(Solved): The Affine Cipher is a form of mono-alphabetic substitution cipher. Start with two integers a and b ...

The Affine Cipher is a form of mono-alphabetic substitution cipher. Start with two integers $a$ and $b$, such that $\gcd (a,26)=1$. In order to encrypt a plaintext message, each letter in the plaintext is converted into its numerical equivalent, then apply the decryption formula: $E(x)=ax+b\mathrm{mod}26$ then convert the result back to a letter in the ciphertext. To decrypt a ciphertext obtained from an affine cipher, we convert each letter in the ciphertext to it numerical equivalent, then apply the decryption formula: $D(y)=a^{-1}(y-b)\mathrm{mod}26$ then convert back to a letter in the plaintext. (Here, $a^{-1}$ is the ( $\mathrm{mod}26)$-multiplicative inverse of $a$.) The standard letter-to-number conversion is: (a) Given that the plaintext letter $\mathbf{J}$ becomes ciphertext $\mathbf{K}$ and that the plaintext $\mathbf{B}$ becomes ciphertext $\mathbf{I}$. Use these clues to find the $a$ and $b$ that were used in the affine cipher. Explain how you were able to find $a$ and $b$. (b) Given the $a$ and $b$ from part (a), decode the following ciphertext?