Universal kwise independent classes of hash functions are recommended along with their construction mechanisms 16. It would be desirable to store and query a fewer number of bits in order to compute a k wise independent hash function. Typically, to obtain the required guarantees, we would need not just one function, but a family of functions, where we would use randomness to sample a hash function from this. Sept 27, 2017 problem 1 twise independent hash 10 pts a hash function h. A natural question regarding, k wise independent distributions is how close they are to some k. There are other interesting k wise independent hash functions if we allow on space. T is a randomized function that provides the guarantee that, for any kdistinct. How to prove pairwise independence of a family of hash.
Almost kwise independence versus kwise independence. Yun kuen cheung, aleksandar nikolov 1 overview in this lecture, we will introduce k wise independence and k wise independent hashing. Pairwise independent hash functions 1 hash functions the goal of hash functions is to map elements from a large domain to a small one. Cs621 theory gems lecture 17 massachusetts institute of. Several techniques have been devised to aid in the selection of hash functions. Another hash function that takes up on space is presnted by siegel 5. One such hash function presented by thorup and zhang has query time as a function of k 4. I want to prove pairwise independence of a family of hash functions, but i dont know where to start. The reason why it works is exactly the interpolation theorem for finite fields. We say that a distribution over 0,1n is, k wise independent if its restriction to every k coordinates results in a distribution that is close to the uniform distribution.
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