multiplicative one time pad : We define a multiplicative mod p variation of the one time pad $.$ This is a cipher depined over $K$:$=M$:$=C=\{1,...,p-1\}$ where $pis$ a prime. Encryption and decryption are defined $as$ follows:

Enc$(k,m)$:$=k.m$ mod $p$

Dec$(k,m)$:$=k^{-1}.c$ mod $p$

here $k^{-1}$denotes the multiplicative inverse $ofk$ modulo $p.$ Prove that the cipher $is$ perfectly $secure.[$ prove $it$ with mathematically$]$