Question

What is the decryption for a affine cipher if the encryption function is $\mathbf{c}\mathbf{=}\mathbf{(}\mathbf{15}\mathbf{p}\mathbf{+}\mathbf{13}\mathbf{)}\mathbf{mod}\mathbf{26}$

Short answer

$\mathbf{p}\mathbf{\equiv }{\mathbf{7}}^{\mathbf{\ast }}\mathbf{(}\mathbf{c}\mathbf{-}\mathbf{13}\mathbf{)}\mathbf{mod}\mathbf{26}$

Step-by-step solution

Step

Encryption function is:

$\mathbf{c}\mathbf{=}\mathbf{(}\mathbf{15}\mathbf{p}\mathbf{+}\mathbf{13}\mathbf{)}\mathbf{mod}\mathbf{26}$

_{${\mathbf{15}}^{\mathbf{\ast }}\mathbf{7}\mathbf{=}\mathbf{105}\mathbf{\equiv }\mathbf{1}\mathbf{mod}\mathbf{26}$}

So the decryption function is

$\mathbf{p}\mathbf{\equiv }{\mathbf{7}}^{\mathbf{\ast }}\mathbf{(}\mathbf{c}\mathbf{-}\mathbf{13}\mathbf{)}\mathbf{mod}\mathbf{26}$