Let H, H' be collision-resistant hash functions. Which of the following functions H'' is NOT necessarily collision-resistant? 1) H''(x) = H(H'(x)) 2) H''(x) = H(x)||H'(x), where || denotes concatenation. 3) H''(x) = H(x)||0...0, where || denotes concatenation. 4) H''(x) = H(x) xor H'(x)
My conclusion is the following:
1. H(H'(x)) is the collision resistant as H(x) is collision resistant thus it will return the output as collision resistant. 2. In this there is concatenation of two collision resistant functions thus the output will also be collision resistant. 3. It is also collision resistant as this is just concatenation of collision resistant and 0.'s thus it will also be collision resistant. 4. As H''(x) is the XOR operation thus there could be chances that result of both of them would be same due to which it will always return 0. Thus it may not be collision resistant.
I appreciate if experts correct me if i am wrong.