Vernam Cypher

The Vernam cypher is a one-time pad cypher where the encryption key is chosen to be of the same size as the plain-text to encrypt. There are several takes on the one-time pad encryption, but generally the encryption is symmetric to its decryption and consists in combining the plain-text with the key-text letter-by letter.

Supposing that the index of the plain-text letter is $l_{p_{i}}$ and that the index of the key-text letter is $l_{k_{i}}$ , we obtain the cypher-text letter $l_{c}$ through:

$\begin{eqnarray*} l_{c} &=& (l_{p_{i}}+l_{k_{i}})\mod{26} \end{eqnarray*}$

In order to reverse the cypher, the verse operation is performed:

$\begin{eqnarray*} p_{c} &=& (l_{c_{i}}-l_{k_{i}})\mod{26} \end{eqnarray*}$

The operation used for encryption (in this case addition) has to have an inverse operation (in this case subtraction) in order to be able to decrypt.