Suppose that keys are tbit integers For a modular hash funct

Suppose that keys are t-bit integers. For a modular hash function with prime M, prove that each key bit has the property that there exist two keys differing only in that bit that have different hash values.

Solution

For a modular hash function with prime M, yes, the two keys differing only in one bit have different hash values.

Explanation and the proof is given as follows:

Hence, as per the above explanation the keys are differing from exactly one bit and having different value of hash.