A Space Lower Bound for Dynamic Approximate Membership Data Structures

@article{Lovett2013ASL,
  title={A Space Lower Bound for Dynamic Approximate Membership Data Structures},
  author={Shachar Lovett and Ely Porat},
  journal={SIAM J. Comput.},
  year={2013},
  volume={42},
  pages={2182-2196}
}
An approximate membership data structure is a randomized data structure representing a set which supports membership queries. It allows for a small false positive error rate but has no false negative errors. Such data structures were first introduced by Bloom in the 1970s and have since had numerous applications, mainly in distributed systems, database systems, and networks. The algorithm of Bloom (known as a Bloom filter) is quite effective: it can store an approximation of a set $S$ of size… 
1 Citations
Bloom Filter Encryption and Applications to Efficient Forward-Secret 0-RTT Key Exchange
TLDR
Bloom filter encryption (BFE), which is derived from the probabilistic Bloom filter data structure, is introduced and different constructions of BFE schemes are described and it is shown how these yield new puncturable encryption mechanisms with extremely efficient puncturing.

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