Suppose Hm is a collisionresistant hash function that maps a

Suppose H(m) is a collision-resistant hash function that maps a message of arbitrary bit length into an n-bit hash value. Is it true that, for all messages x, x\' with x notequalto x, we have H(x) notequalto H(x\')? Explain your answer.

Solution

Flase.

As the number of inputs to the function is of arbitrary length the function should not be one to one. The number of unique outputs is 2^n. Hence, there are several inputs that map to the same output.