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Table 1 Functions for basic operations of Bloom filters

From: Secure and scalable deduplication of horizontally partitioned health data for privacy-preserving distributed statistical computation

Functions

Description

add(CBF i r , CBF i I )

Returns counting Bloom filter CBF i r ∪ I that represents the summation of CBF i r and CBF i I

sub(CBF R ∪ S , CBF R )

Returns counting Bloom filter CBF S that represents the subtraction of CBF R from CBF R ∪ S

intersect(CBF S , BF i I )

Returns counting Bloom filter CBF i S ∩ I that represents the intersection between CBF S and BF i I

count(CBF i S ∩ I , {b 1(x), b 2(x), …, b k (x)})

Returns f that is equal to the number of occurrences of x in CBF i S ∩ I

toBloomFilter(CBF i I )

Returns Bloom filter BF i I that represents CBF i I