Question

What is so special about defining OTP using the XOR operation? Suppose we use the bitwise-and operation (which we will write as ‘&’) and define a variant of OTP as follows:

Gen: a key k is chosen from {0,1} n according to the uniform distribution
Enc: c: = k&m where, m ∈ {0, 1} n

Is it still a good choice for encryption? Why/Why not?

Answer 1

The encryption function Enc: is not a good encryption function, because it is not an into function i.e. there may be multiple messages that lead to the same encrypted string.

Let there be some position in k which is 0. Then consider the same position in m. Whether the position in m contains a 0 or 1, the AND with the corresponding position in k will be 0, therefore both the messages will lead to the same encrypted string.

Therefore there is no way to recover the original message given the encrypted string, even when the key is known. This makes this not a suitable encryption.

Comment in case of any doubts.