This Vernam Cipher system works on binary data (bits) rather than letters.
The Vernam Cipher technique can be expressed as follows: Ci = Pi El) Ki
Pi = ith binary digit of plaintext.
KL = ith binary digit of key.
Ci = ith binary digit of ciphertext.
ED = exclusive-or (XOR) operation
Thus, the ciphertext is generated by performing the bitwise XOR of the plaintext and the key.
Decryption simply involves the same bitwise operation: Pi = Ci ⊕ Ki
The essence of this technique is the means of construction of the key.
It was produced by the use of a running loop of tape that eventually repeated the key so that in fact the system worked with a very long but repeating keyword.
Although such a scheme has cryptanalytic difficulties, it can broken with a very long ciphertext or known plaintext as the key repeated.
- In this scheme, a random key that is as long as the message used.
- The key used to encrypt and decrypt a single message and then discarded. Each new message requires a new key of the same length as the new message.
- This scheme is unbreakable.
- It produces random output that bears no statistical relationship to the plaintext.
- Because the ciphertext contains no information whatsoever about the plaintext, there is simply no way to break the code.
- For any plaintext of equal length to the ciphertext, there is a key that produces that plaintext.
- Therefore, if you did an exhaustive search of all possible keys, you would end up with many legible plaintexts, with no way of knowing which the intended plaintext was.
- Therefore, the code is unbreakable.
- The security of the one-time pad is entirely due to the randomness of the key.
- The one-time pad offers complete security but, in practice, has two fundamental difficulties:
There is the practical problem of making large quantities of random keys. Any heavily used system might require millions of random characters on a regular basis. Supplying truly random characters in this volume is a significant task.
Another problem is that of key distribution and protection. For every message to sent, a key of equal length needed by both sender and receiver.
Because of these difficulties, the one-time pad used where very high security required.
The one-time pad is the only cryptosystem that exhibits perfect secrecy.