First, we observe that the expression X*Y mod P (where X and Y are secret and P is a large public prime) reveals no useful information.
Next we define an extending function E(U, M) which "somehow" transforms U in such a way to guarantee that the result consists of at least M bits. For example, by returning the bit pattern of U with the Mth bit set. (In practice we might add a few more constraints there in order to satisfy non-malleability).
Finally, we have a function F defined as follows:
Q = E(V, N)
F = (Q * E((Q * A) mod B, N)) mod C
Where A, B, C are large public primes, V is secret, and N is the number of bits of the largest prime.
So my question is, does F satisfy all of the following properties: non-reversibility, preimage resistance, and collision resistance?