Alice and Bob are using the ElGamal cipher with the parameters $=157$

and $=5$

$.$

Alice makes the mistake of using the same ephemeral key for two plaintexts, $1$

and $2$

$.$ The eavesdropper Eve suspects that $1=45$

$.$ She sees the two ciphertexts $1=112$

and $2=137$

in transit; these are the encryptions of $1$

and $2$

$,$ respectively.

a$)$ What is the masking key $$

$?$

$79$

b$)$ What is the plaintext $2$

$?$

$45$