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? $($hint: you should explain if $P(M|C)?=P(M)$ by using

mathematical proof. Only textual explanation without the inclusion of mathematical

formulas will result in an incomplete analysis and, therefore, may lead to a deduction in

grading.$)$