Question
If the bit composition of a data character is 01011010 and the encryption key for that character is 10100111 , what would be the modulo-2 encrypted data character?
Step 1
In this context, modulo-2 encryption refers to the XOR (exclusive OR) operation between the data character and the encryption key. Show more…
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All of the results of this section can be generalized to the case where the plaintext is a binary message; that is, it is a sequence of 0's and 1's. In this case we do all of our modular arithmetic using modulus 2 rather than modulus $26 .$ Thus, for example, $1+1=0(\bmod 2) .$ Suppose we want to encrypt the message $110101111 .$ Let us first break it into triplets to form the three and let us take $\left[\begin{array}{lll}1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$ as our $\left[\begin{array}{l}1 \\ 1 \\ 0\end{array}\right],\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right],\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ vectors enciphering matrix. (a) Find the encoded message. (b) Find the inverse modulo 2 of the enciphering matrix, and verify that it decodes your encoded message.
Applications of Linear Algebra
Cryptography
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