First, an amount of time needs to be spent beforehand to precompute the hashes for the two sequences.

At each node in the tree, we can precompute the bounding sphere .

We precompute m such that .

Approaches that precompute visibility for zones are referred to as potentially visible set or PVS methods.

It is possible to precompute a list of at most n values such that every composite n-bit number will be certain to have a witness a in the list.

Furthermore Bob by providing his own randomly generated string guarantees that Alice wasn't able to precompute an image pair of "tail/random string" or "head/random string".

Gal's idea is to not precompute equally spaced values, but rather to perturb the points x so that both x and f(x) are very nearly exactly representable in the chosen numeric format.

The type of adversary doesn't matter in the case of deterministic algorithms, because the adversary can run a copy of the deterministic algorithm on his own to precompute the most disastrous sequence.

Note : The first index for p is 0 and the first index for m and s is 1 Another solution is to anticipate which costs we will need and precompute them.

Disadvantages of this technique include the time required to precompute these addresses every time the shared libraries change, the inability to use address space layout randomization, and the requirement of sufficient virtual address space for use (a problem that will be alleviated by the adoption of 64-bit architectures, at least for the time being).