to my current understanding Universal Hashing is a method whereby the hash function is chosen randomly at runtime in order to guarantee reasonable performance for any kind of input.
I understand we may do this in order to prevent manipulation by somebody choosing malicious input deliberately (a possibility of a deterministic hash function is know).
My Question is the following: Is it not true, that we still need to guarantee that a key will be mapped to the same address every time we hash it ? For instance if we want to retrieve information, but the hash function is chosen at random, how do we guarantee we can get back at our data ?
A universal hash function is a family of different hash functions that have the property that with high probability, two randomly-chosen elements from the universe will not collide no matter which hash function is chosen. Typically, this is implemented by having the implementation pick a random hash function from a family of hash functions to use inside the implementation. Once this hash function is chosen, the hash table works as usual - you use this hash function to compute a hash code for an object, then put the object into the appropriate location. The hash table has to remember the choice of the hash function it made and has to use it consistently throughout the program, since otherwise (as you've noted) it would forget where it mapped each element.
Hope this helps!