Succinct Encrypted Filters for Low-Bandwidth Set Membership

The Bloom filter is divided into multiple independent segments or sections. Each segment maintains its own bit array and hash function set, allowing the system to process queries in parallel across segments. This segmentation reduces the false positive rate for each individual segment while maintaining overall efficiency, as the false positives are distributed across multiple smaller units rather than concentrated in a single large filter.

The patent combines Bloom filters with other data structures or filtering mechanisms to create a composite filtering system. This hybrid approach integrates the space efficiency of Bloom filters with the precision of alternative structures, achieving a balance between low communication overhead and reduced false positive rates through the synergistic properties of the combined system.

By segmenting the Bloom filter into multiple smaller filters, each with its own bit array, the system maintains space efficiency while reducing the probability of false positives. The segmented structure allows for more granular control over false positive rates without significantly increasing overall space requirements, as each segment can be optimized independently.

The patent modifies key parameters of the Bloom filter, such as the number of hash functions, bit array size, and segment count, to optimize the balance between space efficiency and precision. By adjusting these parameters dynamically or through careful selection, the system achieves better false positive rates while maintaining compact representation suitable for bandwidth-constrained environments.

Set difference operations are performed on segmented Bloom filters rather than single monolithic filters. This segmentation allows the system to identify and eliminate false positives more effectively, as errors are localized to specific segments. The communication bandwidth savings are maintained while precision improves through the ability to selectively process and validate results from individual segments.

The patent introduces intermediary verification mechanisms or additional filtering stages that act as mediators between the Bloom filter difference operation and the final result. These intermediaries help validate whether detected differences are genuine or false positives, thereby improving precision without requiring additional communication bandwidth for the core set difference operation.