Suppose Alice designs a one$-$time pad variant: the plaintext is to no longer XOR, but

bite$-$wise multiply the one$-$time key that is generated uniformly at random. For example:

plaintext: $001101$

key: $101110$

ciphertext: $001100$

Is Alice$$s design good?

You should explain if P$($M$|$C$)=$ P$($M$)$ by using mathematical proof.