First we note that the condition \(\mathtt{hash(x)}=\mathtt{hash(y)}\) is equivalent to the statement "the highest-order \(\mathtt{d}\) bits of \(\mathtt{z} \mathtt{x}\bmod2^{\mathtt{w}}\) and the hig...First we note that the condition \(\mathtt{hash(x)}=\mathtt{hash(y)}\) is equivalent to the statement "the highest-order \(\mathtt{d}\) bits of \(\mathtt{z} \mathtt{x}\bmod2^{\mathtt{w}}\) and the highest-order \(\mathtt{d}\) bits of \(\mathtt{z} \mathtt{y}\bmod 2^{\mathtt{w}}\) are the same."
Depending on how good the implementation is, you may be able to do this just by inspecting the code for the implementation, or you may have to write some code that does trial insertions and searches, ...Depending on how good the implementation is, you may be able to do this just by inspecting the code for the implementation, or you may have to write some code that does trial insertions and searches, timing how long it takes to add and find particular values. (This can be, and has been, used to launch denial of service attacks on web servers [17].)
