Hash function construction I recently studied a Hash function and its security requirement. I have studied that simple hash construction from XOR is weak. My question is, based on Xor property the following Hash based on RSA Mi&lt;n calculated by
$H(M_1,M_2)=(M_1^e \bmod n) \oplus (M_2^e \bmod n)$, where $(n,e)$ is an RSA public key.
satisfy the collision resistant and 2nd preimage resistant?
The construction is trivially neither collision resistant nor second preimage resistant, since XOR is commutative. I.e. for any $a,b$ it holds that $a\oplus b = b \oplus a$.
Consequently, given $M_1,M_2$ as a first preimage, we can trivially find $M_2,M_1$ as a second preimage. To break collision resistance, simply choose $M_1,M_2$ arbitrarily.