# Thread: Cryptography questions

1. ## Cryptography questions

Explain why not all encryptors have corresponding decryptors, providing at least two examples of cncryptors wihch cannot be decrypted.

of the (26)^2=676 possible encryptors, determine precisely which have decryptors and which don't. How many decryptable encryptors are there?

Explain a procedure indicating how to find a decryptor, that is, if one exists for any given encryptor

Help would be greatly appreciated

For these problems we are using linear congruences. A linear encryptor is a function of the form E(w)=Aw+B (mod N)

2. From the encryption law...

$\displaystyle E(w)= A\cdot w + B \mod N$ (1)

... we derive the 'decryption law'...

$\displaystyle w = A^{-1}\cdot (E - B) \mod N$ (2)

The problem in this case is represented by the term $\displaystyle A^{-1}$, that is the 'multiplicative inverse' of the element $\displaystyle A \in W$. But $\displaystyle N=26$ is not prime so that not all the $\displaystyle A \in W$ do have multiplicative inverse...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$