Introduction to Cryptography with Coding Theory, 3rd Edition

6.6 Exercises

1. The ciphertext YIFZMA was encrypted by a Hill cipher with matrix $\left(\begin{array}{cc}9& 13\\ 2& 3\end{array}\right)$. Find the plaintext.

2. The matrix $\left(\begin{array}{cc}1& 1\\ 1& 1\end{array}\right)$ mod 26 is not suitable for the matrix in a Hill cipher. Why?

3. The ciphertext text GEZXDS was encrypted by a Hill cipher with a $2\times 2$ matrix. The plaintext is solved. Find the encryption matrix $M$.

4. Consider the following combination of Hill and Vigenère ciphers: The key consists of three $2\times 2$ matrices, $M_1$, $M_2$, $M_3$. The plaintext letters are represented as integers mod 26. The first two are encrypted by $M_1$, the next two by $M_2$, the 5th and 6th by $M_3$. This is repeated cyclically, as in the Vigenère cipher. Explain how to do a chosen plaintext attack on this system. Assume that you know that three $2\times 2$ matrices are being used. State ...