[anilgulecha]

> Here's a problem. If an attacker knows the hash function, she can produce many strings that will give the same number in return.

I may be misunderstanding you, but isn't the point of a (good) cryptographic hash function that you cannot produce the multiple plaintext which will give the same value, despite knowing the hash function?

[majke]

In practice you take X lower bits of the hash value. For example 10 bits if the hash table size is 1024. It's trivial to find many input stings which hash(string) % 1024 == fixed value, for any, even best cryptographic hash function.