
# The ciphertext or encryption of "LOGIC" is:
11100011 00100010 11010010 001000010 10010111
-----------------------------------------------------
# Optionally, we can go further by converting the key and ciphertext into readable format e.g hexadecimal format
# Hexadecimal representation of the secret key
AF 6D 95 6B D4
# Hexadecimal representation of the ciphertext
E3 22 D2 42 97Using the secret key
10101111 01101101 10010101 01101011 11010100
Lets decrypt the message from the below binary representation of the ciphertext:
11100011 00100010 11010010 001000010 10010111
Ciphertext(Ci) | Secret key (Ki) | Message (XOR) | ASCII value | Character
---------------+-----------------+---------------+-------------+------------+
11100011 | 10101111 | 01001100 | 76 | L
00100010 | 01101101 | 01001111 | 79 | O
11010010 | 10010101 | 01000111 | 71 | G
00100010 | 01101011 | 01001001 | 73 | I
10010111 | 11010100 | 01000011 | 67 | C